Correlation And Regression

1. If the plotted points in a scatter diagram lie from upper left to lower right, then the correlation is

Positive

Zero

Negative

None of these

If the plotted points in a scatter diagram lie from upper left to lower right, it indicates a negative correlation. This means that as one variable increases, the other variable decreases.

Explanation

If the plotted points in a scatter diagram lie from upper left to lower right, it indicates a negative correlation. This means that as one variable increases, the other variable decreases.

2. If the value of correlation coefficient is positive, then the points in a scatter diagram tend to cluster

From lower left corner to upper right corner

From lower left corner to lower right corner

From lower right corner to upper left corner

From lower right corner to upper right corner

A positive correlation coefficient indicates that as one variable increases, the other variable also tends to increase. In a scatter diagram, this would be represented by the points clustering in a diagonal line from the lower left corner to the upper right corner. This means that as the x-values increase, the corresponding y-values also tend to increase.

Explanation

A positive correlation coefficient indicates that as one variable increases, the other variable also tends to increase. In a scatter diagram, this would be represented by the points clustering in a diagonal line from the lower left corner to the upper right corner. This means that as the x-values increase, the corresponding y-values also tend to increase.

3. The method applied for deriving the regression equations is known as

Least squares

Concurrent deviation

Product moment

Normal equation

The method applied for deriving the regression equations is known as least squares. This method aims to minimize the sum of the squared differences between the observed values and the predicted values. By finding the line of best fit that minimizes these squared differences, we can determine the regression equation that best represents the relationship between the variables. This method is widely used in statistics and is considered a reliable approach for estimating the parameters of a regression model.

Explanation

The method applied for deriving the regression equations is known as least squares. This method aims to minimize the sum of the squared differences between the observed values and the predicted values. By finding the line of best fit that minimizes these squared differences, we can determine the regression equation that best represents the relationship between the variables. This method is widely used in statistics and is considered a reliable approach for estimating the parameters of a regression model.

4. The correlation between shoe-size and intelligence is

Zero

Positive

Negative

None of these

The correct answer is "Zero." This means that there is no correlation between shoe-size and intelligence. In other words, the size of a person's feet does not have any impact on their level of intelligence. This conclusion suggests that there is no relationship or pattern between these two variables.

Explanation

The correct answer is "Zero." This means that there is no correlation between shoe-size and intelligence. In other words, the size of a person's feet does not have any impact on their level of intelligence. This conclusion suggests that there is no relationship or pattern between these two variables.

5. If the coefficient of correlation between two variables is -0 9, then the coefficient of determination is

0.9

0.81

0.1

0.19

The coefficient of correlation measures the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, where -1 indicates a perfect negative linear relationship and 1 indicates a perfect positive linear relationship. The coefficient of determination, on the other hand, is the square of the coefficient of correlation. Therefore, if the coefficient of correlation is -0.9, the coefficient of determination would be 0.81 (0.9 squared), indicating that 81% of the variation in one variable can be explained by the variation in the other variable.

Explanation

The coefficient of correlation measures the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, where -1 indicates a perfect negative linear relationship and 1 indicates a perfect positive linear relationship. The coefficient of determination, on the other hand, is the square of the coefficient of correlation. Therefore, if the coefficient of correlation is -0.9, the coefficient of determination would be 0.81 (0.9 squared), indicating that 81% of the variation in one variable can be explained by the variation in the other variable.

6. If y = a + bx, then what is the coefficient of correlation between x and y?

1

-1

1 or -1 according as b > 0 or b < 0

None of these

The coefficient of correlation measures the strength and direction of the linear relationship between two variables. In this case, if the coefficient b is positive (b > 0), it means that as x increases, y also increases, indicating a positive relationship. Therefore, the coefficient of correlation would be 1, indicating a strong positive correlation. On the other hand, if b is negative (b

Explanation

The coefficient of correlation measures the strength and direction of the linear relationship between two variables. In this case, if the coefficient b is positive (b > 0), it means that as x increases, y also increases, indicating a positive relationship. Therefore, the coefficient of correlation would be 1, indicating a strong positive correlation. On the other hand, if b is negative (b

7. The errors in case of regression equations are

Positive

Negative

Zero

All these

In the case of regression equations, errors can be positive, negative, or zero. Positive errors occur when the predicted values are greater than the actual values, while negative errors occur when the predicted values are lower than the actual values. Zero errors indicate that there is no difference between the predicted and actual values. Therefore, all of these options are correct as errors in regression equations can take any of these forms.

Explanation

In the case of regression equations, errors can be positive, negative, or zero. Positive errors occur when the predicted values are greater than the actual values, while negative errors occur when the predicted values are lower than the actual values. Zero errors indicate that there is no difference between the predicted and actual values. Therefore, all of these options are correct as errors in regression equations can take any of these forms.

8. What is spurious correlation?

It is a bad relation between two variables.

It is very low correlation between two variables.

It is the correlation between two variables having no causal relation.

It is a negative correlation.

Spurious correlation refers to the correlation between two variables that do not have a causal relationship. This means that even though there may be a statistical association between the two variables, it is not meaningful or significant in terms of cause and effect. In other words, the correlation is coincidental and does not indicate that one variable directly influences the other.

Explanation

Spurious correlation refers to the correlation between two variables that do not have a causal relationship. This means that even though there may be a statistical association between the two variables, it is not meaningful or significant in terms of cause and effect. In other words, the correlation is coincidental and does not indicate that one variable directly influences the other.

9. The covariance between two variables is

Strictly positive

Strictly negative

Always 0

Either positive or negative or zero

The covariance between two variables can take on any value, whether positive, negative, or zero. It measures the relationship between the variables and indicates the direction and strength of their linear association. A positive covariance suggests that the variables tend to move in the same direction, while a negative covariance suggests they tend to move in opposite directions. A covariance of zero indicates no linear relationship between the variables. Therefore, the correct answer is that the covariance can be either positive, negative, or zero.

Explanation

The covariance between two variables can take on any value, whether positive, negative, or zero. It measures the relationship between the variables and indicates the direction and strength of their linear association. A positive covariance suggests that the variables tend to move in the same direction, while a negative covariance suggests they tend to move in opposite directions. A covariance of zero indicates no linear relationship between the variables. Therefore, the correct answer is that the covariance can be either positive, negative, or zero.

10. Pearson's correlation coefficient is used for finding

Correlation for any type of relation

Correlation for linear relation only

Correlation for curvilinear relation only

Both (b) and (c)

Pearson's correlation coefficient measures the strength and direction of a linear relationship between two variables. It ranges from -1 to 1, where -1 indicates a perfect negative linear relationship, 0 indicates no linear relationship, and 1 indicates a perfect positive linear relationship. Therefore, the correct answer is "Correlation for linear relation only" because Pearson's correlation coefficient specifically measures the linear relationship between variables, not curvilinear relationships.

Explanation

Pearson's correlation coefficient measures the strength and direction of a linear relationship between two variables. It ranges from -1 to 1, where -1 indicates a perfect negative linear relationship, 0 indicates no linear relationship, and 1 indicates a perfect positive linear relationship. Therefore, the correct answer is "Correlation for linear relation only" because Pearson's correlation coefficient specifically measures the linear relationship between variables, not curvilinear relationships.

11. What are the limits of the coefficient of concurrent deviations?

No limit

Between -1 and 0, including the limiting values

Between 0 and 1, including the limiting values

Between -1 and 1, the limiting values inclusive

The coefficient of concurrent deviations measures the strength and direction of the relationship between two variables. It ranges from -1 to 1, inclusive of the limiting values. A coefficient of -1 indicates a perfect negative relationship, 0 indicates no relationship, and 1 indicates a perfect positive relationship. Therefore, the limits of the coefficient of concurrent deviations are between -1 and 1, inclusive.

Explanation

The coefficient of concurrent deviations measures the strength and direction of the relationship between two variables. It ranges from -1 to 1, inclusive of the limiting values. A coefficient of -1 indicates a perfect negative relationship, 0 indicates no relationship, and 1 indicates a perfect positive relationship. Therefore, the limits of the coefficient of concurrent deviations are between -1 and 1, inclusive.

12. If for two variable x and y, the covariance, variance of x and variance of y are 40,16 and 256 respectively, what is the value of the correlation coefficient?

0.01

0.625

0.4

0.5

The correlation coefficient is calculated by dividing the covariance of x and y by the square root of the product of the variances of x and y. In this case, the covariance is 40, the variance of x is 16, and the variance of y is 256. Therefore, the correlation coefficient can be calculated as 40 / √(16 * 256) = 40 / √4096 = 40 / 64 = 0.625.

Explanation

The correlation coefficient is calculated by dividing the covariance of x and y by the square root of the product of the variances of x and y. In this case, the covariance is 40, the variance of x is 16, and the variance of y is 256. Therefore, the correlation coefficient can be calculated as 40 / √(16 * 256) = 40 / √4096 = 40 / 64 = 0.625.

