Section B Quiz 1 Advance Machine Learning

1. The straight line graph of the linear equation Y = a + bX, slope will be downward If:

B = 0

B < 0

B > 0

B ≠ 0

If the value of b is less than 0, it means that the coefficient of X in the equation Y = a + bX is negative. This indicates that as the value of X increases, the value of Y decreases. Therefore, the graph of this linear equation will have a downward slope.

Explanation

If the value of b is less than 0, it means that the coefficient of X in the equation Y = a + bX is negative. This indicates that as the value of X increases, the value of Y decreases. Therefore, the graph of this linear equation will have a downward slope.

2. In simple regression equation, the numbers of variables involved are:

0

1

2

3

In a simple regression equation, there are two variables involved: one