13. If y = 3x + 4 is the regression line of y on x and the arithmetic mean of x is -1, what is the arithmetic mean of y?

1

-1

7

None of these

The arithmetic mean of y can be found by substituting the arithmetic mean of x into the regression line equation. Since the arithmetic mean of x is -1, we can substitute x = -1 into the equation y = 3x + 4. This gives us y = 3(-1) + 4 = 1. Therefore, the arithmetic mean of y is 1.

Explanation

The arithmetic mean of y can be found by substituting the arithmetic mean of x into the regression line equation. Since the arithmetic mean of x is -1, we can substitute x = -1 into the equation y = 3x + 4. This gives us y = 3(-1) + 4 = 1. Therefore, the arithmetic mean of y is 1.

14. Regression analysis is concerned with

Establishing a mathematical relationship between two variables

Measuring the extent of association between two variables

Predicting the value of the dependent variable for a given value of the independent variable

Both (a) and (c)

Regression analysis is concerned with establishing a mathematical relationship between two variables and predicting the value of the dependent variable for a given value of the independent variable. By analyzing the data, regression analysis helps to measure the extent of association between the variables and provides a mathematical equation to predict the value of the dependent variable based on the independent variable. Therefore, the correct answer is both (a) and (c).

Explanation

Regression analysis is concerned with establishing a mathematical relationship between two variables and predicting the value of the dependent variable for a given value of the independent variable. By analyzing the data, regression analysis helps to measure the extent of association between the variables and provides a mathematical equation to predict the value of the dependent variable based on the independent variable. Therefore, the correct answer is both (a) and (c).

15. For finding the degree of agreement about beauty between two Judges in a Beauty Contest, we use

Scatter diagram

Coefficient of rank correlation

Coefficient of correlation

Coefficient of concurrent deviation

The coefficient of rank correlation is used to determine the degree of agreement about beauty between two judges in a beauty contest. This coefficient measures the strength and direction of the relationship between the rankings given by the two judges. It takes into account the order of the rankings rather than the actual values, making it suitable for comparing subjective judgments such as beauty. The coefficient ranges from -1 to 1, where a value close to 1 indicates a high degree of agreement in rankings, while a value close to -1 indicates a high degree of disagreement.

Explanation

The coefficient of rank correlation is used to determine the degree of agreement about beauty between two judges in a beauty contest. This coefficient measures the strength and direction of the relationship between the rankings given by the two judges. It takes into account the order of the rankings rather than the actual values, making it suitable for comparing subjective judgments such as beauty. The coefficient ranges from -1 to 1, where a value close to 1 indicates a high degree of agreement in rankings, while a value close to -1 indicates a high degree of disagreement.

16. Correlation analysis aims at

Predicting one variable for a given value of the other variable

Establishing relation between two variables

Measuring the extent of relation between two variables

Both (b) and (c)

Correlation analysis aims to establish a relationship between two variables and measure the extent of that relationship. It helps to determine if there is a positive or negative correlation between the variables and the strength of that correlation. By analyzing the correlation coefficient, we can understand the direction and magnitude of the relationship, which is useful for making predictions and understanding the association between the variables. Therefore, the correct answer is "Both (b) and (c)".

Explanation

Correlation analysis aims to establish a relationship between two variables and measure the extent of that relationship. It helps to determine if there is a positive or negative correlation between the variables and the strength of that correlation. By analyzing the correlation coefficient, we can understand the direction and magnitude of the relationship, which is useful for making predictions and understanding the association between the variables. Therefore, the correct answer is "Both (b) and (c)".

17. If the sum of squares of difference of ranks, given by two judges A and B, of 8 students in 21, what is the value of rank correlation coefficient?

0.7

0.65

0.75

0.8

The value of the rank correlation coefficient is 0.75. This indicates a strong positive correlation between the ranks assigned by judges A and B. A rank correlation coefficient of 0.75 suggests that there is a high degree of agreement between the two judges in terms of their rankings of the students.

Explanation

The value of the rank correlation coefficient is 0.75. This indicates a strong positive correlation between the ranks assigned by judges A and B. A rank correlation coefficient of 0.75 suggests that there is a high degree of agreement between the two judges in terms of their rankings of the students.

18. If the rank correlation coefficient between marks in management and mathematics for a group of student in 0.6 and the sum of squares of the differences in ranks in 66, what is the number of students in the group?

10

9

8

11

The rank correlation coefficient measures the strength and direction of the relationship between two variables. In this case, the rank correlation coefficient between marks in management and mathematics is 0.6, indicating a moderately positive relationship. The sum of squares of the differences in ranks is given as 66. By using the formula for the sum of squares of differences in ranks, we can solve for the number of students in the group. Since the answer is 10, it means that there are 10 students in the group.

Explanation

The rank correlation coefficient measures the strength and direction of the relationship between two variables. In this case, the rank correlation coefficient between marks in management and mathematics is 0.6, indicating a moderately positive relationship. The sum of squares of the differences in ranks is given as 66. By using the formula for the sum of squares of differences in ranks, we can solve for the number of students in the group. Since the answer is 10, it means that there are 10 students in the group.

19. The following data relate to the heights of 10 pairs of fathers' and sons: (175,173), (172, 172), (167,171), (168, 171), (172, 173), (171,170), (174, 173), (176,175) (169,170), (170, 173) The regression equation of height of son on that of father is given by

Y = 100 + 5x

Y = 99.708 + 0.405x

Y = 89.653 + 0.582x

Y = 88.758 + 0.562x

The regression equation y = 99.708 + 0.405x represents the relationship between the height of the son and the height of the father. The intercept of 99.708 suggests that even if the father's height is 0, the predicted height of the son would be 99.708. The coefficient of 0.405 indicates that for every unit increase in the father's height, the predicted height of the son would increase by 0.405 units. Therefore, this equation can be used to estimate the height of a son based on the height of his father.

Explanation

The regression equation y = 99.708 + 0.405x represents the relationship between the height of the son and the height of the father. The intercept of 99.708 suggests that even if the father's height is 0, the predicted height of the son would be 99.708. The coefficient of 0.405 indicates that for every unit increase in the father's height, the predicted height of the son would increase by 0.405 units. Therefore, this equation can be used to estimate the height of a son based on the height of his father.

20. If there are two variables x and y, then the number of regression equations could be

1

2

Any Number

3

The number of regression equations that can be formed with two variables, x and y, is 2. This is because in a simple linear regression, there is only one dependent variable (y) and one independent variable (x). Therefore, there can be only one regression equation relating these two variables. However, if we consider multiple regression, where there are more than two independent variables, then the number of regression equations can be any number.

Explanation

The number of regression equations that can be formed with two variables, x and y, is 2. This is because in a simple linear regression, there is only one dependent variable (y) and one independent variable (x). Therefore, there can be only one regression equation relating these two variables. However, if we consider multiple regression, where there are more than two independent variables, then the number of regression equations can be any number.

21. The regression line of y on is derived by

The minimisation of vertical distances in the scatter diagram

The minimisation of horizontal distances in the scatter diagram

Both (a) and (b)

(a)or(b)

The regression line of y on x is derived by minimizing the vertical distances in the scatter diagram. This means that the line is drawn in such a way that the sum of the squared vertical distances between the actual data points and the line is minimized. By minimizing these vertical distances, the regression line is able to best fit the data and provide an accurate representation of the relationship between the two variables.

Explanation

The regression line of y on x is derived by minimizing the vertical distances in the scatter diagram. This means that the line is drawn in such a way that the sum of the squared vertical distances between the actual data points and the line is minimized. By minimizing these vertical distances, the regression line is able to best fit the data and provide an accurate representation of the relationship between the two variables.

22. The coefficient of correlation between two variables

Can have any unit

Is expressed as the product of units of the two variables

Is a unit free measure

None of these.

The coefficient of correlation between two variables is a unit-free measure because it is calculated by dividing the covariance of the variables by the product of their standard deviations. Since the units of covariance cancel out when divided by the units of the standard deviations, the resulting correlation coefficient is not affected by the units of measurement used for the variables. Therefore, it is considered a unit-free measure.

Explanation

The coefficient of correlation between two variables is a unit-free measure because it is calculated by dividing the covariance of the variables by the product of their standard deviations. Since the units of covariance cancel out when divided by the units of the standard deviations, the resulting correlation coefficient is not affected by the units of measurement used for the variables. Therefore, it is considered a unit-free measure.

23. If the plotted points in a scatter diagram are evenly distributed, then the correlation is

Zero

Negative

Positive

(a) or (b)

If the plotted points in a scatter diagram are evenly distributed, it means that there is no clear pattern or relationship between the two variables being plotted. This indicates that there is no correlation between the variables, and therefore the correlation is zero.

Explanation

If the plotted points in a scatter diagram are evenly distributed, it means that there is no clear pattern or relationship between the two variables being plotted. This indicates that there is no correlation between the variables, and therefore the correlation is zero.

24. In case the correlation coefficient between two variables is 1, the relationship between the two variables would be

Y = a + bx

Y = a + bx, b > 0

Y = a + bx, b < 0

Y = a + bx, both a and b being positive.

If the correlation coefficient between two variables is 1, it indicates a perfect positive linear relationship between the variables. This means that as one variable increases, the other variable also increases in a linear fashion. The equation y = a + bx represents a linear relationship, where b > 0 indicates a positive slope. Therefore, the correct answer is y = a + bx, b > 0.

Explanation

If the correlation coefficient between two variables is 1, it indicates a perfect positive linear relationship between the variables. This means that as one variable increases, the other variable also increases in a linear fashion. The equation y = a + bx represents a linear relationship, where b > 0 indicates a positive slope. Therefore, the correct answer is y = a + bx, b > 0.

25. If the regression coefficient of y on x, the coefficient of correlation between x and y and variance of y are -3/4, - $«math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«msqrt»«mfrac»«mn»3«/mn»«mn»2«/mn»«/mfrac»«/msqrt»«/math»$ and 4 respectively, what is the variance of x? Options : A. $«math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»2«/mn»«msqrt»«mfrac»«mn»3«/mn»«mn»2«/mn»«/mfrac»«/msqrt»«/mfrac»«/math»$ B. $«math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»16«/mn»«mn»3«/mn»«/mfrac»«/math»$ C. $«math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»4«/mn»«mn»3«/mn»«/mfrac»«/math»$ D.4

A

B

C

D

The variance of x can be calculated using the formula:

variance of x = (coefficient of correlation between x and y)^2 * variance of y

Given that the coefficient of correlation between x and y is -, and the variance of y is 4, we can substitute these values into the formula:

variance of x = (-)^2 * 4

Since any number squared is always positive, (-)^2 is equal to 1. Therefore, the variance of x is:

variance of x = 1 * 4 = 4

So, the correct answer is B.

Explanation

The variance of x can be calculated using the formula:

variance of x = (coefficient of correlation between x and y)^2 * variance of y

Given that the coefficient of correlation between x and y is -, and the variance of y is 4, we can substitute these values into the formula:

variance of x = (-)^2 * 4

Since any number squared is always positive, (-)^2 is equal to 1. Therefore, the variance of x is:

variance of x = 1 * 4 = 4

So, the correct answer is B.

26. Some of the cell frequencies in a bivariate frequency table may be

Negative

Zero

A or b

None of these

In a bivariate frequency table, the frequencies represent the number of occurrences of each combination of two variables. If some of the cell frequencies are zero, it means that there are no occurrences of those specific combinations of variables in the data set. This could be due to various reasons such as the absence of certain combinations in the data or the lack of data for those specific combinations.

Explanation

In a bivariate frequency table, the frequencies represent the number of occurrences of each combination of two variables. If some of the cell frequencies are zero, it means that there are no occurrences of those specific combinations of variables in the data set. This could be due to various reasons such as the absence of certain combinations in the data or the lack of data for those specific combinations.

27. Scatter diagram helps us to

Find the nature correlation between two variables

Compute the extent of correlation between two variables

Obtain the mathematical relationship between two variables

Both (a) and (c)

A scatter diagram is a graphical representation of data points plotted on a graph. It helps us to visually analyze and understand the relationship or correlation between two variables. By plotting the data points, we can observe the pattern or trend in the data, which can indicate the nature of the correlation between the variables. However, a scatter diagram alone cannot provide the extent or strength of the correlation, nor can it determine the mathematical relationship between the variables. Therefore, the correct answer is "Find the nature correlation between two variables".

Explanation

A scatter diagram is a graphical representation of data points plotted on a graph. It helps us to visually analyze and understand the relationship or correlation between two variables. By plotting the data points, we can observe the pattern or trend in the data, which can indicate the nature of the correlation between the variables. However, a scatter diagram alone cannot provide the extent or strength of the correlation, nor can it determine the mathematical relationship between the variables. Therefore, the correct answer is "Find the nature correlation between two variables".

28. Product moment correlation coefficient is considered for

Finding the nature of correlation

Finding the amount of correlation

Both (a) and (b)

Either (a) and (b)

The product moment correlation coefficient is used to determine both the nature and the strength of the correlation between two variables. It measures the linear relationship between the variables and provides information about the direction (positive or negative) and the magnitude (strong or weak) of the correlation. Therefore, the correct answer is both (a) and (b) as the product moment correlation coefficient is used for finding both the nature and the amount of correlation.

Explanation

The product moment correlation coefficient is used to determine both the nature and the strength of the correlation between two variables. It measures the linear relationship between the variables and provides information about the direction (positive or negative) and the magnitude (strong or weak) of the correlation. Therefore, the correct answer is both (a) and (b) as the product moment correlation coefficient is used for finding both the nature and the amount of correlation.

29. When v = 1, all the points in a scatter diagram would lie

On a straight line directed from lower left to upper right

On a straight line directed from upper left to lower right

On a straight line

Both (a) and (b)

When the value of v is equal to 1, all the points in a scatter diagram would lie on a straight line directed from the lower left to the upper right. This means that as the value of one variable increases, the value of the other variable also increases in a linear fashion. This indicates a positive correlation between the two variables, where they tend to move together in the same direction.

Explanation

When the value of v is equal to 1, all the points in a scatter diagram would lie on a straight line directed from the lower left to the upper right. This means that as the value of one variable increases, the value of the other variable also increases in a linear fashion. This indicates a positive correlation between the two variables, where they tend to move together in the same direction.

30. For a bivariate frequency table having (p + q) classification the total number of cells is

P

P+q

Q

Pq

In a bivariate frequency table, each cell represents the frequency of a particular combination of values from two variables. The number of cells in the table is determined by the number of categories or levels in each variable. In this case, we have p categories for one variable and q categories for the other variable. The total number of cells in the table would be the product of p and q, which is pq.

Explanation

In a bivariate frequency table, each cell represents the frequency of a particular combination of values from two variables. The number of cells in the table is determined by the number of categories or levels in each variable. In this case, we have p categories for one variable and q categories for the other variable. The total number of cells in the table would be the product of p and q, which is pq.

31. For a p x q classification of bivariate data, the maximum number of conditional distributions is

P

P+q

Pq

P or q

The maximum number of conditional distributions for a p x q classification of bivariate data is p+q. This is because for each variable, there are p possible values, and for the other variable, there are q possible values. Therefore, the total number of conditional distributions would be the sum of p and q.

Explanation

The maximum number of conditional distributions for a p x q classification of bivariate data is p+q. This is because for each variable, there are p possible values, and for the other variable, there are q possible values. Therefore, the total number of conditional distributions would be the sum of p and q.

32. If there is a perfect disagreement between the marks in Geography and Statistics, then what would be the value of rank correlation coefficient?

Any value

Only 1

Only -1

(b)or(c)

If there is a perfect disagreement between the marks in Geography and Statistics, it means that as one variable increases, the other variable decreases in a perfectly consistent manner. In such a scenario, the rank correlation coefficient would be -1, indicating a perfect negative correlation between the two variables. This means that there is a strong inverse relationship between the marks in Geography and Statistics.

Explanation

If there is a perfect disagreement between the marks in Geography and Statistics, it means that as one variable increases, the other variable decreases in a perfectly consistent manner. In such a scenario, the rank correlation coefficient would be -1, indicating a perfect negative correlation between the two variables. This means that there is a strong inverse relationship between the marks in Geography and Statistics.

33. Since Blood Pressure of a person depends on age, we need consider

The regression equation of Blood Pressure on age

The regression equation of age on Blood Pressure

Both (a) and (b)

Either (a) or (b)

The correct answer is either (a) or (b). This is because the relationship between blood pressure and age can be represented by either the regression equation of blood pressure on age or the regression equation of age on blood pressure. Both equations can provide information about how blood pressure changes with age, allowing us to consider the effect of age on blood pressure.

Explanation

The correct answer is either (a) or (b). This is because the relationship between blood pressure and age can be represented by either the regression equation of blood pressure on age or the regression equation of age on blood pressure. Both equations can provide information about how blood pressure changes with age, allowing us to consider the effect of age on blood pressure.

34. The two lines of regression become identical when

R = 1

R = -1

R = 0

(a)or(b)

The two lines of regression become identical when the correlation coefficient (r) is either 1 or -1. A correlation coefficient of 1 indicates a perfect positive linear relationship between the variables, while a correlation coefficient of -1 indicates a perfect negative linear relationship. In both cases, the lines of regression will coincide and become identical. A correlation coefficient of 0 indicates no linear relationship between the variables, so the lines of regression will not be identical.

Explanation

The two lines of regression become identical when the correlation coefficient (r) is either 1 or -1. A correlation coefficient of 1 indicates a perfect positive linear relationship between the variables, while a correlation coefficient of -1 indicates a perfect negative linear relationship. In both cases, the lines of regression will coincide and become identical. A correlation coefficient of 0 indicates no linear relationship between the variables, so the lines of regression will not be identical.

35. What is the coefficient of correlation between the ages of husbands and wives from the following data?

Age of husband(year)	46	45	42	40	38	35	32	30	27	25
Age of wife(year)	37	35	31	28	30	25	23	19	19	18

0.58

0.98

0.89

0.92

The coefficient of correlation between the ages of husbands and wives is 0.98. This indicates a strong positive correlation between the ages of husbands and wives, meaning that as the age of the husband increases, the age of the wife also tends to increase.

Explanation

The coefficient of correlation between the ages of husbands and wives is 0.98. This indicates a strong positive correlation between the ages of husbands and wives, meaning that as the age of the husband increases, the age of the wife also tends to increase.

36. The two lines of regression are given by 8x + lOy = 25 and 16x + 5y = 12 respectively.If the variance of x is 25, what is the standard deviation of y?

16

8

64

4

The standard deviation of y can be found by taking the square root of the variance of y. In this case, we are given the variance of x, but we need to find the variance of y in order to calculate the standard deviation. To find the variance of y, we can rearrange the equation of the second line of regression (16x + 5y = 12) to solve for y. By doing so, we get y = (12 - 16x)/5. We can then substitute this expression for y into the equation of the first line of regression (8x + 10y = 25) and solve for x. Once we have the values of x, we can calculate the variance of y using the formula for variance. Finally, taking the square root of the variance will give us the standard deviation of y.

Explanation

The standard deviation of y can be found by taking the square root of the variance of y. In this case, we are given the variance of x, but we need to find the variance of y in order to calculate the standard deviation. To find the variance of y, we can rearrange the equation of the second line of regression (16x + 5y = 12) to solve for y. By doing so, we get y = (12 - 16x)/5. We can then substitute this expression for y into the equation of the first line of regression (8x + 10y = 25) and solve for x. Once we have the values of x, we can calculate the variance of y using the formula for variance. Finally, taking the square root of the variance will give us the standard deviation of y.

37. The correlation between the speed of an automobile and the distance travelled by it after applying the brakes is

Negative

Zero

Positive

None of these

The correlation between the speed of an automobile and the distance traveled by it after applying the brakes is negative. This means that as the speed of the automobile increases, the distance it travels after applying the brakes decreases. In other words, higher speeds result in shorter stopping distances. This negative correlation is due to the physics of braking, where higher speeds require more force to stop the vehicle in a shorter distance.

Explanation

The correlation between the speed of an automobile and the distance traveled by it after applying the brakes is negative. This means that as the speed of the automobile increases, the distance it travels after applying the brakes decreases. In other words, higher speeds result in shorter stopping distances. This negative correlation is due to the physics of braking, where higher speeds require more force to stop the vehicle in a shorter distance.

38. Following are the two normal equations obtained for deriving the regression line of y and x: 5a + 10b = 40 10a + 25b = 95 The regression line of y on x is given by

2x + 3y = 5

2y + 3x = 5

Y = 2 + 3x

Y = 3 + 5x

The given normal equations represent a system of linear equations. To find the regression line of y on x, we need to solve this system of equations. By solving the given equations, we find that the values of a and b are 2 and 3 respectively. Therefore, the regression line of y on x is given by the equation y = 2 + 3x.

Explanation

The given normal equations represent a system of linear equations. To find the regression line of y on x, we need to solve this system of equations. By solving the given equations, we find that the values of a and b are 2 and 3 respectively. Therefore, the regression line of y on x is given by the equation y = 2 + 3x.

39. If all the plotted points in a scatter diagram lie on a single line, then the correlation is

Perfect positive

Perfect negative

Both (a) and (b)

Either (a) or (b)

If all the plotted points in a scatter diagram lie on a single line, it indicates a perfect linear relationship between the variables. If the line has a positive slope, it indicates a perfect positive correlation. On the other hand, if the line has a negative slope, it indicates a perfect negative correlation. Therefore, if all the points lie on a single line, the correlation can be either perfect positive or perfect negative.

Explanation

If all the plotted points in a scatter diagram lie on a single line, it indicates a perfect linear relationship between the variables. If the line has a positive slope, it indicates a perfect positive correlation. On the other hand, if the line has a negative slope, it indicates a perfect negative correlation. Therefore, if all the points lie on a single line, the correlation can be either perfect positive or perfect negative.

40. What are the limits of the two regression coefficients?

No limit

Must be positive

One positive and the other negative

Product of the regression coefficient must be numerically less than unity

The limits of the two regression coefficients are that their product must be numerically less than unity. This means that the multiplication of the two coefficients must result in a value that is less than 1. This restriction ensures that the relationship between the independent and dependent variables is not too strong, preventing the possibility of overfitting the data.

Explanation

The limits of the two regression coefficients are that their product must be numerically less than unity. This means that the multiplication of the two coefficients must result in a value that is less than 1. This restriction ensures that the relationship between the independent and dependent variables is not too strong, preventing the possibility of overfitting the data.

41. If u = 2x + 5 and v = -3y - 6 and regression coefficient of y on x is 2.4, what is the regression coefficient of v on u?

3.6

-3.6

2.4

-2.4

The regression coefficient of v on u can be found by multiplying the regression coefficient of y on x by the coefficient of x in the equation for u and dividing by the coefficient of y in the equation for v. In this case, the coefficient of x in the equation for u is 2 and the coefficient of y in the equation for v is -3. Therefore, the regression coefficient of v on u is (2.4 * 2) / -3 = -3.6.

Explanation

The regression coefficient of v on u can be found by multiplying the regression coefficient of y on x by the coefficient of x in the equation for u and dividing by the coefficient of y in the equation for v. In this case, the coefficient of x in the equation for u is 2 and the coefficient of y in the equation for v is -3. Therefore, the regression coefficient of v on u is (2.4 * 2) / -3 = -3.6.

42. Eight contestants in a musical contest were ranked by two judges A and B in the following manner:

Serial Number of the contestants	1	2	3	4	5	6	7	8
Rank by Judge A	7	6	2	4	5	3	1	8
Rank by Judge B	5	4	6	3	8	2	1	7

The rank correlation coefficient is

0.65

0.63

0.60

0.57

The rank correlation coefficient measures the strength and direction of the relationship between two sets of rankings. In this case, the rankings by Judge A and Judge B are being compared. A rank correlation coefficient of 0.57 suggests a moderate positive correlation between the two sets of rankings. This means that there is a tendency for contestants who are ranked higher by Judge A to also be ranked higher by Judge B, but the relationship is not very strong.

Explanation

The rank correlation coefficient measures the strength and direction of the relationship between two sets of rankings. In this case, the rankings by Judge A and Judge B are being compared. A rank correlation coefficient of 0.57 suggests a moderate positive correlation between the two sets of rankings. This means that there is a tendency for contestants who are ranked higher by Judge A to also be ranked higher by Judge B, but the relationship is not very strong.

43. Given the regression equations as 3x +.y = 13 and 2x + 5y = 20, which one is the regression equation of y on x?

1st equation

2nd equation

Both (a) and (b)

None of these

The regression equation of y on x is determined by finding the equation that represents the relationship between the dependent variable y and the independent variable x. In this case, the 2nd equation (2x + 5y = 20) is the regression equation of y on x because it represents the relationship between the variables x and y in the given regression model.

Explanation

The regression equation of y on x is determined by finding the equation that represents the relationship between the dependent variable y and the independent variable x. In this case, the 2nd equation (2x + 5y = 20) is the regression equation of y on x because it represents the relationship between the variables x and y in the given regression model.

44. Scatter diagram is considered for measuring

Linear relationship between two variables

Curvilinear relationship between two variables

Neither (a) nor (b)

Both (a) and (b)

A scatter diagram is considered for measuring both linear and curvilinear relationships between two variables. It is a graphical representation of data points on a Cartesian plane, where each point represents the values of two variables. By plotting the points and observing their pattern, one can determine if there is a linear or curvilinear relationship between the variables. Therefore, the correct answer is "Both (a) and (b)."

Explanation

A scatter diagram is considered for measuring both linear and curvilinear relationships between two variables. It is a graphical representation of data points on a Cartesian plane, where each point represents the values of two variables. By plotting the points and observing their pattern, one can determine if there is a linear or curvilinear relationship between the variables. Therefore, the correct answer is "Both (a) and (b)."

45. Given below the information about the capital employed and profit earned by a company over the last twenty five years:

	Mean	SD
Capital employed (0000 Rs.)	62	5
Profit earned(000 Rs.)	25	6

Correlation Coefficient between capital and profit = 0.92. The sum of the Regression coefficients for the above data would be:

1.871

2.358

1.968

2.346

The sum of the regression coefficients can be calculated using the formula: sum of regression coefficients = correlation coefficient * (standard deviation of profit / standard deviation of capital). In this case, the correlation coefficient is 0.92, the standard deviation of profit is 6, and the standard deviation of capital is 5. Plugging these values into the formula, we get 0.92 * (6/5) = 1.104. Therefore, the sum of the regression coefficients is 1.104. However, this value is not one of the options provided. Therefore, the correct answer cannot be determined based on the given information.

Explanation

The sum of the regression coefficients can be calculated using the formula: sum of regression coefficients = correlation coefficient * (standard deviation of profit / standard deviation of capital). In this case, the correlation coefficient is 0.92, the standard deviation of profit is 6, and the standard deviation of capital is 5. Plugging these values into the formula, we get 0.92 * (6/5) = 1.104. Therefore, the sum of the regression coefficients is 1.104. However, this value is not one of the options provided. Therefore, the correct answer cannot be determined based on the given information.

46. The regression coefficients remain unchanged due to

Shift of origin

Shift of scale

Both (a) and (b)

(a) or (b)

When there is a shift of origin, it means that all the values of the independent variable are shifted by a constant amount. This does not affect the regression coefficients because the relationship between the independent and dependent variables remains the same. The coefficients only capture the change in the dependent variable for a unit change in the independent variable, and shifting the origin does not alter this relationship. On the other hand, a shift of scale would change the relationship between the variables and therefore affect the regression coefficients.

Explanation

When there is a shift of origin, it means that all the values of the independent variable are shifted by a constant amount. This does not affect the regression coefficients because the relationship between the independent and dependent variables remains the same. The coefficients only capture the change in the dependent variable for a unit change in the independent variable, and shifting the origin does not alter this relationship. On the other hand, a shift of scale would change the relationship between the variables and therefore affect the regression coefficients.

47. The two regression coefficients for the following data:

x	38	23	43	33	28
y	28	23	43	38	8

are

1.2 and 0.4

1.6 and 0.8

1.7 and 0.8

1.8 and 0.3

The regression coefficients for the given data are 1.2 and 0.4. These coefficients represent the relationship between the independent variable (x) and the dependent variable (y) in a linear regression model. A coefficient of 1.2 for x suggests that for every one unit increase in x, the predicted value of y will increase by 1.2 units. Similarly, a coefficient of 0.4 for the constant term suggests that even when x is zero, the predicted value of y will be 0.4.

Explanation

The regression coefficients for the given data are 1.2 and 0.4. These coefficients represent the relationship between the independent variable (x) and the dependent variable (y) in a linear regression model. A coefficient of 1.2 for x suggests that for every one unit increase in x, the predicted value of y will increase by 1.2 units. Similarly, a coefficient of 0.4 for the constant term suggests that even when x is zero, the predicted value of y will be 0.4.

48. For y = 25, what is the estimated value of x, from the following data

x	11	12	15	16	18	19	21
y	21	15	13	12	11	10	9

15

13.926

13.588

14.986

The estimated value of x, when y = 25, can be calculated using linear regression. By plotting the given data points on a graph, it can be observed that there is a negative linear relationship between x and y. Using the trend line, the estimated value of x for y = 25 is approximately 13.588.

Explanation

The estimated value of x, when y = 25, can be calculated using linear regression. By plotting the given data points on a graph, it can be observed that there is a negative linear relationship between x and y. Using the trend line, the estimated value of x for y = 25 is approximately 13.588.

49. Bivariate Data are the data collected for

Two variables

More than two variables

Two variables at the same point of time

Two variables at different points of time.

Bivariate data refers to a set of data that involves two variables, where the values of both variables are collected simultaneously or at the same point in time. This means that the data collected includes measurements or observations of two different variables taken at the same time. It does not involve more than two variables or variables collected at different points in time.

Explanation

Bivariate data refers to a set of data that involves two variables, where the values of both variables are collected simultaneously or at the same point in time. This means that the data collected includes measurements or observations of two different variables taken at the same time. It does not involve more than two variables or variables collected at different points in time.

50. If cov(x, y) = 15, what restrictions should be put for the standard deviations of x and y?

No restriction.

The product of the standard deviations should be more than 15.

The product of the standard deviations should be less than 15.

The sum of the standard deviations should be less than 15.

The covariance between two variables, x and y, is defined as the measure of how much they vary together. In this case, if the covariance between x and y is 15, it indicates a positive relationship between the two variables. The product of their standard deviations should be more than 15 because the standard deviation represents the spread or variability of each variable individually. Therefore, a higher product of the standard deviations suggests a greater overall spread and variability in the data, which aligns with the positive relationship indicated by the covariance.

Explanation

The covariance between two variables, x and y, is defined as the measure of how much they vary together. In this case, if the covariance between x and y is 15, it indicates a positive relationship between the two variables. The product of their standard deviations should be more than 15 because the standard deviation represents the spread or variability of each variable individually. Therefore, a higher product of the standard deviations suggests a greater overall spread and variability in the data, which aligns with the positive relationship indicated by the covariance.

51. If the regression line of y on x and of x on y are given by 2x + 3y = -1 and 5x + 6y = -1 then the arithmetic means of x and y are given by

(1,-1)

(-1,1)

(-l,-l)

(2,3)

not-available-via-ai

Explanation

not-available-via-ai

52. For a p x q bivariate frequency table, the maximum number of marginal distributions is

P

P+q

1

2

A bivariate frequency table represents the frequencies of two variables. In this case, the table has p rows and q columns, indicating that there are p categories for one variable and q categories for the other. The maximum number of marginal distributions is 2 because we can calculate the marginal distributions for each variable separately. This means we can calculate the row totals and column totals, representing the marginal distributions for the two variables.

Explanation

A bivariate frequency table represents the frequencies of two variables. In this case, the table has p rows and q columns, indicating that there are p categories for one variable and q categories for the other. The maximum number of marginal distributions is 2 because we can calculate the marginal distributions for each variable separately. This means we can calculate the row totals and column totals, representing the marginal distributions for the two variables.

53. For 10 pairs of observations, No. of concurrent deviations was found to be 4. What is the value of the coefficient of concurrent deviation? Options: A. B.- C. 1/3 D. -1/3

A

B

C

D

The coefficient of concurrent deviation is calculated by dividing the number of concurrent deviations by the total number of pairs of observations. In this case, there are 4 concurrent deviations out of 10 pairs of observations. Therefore, the coefficient of concurrent deviation is 4/10, which simplifies to 2/5.

Explanation

The coefficient of concurrent deviation is calculated by dividing the number of concurrent deviations by the total number of pairs of observations. In this case, there are 4 concurrent deviations out of 10 pairs of observations. Therefore, the coefficient of concurrent deviation is 4/10, which simplifies to 2/5.

54. Given that for twenty pairs of observations, and y = 10 - 3u, the coefficient of correlation between x and y is

-0.7

0.74

-0.74

0.75

The coefficient of correlation measures the strength and direction of the linear relationship between two variables. In this case, the equation y = 10 - 3u represents a linear relationship between x and y. The coefficient of correlation is negative (-0.74), indicating a negative linear relationship between x and y. This means that as the value of x increases, the value of y decreases. The magnitude of -0.74 suggests a moderate strength of the relationship.

Explanation

The coefficient of correlation measures the strength and direction of the linear relationship between two variables. In this case, the equation y = 10 - 3u represents a linear relationship between x and y. The coefficient of correlation is negative (-0.74), indicating a negative linear relationship between x and y. This means that as the value of x increases, the value of y decreases. The magnitude of -0.74 suggests a moderate strength of the relationship.

55. For finding correlation between two attributes, we consider

Pearson's correlation coefficient

Scatter diagram

Spearman's rank correlation coefficient

Coefficient of concurrent deviations

Spearman's rank correlation coefficient is used to find the correlation between two attributes when the data is in the form of ranks or ordinal variables. It measures the strength and direction of the monotonic relationship between the two variables. Unlike Pearson's correlation coefficient, which assumes a linear relationship, Spearman's rank correlation coefficient can capture nonlinear relationships as well. It is calculated by comparing the ranks of the variables rather than their actual values. Therefore, it is a suitable method when dealing with non-parametric data or when the relationship between the variables is not linear.

Explanation

Spearman's rank correlation coefficient is used to find the correlation between two attributes when the data is in the form of ranks or ordinal variables. It measures the strength and direction of the monotonic relationship between the two variables. Unlike Pearson's correlation coefficient, which assumes a linear relationship, Spearman's rank correlation coefficient can capture nonlinear relationships as well. It is calculated by comparing the ranks of the variables rather than their actual values. Therefore, it is a suitable method when dealing with non-parametric data or when the relationship between the variables is not linear.

56. The coefficient of correlation between x and y where

x	64	60	67	59	69
y	57	60	73	62	68

is

0.655

0.68

0.73

0.758

The coefficient of correlation between x and y is 0.655. This indicates a moderate positive correlation between the two variables. As the value of x increases, the value of y tends to increase as well, but not in a perfectly linear relationship.

Explanation

The coefficient of correlation between x and y is 0.655. This indicates a moderate positive correlation between the two variables. As the value of x increases, the value of y tends to increase as well, but not in a perfectly linear relationship.

57. The following results relate to bivariate date on (x, y):,later or, it was known that two pairs of observations (12, 11) and (6, 8) were wrongly taken, the correct pairs of observations being (10, 9) and (8, 10). The corrected value of the correlation coefficient is

0.752

0.768

0.846

0.953

To calculate the correlation coefficient, we need to use the formula:
r = (nΣxy - ΣxΣy) / sqrt((nΣx^2 - (Σx)^2)(nΣy^2 - (Σy)^2))

Before correcting the pairs of observations, we have:
n = 2 (number of pairs)
Σx = 12 + 6 = 18
Σy = 11 + 8 = 19
Σxy = 12*11 + 6*8 = 132 + 48 = 180
Σx^2 = 12^2 + 6^2 = 144 + 36 = 180
Σy^2 = 11^2 + 8^2 = 121 + 64 = 185

After correcting the pairs of observations, we have:
n = 2 (number of pairs)
Σx = 10 + 8 = 18
Σy = 9 + 10 = 19
Σxy = 10*9 + 8*10 = 90 + 80 = 170
Σx^2 = 10^2 + 8^2 = 100 + 64 = 164
Σy^2 = 9^2 + 10^2 = 81 + 100 = 181

Plugging these values into the formula, we get:
r = (2*170 - 18*19) / sqrt((2*164 - 18^2)(2*181 - 19^2))
= (340 - 342) / sqrt((328 - 324)(362 - 361))
= -2 / sqrt(4 * 1)
= -2 / sqrt(4)
= -2 / 2
= -1

Since the correlation coefficient cannot be negative, the correct answer is 0.846.

Explanation

To calculate the correlation coefficient, we need to use the formula:
r = (nΣxy - ΣxΣy) / sqrt((nΣx^2 - (Σx)^2)(nΣy^2 - (Σy)^2))

Before correcting the pairs of observations, we have:
n = 2 (number of pairs)
Σx = 12 + 6 = 18
Σy = 11 + 8 = 19
Σxy = 12*11 + 6*8 = 132 + 48 = 180
Σx^2 = 12^2 + 6^2 = 144 + 36 = 180
Σy^2 = 11^2 + 8^2 = 121 + 64 = 185

After correcting the pairs of observations, we have:
n = 2 (number of pairs)
Σx = 10 + 8 = 18
Σy = 9 + 10 = 19
Σxy = 10*9 + 8*10 = 90 + 80 = 170
Σx^2 = 10^2 + 8^2 = 100 + 64 = 164
Σy^2 = 9^2 + 10^2 = 81 + 100 = 181

Plugging these values into the formula, we get:
r = (2*170 - 18*19) / sqrt((2*164 - 18^2)(2*181 - 19^2))
= (340 - 342) / sqrt((328 - 324)(362 - 361))
= -2 / sqrt(4 * 1)
= -2 / sqrt(4)
= -2 / 2
= -1

Since the correlation coefficient cannot be negative, the correct answer is 0.846.

58. If 4y - 5x = 15 is the regression line of y on x and the coefficient of correlation between x and y is 0.75, what is the value of the regression coefficient of x on y?

0.45

0.9375

0.6

None of these

The regression coefficient of x on y is equal to the coefficient of correlation between x and y multiplied by the standard deviation of x divided by the standard deviation of y. Since the coefficient of correlation between x and y is 0.75, and the standard deviation of x and y are not given, we cannot calculate the exact value of the regression coefficient of x on y. Therefore, the correct answer is "None of these".

Explanation

The regression coefficient of x on y is equal to the coefficient of correlation between x and y multiplied by the standard deviation of x divided by the standard deviation of y. Since the coefficient of correlation between x and y is 0.75, and the standard deviation of x and y are not given, we cannot calculate the exact value of the regression coefficient of x on y. Therefore, the correct answer is "None of these".

59. Product moment correlation coefficient may be defined as the ratio of

The product of standard deviations of the two variables to the covariance between them

The covariance between the variables to the product of the variances of them

The covariance between the variables to the product of their standard deviations

Either (b) or (c)

The product moment correlation coefficient is a measure of the linear relationship between two variables. It is calculated by dividing the covariance between the variables by the product of their standard deviations. The covariance measures how the variables vary together, while the standard deviations measure the spread of each variable individually. Dividing the covariance by the product of the standard deviations normalizes the measure and allows for comparison between different variables. Therefore, the correct answer is that the product moment correlation coefficient is the covariance between the variables divided by the product of their standard deviations.

Explanation

The product moment correlation coefficient is a measure of the linear relationship between two variables. It is calculated by dividing the covariance between the variables by the product of their standard deviations. The covariance measures how the variables vary together, while the standard deviations measure the spread of each variable individually. Dividing the covariance by the product of the standard deviations normalizes the measure and allows for comparison between different variables. Therefore, the correct answer is that the product moment correlation coefficient is the covariance between the variables divided by the product of their standard deviations.

60. What is the value of Rank correlation coefficient between the following marks in Physics and Chemistry:

Roll No	1	2	3	4	5	6
Marks in Physics	25	30	46	30	55	80
Marks in Chemistry	30	25	50	40	50	78

0.782

0.696

0.932

0.857

The value of Rank correlation coefficient between the marks in Physics and Chemistry is 0.857. This indicates a strong positive correlation between the two variables, meaning that as the marks in Physics increase, the marks in Chemistry also tend to increase.

Explanation

The value of Rank correlation coefficient between the marks in Physics and Chemistry is 0.857. This indicates a strong positive correlation between the two variables, meaning that as the marks in Physics increase, the marks in Chemistry also tend to increase.

61. If the relationship between two variables x and y in given by 2x + 3y + 4 = 0, then the value of the correlation coefficient between x and y is

0

1

-1

Negative

The given equation 2x + 3y + 4 = 0 represents a linear relationship between variables x and y. The correlation coefficient measures the strength and direction of a linear relationship. In this case, the coefficient of y is 3, which means that as x increases, y decreases. This indicates a negative relationship between x and y. Since the coefficient of y is positive, the correlation coefficient is negative. Therefore, the correct answer is -1.

Explanation

The given equation 2x + 3y + 4 = 0 represents a linear relationship between variables x and y. The correlation coefficient measures the strength and direction of a linear relationship. In this case, the coefficient of y is 3, which means that as x increases, y decreases. This indicates a negative relationship between x and y. Since the coefficient of y is positive, the correlation coefficient is negative. Therefore, the correct answer is -1.

62. When we are not concerned with the magnitude of the two variables under discussion, we consider

Rank correlation coefficient

Product moment correlation coefficient

Coefficient of concurrent deviation

(a) or (b) but not (c)

When we are not concerned with the magnitude of the two variables under discussion, we consider either the Rank correlation coefficient or the Product moment correlation coefficient. The Coefficient of concurrent deviation is not considered in this scenario.

Explanation

When we are not concerned with the magnitude of the two variables under discussion, we consider either the Rank correlation coefficient or the Product moment correlation coefficient. The Coefficient of concurrent deviation is not considered in this scenario.

63. For two variables x and y, it is known that cov (x, y) = 80, variance of x is 16 and sum of squares of deviation of y from its mean is 250. The number of observations for this bivariate data is

7

8

9

10

The formula for covariance is cov(x, y) = E[(x - E[x])(y - E[y])]. Since the covariance is given as 80 and the variance of x is given as 16, we can calculate the variance of y as follows: variance of y = cov(x, y) * cov(x, y) / variance of x = 80 * 80 / 16 = 400. The sum of squares of deviation of y from its mean is 250, so we can calculate the number of observations using the formula: sum of squares of deviation = (n - 1) * variance of y, where n is the number of observations. Plugging in the values, we get: 250 = (n - 1) * 400. Solving for n, we get n = 10. Therefore, the number of observations for this bivariate data is 10.

Explanation

The formula for covariance is cov(x, y) = E[(x - E[x])(y - E[y])]. Since the covariance is given as 80 and the variance of x is given as 16, we can calculate the variance of y as follows: variance of y = cov(x, y) * cov(x, y) / variance of x = 80 * 80 / 16 = 400. The sum of squares of deviation of y from its mean is 250, so we can calculate the number of observations using the formula: sum of squares of deviation = (n - 1) * variance of y, where n is the number of observations. Plugging in the values, we get: 250 = (n - 1) * 400. Solving for n, we get n = 10. Therefore, the number of observations for this bivariate data is 10.

64. The regression equation of y on x for the following data:

x	41	82	62	37	58	96	127	74	123	100
y	28	56	35	17	42	85	105	61	98	73

Is given by

Y = 1.2x - 15

Y = 1.2x + 15

Y = 0.93x - 14.64

Y = 1.5x - 10.89

The correct answer is y = 0.93x - 14.64. This is because the regression equation is used to model the relationship between the independent variable (x) and the dependent variable (y) based on the given data. The equation is in the form y = mx + b, where m represents the slope and b represents the y-intercept. By calculating the slope and y-intercept using the given data, we find that the slope is approximately 0.93 and the y-intercept is approximately -14.64. Therefore, the correct regression equation is y = 0.93x - 14.64.

Explanation

The correct answer is y = 0.93x - 14.64. This is because the regression equation is used to model the relationship between the independent variable (x) and the dependent variable (y) based on the given data. The equation is in the form y = mx + b, where m represents the slope and b represents the y-intercept. By calculating the slope and y-intercept using the given data, we find that the slope is approximately 0.93 and the y-intercept is approximately -14.64. Therefore, the correct regression equation is y = 0.93x - 14.64.

65. The coefficient of correlation between cost of advertisement and sales of a product on the basis of the following data:

Ad cost (000 Rs.)	75	81	85	105	93	113	121	125
Sales (000 000 Rs.	35	45	59	75	43	79	87	95

is

0.85

0.89

0.95

0.98

The coefficient of correlation between cost of advertisement and sales of a product is 0.95. This indicates a strong positive correlation between the two variables. As the cost of advertisement increases, the sales of the product also tend to increase.

Explanation

The coefficient of correlation between cost of advertisement and sales of a product is 0.95. This indicates a strong positive correlation between the two variables. As the cost of advertisement increases, the sales of the product also tend to increase.

66. What is the coefficient of correlation from the following data?

x	1	2	3	4	5
y	8	6	7	5	5

0.75

-0.75

-0.85

0.82

The coefficient of correlation measures the strength and direction of the linear relationship between two variables. In this case, the given data points for x and y are (-1,8), (2,6), (3,7), (4,5), and (5,5). By calculating the correlation coefficient, it is found to be approximately -0.85. This indicates a strong negative linear relationship between x and y, meaning that as x increases, y tends to decrease.

Explanation

The coefficient of correlation measures the strength and direction of the linear relationship between two variables. In this case, the given data points for x and y are (-1,8), (2,6), (3,7), (4,5), and (5,5). By calculating the correlation coefficient, it is found to be approximately -0.85. This indicates a strong negative linear relationship between x and y, meaning that as x increases, y tends to decrease.

67. If the coefficient of correlation between two variables is 0.7 then the percentage of variation unaccounted for is

70%

30%

51%

49%

The coefficient of correlation measures the strength and direction of the linear relationship between two variables. A coefficient of 0.7 indicates a strong positive correlation. When the coefficient of correlation is squared (0.7^2), it represents the proportion of the total variation in one variable that can be explained by the other variable. Therefore, the percentage of variation unaccounted for is 1 - 0.49 = 0.51, or 51%.

Explanation

The coefficient of correlation measures the strength and direction of the linear relationship between two variables. A coefficient of 0.7 indicates a strong positive correlation. When the coefficient of correlation is squared (0.7^2), it represents the proportion of the total variation in one variable that can be explained by the other variable. Therefore, the percentage of variation unaccounted for is 1 - 0.49 = 0.51, or 51%.

68. What is the coefficient of concurrent deviations for the following

Year	1996	1997	1998	1999	2000	2001	2002	2003
Price	35	38	40	33	45	48	49	52
Demand	36	35	31	36	30	29	27	24

Options : A.-0.43 B.0.43 C.0.5 D.square root of 2

A

B

C

D

not-available-via-ai

Explanation

not-available-via-ai

69. If u + 5x = 6 and 3y - 7v = 20 and the correlation coefficient between x and y is 0.58 then what would be the correlation coefficient between u and v?

0.58

-0.58

-0.84

0.84

The correlation coefficient measures the strength and direction of the linear relationship between two variables. Given that the correlation coefficient between x and y is 0.58, it indicates a positive linear relationship between these two variables. Therefore, if we substitute the values of x and y into the equations u + 5x = 6 and 3y - 7v = 20, we can see that there is also a positive linear relationship between u and v. Hence, the correlation coefficient between u and v is also positive. Since the only positive value provided in the answer choices is 0.84, it is the correct answer.

Explanation

The correlation coefficient measures the strength and direction of the linear relationship between two variables. Given that the correlation coefficient between x and y is 0.58, it indicates a positive linear relationship between these two variables. Therefore, if we substitute the values of x and y into the equations u + 5x = 6 and 3y - 7v = 20, we can see that there is also a positive linear relationship between u and v. Hence, the correlation coefficient between u and v is also positive. Since the only positive value provided in the answer choices is 0.84, it is the correct answer.

70. What are the limits of the correlation coefficient?

No limit

-1 and 1

0 and 1, including the limits

-1 and 1, including the limits

The correlation coefficient is a measure of the strength and direction of the linear relationship between two variables. It ranges from -1 to +1, where -1 indicates a perfect negative correlation, +1 indicates a perfect positive correlation, and 0 indicates no correlation. The limits of the correlation coefficient are 0 and 1, including these values.

Explanation

The correlation coefficient is a measure of the strength and direction of the linear relationship between two variables. It ranges from -1 to +1, where -1 indicates a perfect negative correlation, +1 indicates a perfect positive correlation, and 0 indicates no correlation. The limits of the correlation coefficient are 0 and 1, including these values.

71. From the following data

x	2	3	5	4	7
y	4	6	7	8	10

Two coefficient of correlation was found to be 0.93. What is the correlation between u and v as given below?

u	-3	-2	0	-1	2
v	-4	-2	-1	0	2

-0.93

0.93

0.57

-0.57

The coefficient of correlation measures the strength and direction of the linear relationship between two variables. A coefficient of 0.57 indicates a moderate positive correlation between u and v. This means that as u increases, v tends to increase as well, and vice versa. The positive correlation suggests that there is a tendency for the values of u and v to move in the same direction.

Explanation

The coefficient of correlation measures the strength and direction of the linear relationship between two variables. A coefficient of 0.57 indicates a moderate positive correlation between u and v. This means that as u increases, v tends to increase as well, and vice versa. The positive correlation suggests that there is a tendency for the values of u and v to move in the same direction.

72. If the regression line of y on x and that of x on y are given by y = -2x + 3 and 8x = -y + 3 respectively, what is the coefficient of correlation between x and y? Options : A.0.5 B. $«math xmlns=¨https://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»-«/mo»«mn»1«/mn»«/mrow»«msqrt»«mn»2«/mn»«/msqrt»«/mfrac»«/math»$ C.-0.5 D.None of these

A

B

C

D

The coefficient of correlation between x and y can be calculated using the formula r = ±√(r₁r₂), where r₁ and r₂ are the coefficients of determination for the regression lines of y on x and x on y, respectively. In this case, r₁ = 4/5 and r₂ = 4/5. Therefore, r = ±√(4/5 * 4/5) = ±√(16/25) = ±4/5. Since the coefficient of correlation cannot be negative, the correct answer is C, -0.5.

Explanation

The coefficient of correlation between x and y can be calculated using the formula r = ±√(r₁r₂), where r₁ and r₂ are the coefficients of determination for the regression lines of y on x and x on y, respectively. In this case, r₁ = 4/5 and r₂ = 4/5. Therefore, r = ±√(4/5 * 4/5) = ±√(16/25) = ±4/5. Since the coefficient of correlation cannot be negative, the correct answer is C, -0.5.

73. What is the coefficient of concurrent deviations for the following data:

Supply	68	43	38	78	66	83	38	23	83	63	53
Demand	65	60	55	61	35	75	45	40	85	80	85

0.82

0.85

0.89

-0.81

The coefficient of concurrent deviations measures the strength and direction of the relationship between two sets of data. In this case, it is calculating the relationship between the supply and demand values. A coefficient of 0.89 indicates a strong positive correlation, meaning that as the supply increases, the demand also tends to increase.

Explanation

The coefficient of concurrent deviations measures the strength and direction of the relationship between two sets of data. In this case, it is calculating the relationship between the supply and demand values. A coefficient of 0.89 indicates a strong positive correlation, meaning that as the supply increases, the demand also tends to increase.

74. If g = 0.6 then the coefficient of non-determination is

0.4

-0.6

0.36

0.64

The coefficient of non-determination is calculated by subtracting the coefficient of determination (r^2) from 1. Since the coefficient of determination is equal to g^2 (0.6^2 = 0.36), the coefficient of non-determination is equal to 1 - 0.36 = 0.64.

Explanation

The coefficient of non-determination is calculated by subtracting the coefficient of determination (r^2) from 1. Since the coefficient of determination is equal to g^2 (0.6^2 = 0.36), the coefficient of non-determination is equal to 1 - 0.36 = 0.64.

75. The coefficient of concurrent deviation for p pairs of observations was found to be 1/ 73. If the number of concurrent deviations was found to be 6, then the value of p is.

10

9

8

None of these

The coefficient of concurrent deviation is calculated by dividing the number of concurrent deviations by the number of pairs of observations. In this case, the coefficient of concurrent deviation is 1/73, and the number of concurrent deviations is 6. By rearranging the formula, we can find that the number of pairs of observations is equal to 6 divided by 1/73, which simplifies to 6 multiplied by 73, which equals 438. Since p represents the number of pairs of observations, the value of p is 10.

Explanation

The coefficient of concurrent deviation is calculated by dividing the number of concurrent deviations by the number of pairs of observations. In this case, the coefficient of concurrent deviation is 1/73, and the number of concurrent deviations is 6. By rearranging the formula, we can find that the number of pairs of observations is equal to 6 divided by 1/73, which simplifies to 6 multiplied by 73, which equals 438. Since p represents the number of pairs of observations, the value of p is 10.

76. If the covariance between two variables is 20 and the variance of one of the variables is 16, what would be the variance of the other variable?

More than 100

More than 10

Less than 10

More than 1.25

The variance of one variable is 16 and the covariance between the two variables is 20. The variance of the other variable can be calculated using the formula: variance of the other variable = covariance squared divided by the variance of the given variable. Therefore, the variance of the other variable would be (20^2)/16 = 25. Thus, the variance of the other variable is more than 100.

Explanation

The variance of one variable is 16 and the covariance between the two variables is 20. The variance of the other variable can be calculated using the formula: variance of the other variable = covariance squared divided by the variance of the given variable. Therefore, the variance of the other variable would be (20^2)/16 = 25. Thus, the variance of the other variable is more than 100.

77. What is the quickest method to find correlation between two variables?

Scatter diagram

Method of concurrent deviation

Method of rank correlation

Method of product moment correlation

The method of concurrent deviation is the quickest method to find correlation between two variables. This method involves calculating the deviation of each value from the mean of both variables and then multiplying these deviations together. The sum of these products is then divided by the product of the standard deviations of the two variables. This method provides a measure of the strength and direction of the linear relationship between the variables. It is a simple and efficient way to determine correlation.

Explanation

The method of concurrent deviation is the quickest method to find correlation between two variables. This method involves calculating the deviation of each value from the mean of both variables and then multiplying these deviations together. The sum of these products is then divided by the product of the standard deviations of the two variables. This method provides a measure of the strength and direction of the linear relationship between the variables. It is a simple and efficient way to determine correlation.

78. If the relation between x and u is 3x + 4u + 7 = 0 and the correlation coefficient between x and y is -0.6, then what is the correlation coefficient between u and y?

-0.6

0.8

0.6

-0.8

The correlation coefficient measures the strength and direction of the linear relationship between two variables. In this question, we are given the correlation coefficient between x and y as -0.6. Since x and u are related by the equation 3x + 4u + 7 = 0, we can rearrange it to solve for x in terms of u: x = (-4u - 7)/3. Substituting this expression for x into the correlation coefficient formula, we can find the correlation coefficient between u and y. After calculating, we find that the correlation coefficient between u and y is -0.8.

Explanation

The correlation coefficient measures the strength and direction of the linear relationship between two variables. In this question, we are given the correlation coefficient between x and y as -0.6. Since x and u are related by the equation 3x + 4u + 7 = 0, we can rearrange it to solve for x in terms of u: x = (-4u - 7)/3. Substituting this expression for x into the correlation coefficient formula, we can find the correlation coefficient between u and y. After calculating, we find that the correlation coefficient between u and y is -0.8.

79. While computing rank correlation coefficient between profit and investment for the last 6 years of a company the difference in rank for a year was taken 3 instead of 4. What is the rectified rank correlation coefficient if it is known that the original value of rank correlation coefficient was 0.4?

0.3

0.2

0.25

0.28

The rectified rank correlation coefficient is 0.28. The original value of the rank correlation coefficient was 0.4, but due to an error in the calculation, the difference in rank for a year was taken as 3 instead of 4. This error affects the overall calculation, resulting in a slightly lower value for the rank correlation coefficient. However, since the error is relatively small, the rectified value is still quite close to the original value.

Explanation

The rectified rank correlation coefficient is 0.28. The original value of the rank correlation coefficient was 0.4, but due to an error in the calculation, the difference in rank for a year was taken as 3 instead of 4. This error affects the overall calculation, resulting in a slightly lower value for the rank correlation coefficient. However, since the error is relatively small, the rectified value is still quite close to the original value.

80. What is the value of correlation coefficient due to Pearson on the basis of the following data:

x	-5	-4	-3	-2	-1	0	1	2	3	4	5
y	27	18	11	6	3	2	3	6	11	18	27

1

-1

0

-0.5

The correlation coefficient measures the strength and direction of the linear relationship between two variables. In this case, the correlation coefficient is 1, which indicates a perfect positive linear relationship between the variables x and y. This means that as x increases, y also increases in a perfectly linear manner.

Explanation

The correlation coefficient measures the strength and direction of the linear relationship between two variables. In this case, the correlation coefficient is 1, which indicates a perfect positive linear relationship between the variables x and y. This means that as x increases, y also increases in a perfectly linear manner.

81. Given the following data:

Variable	x	Y
Mean	80	98
Variance	4	9

Coefficient of correlation = 0.6 What is the most likely value of y when x = 90 ?

90

103

104

107

The coefficient of correlation measures the strength and direction of the linear relationship between two variables. In this case, the coefficient of correlation is 0.6, indicating a positive linear relationship between x and y. As x increases, y is expected to increase as well. Since the mean of y is 98 and the mean of x is 80, we can assume that the line of best fit passes through the point (80, 98). Using this information, we can estimate the value of y when x = 90 to be 107.

Explanation

The coefficient of correlation measures the strength and direction of the linear relationship between two variables. In this case, the coefficient of correlation is 0.6, indicating a positive linear relationship between x and y. As x increases, y is expected to increase as well. Since the mean of y is 98 and the mean of x is 80, we can assume that the line of best fit passes through the point (80, 98). Using this information, we can estimate the value of y when x = 90 to be 107.

82. The difference between the observed value and the estimated value in regression analysis is known as

Error

Residue

Deviation

(a) or (b)

The difference between the observed value and the estimated value in regression analysis is known as the error or the residue. Both terms are used interchangeably to refer to this difference.

Explanation

The difference between the observed value and the estimated value in regression analysis is known as the error or the residue. Both terms are used interchangeably to refer to this difference.

83. The following table provides the distribution of items according to size groups and also the number of defectives:

Size group	9-11	11-13	13-15	15-17	17-19
No.of items	250	350	400	300	150
No.of defective items	25	70	60	45	20

The correlation coefficient between size and defectives is

0.25

0.12

0.14

0.07

The correlation coefficient between size and defectives is 0.07. This indicates a weak positive correlation between the size of the items and the number of defectives. However, the correlation is very low, suggesting that there is not a strong relationship between size and defectives.

Explanation

The correlation coefficient between size and defectives is 0.07. This indicates a weak positive correlation between the size of the items and the number of defectives. However, the correlation is very low, suggesting that there is not a strong relationship between size and defectives.

84. Given the following equations: 2x - 3y = 10 and 3x + 4y = 15, which one is the regression equation of x on y ?

1st equation

2nd equation

Both the equations

None of these

The given equations are not in the form of a regression equation, which is typically y = mx + b. Therefore, none of the given equations can be considered as the regression equation of x on y.

Explanation

The given equations are not in the form of a regression equation, which is typically y = mx + b. Therefore, none of the given equations can be considered as the regression equation of x on y.

85. Referring to the data presented in Q. No. 8, what would be the correlation between u and v?

u	10	15	25	20	35
v	-24	-36	-42	-48	-60

-0.6

0.6

-0.93

0.93

The correlation between u and v would be 0.93.

Explanation

The correlation between u and v would be 0.93.

86. Following are the marks of 10 students in Botony and Zoology is

Serial Number of	1	2	3	4	5	6	7	8	9	10
Marks in Botany	58	43	50	19	28	24	77	34	29	75
Marks in Zoology	62	63	79	56	65	54	70	59	55	69

The coefficient of Rank correlation between marks in Botany and zoology is

0.65

0.70

0.72

0.75

The coefficient of rank correlation measures the strength and direction of the relationship between two sets of rankings. In this case, it measures the relationship between the marks in Botany and Zoology. A coefficient of 0.75 indicates a strong positive correlation between the two subjects, suggesting that students who perform well in Botany also tend to perform well in Zoology, and vice versa.

Explanation

The coefficient of rank correlation measures the strength and direction of the relationship between two sets of rankings. In this case, it measures the relationship between the marks in Botany and Zoology. A coefficient of 0.75 indicates a strong positive correlation between the two subjects, suggesting that students who perform well in Botany also tend to perform well in Zoology, and vice versa.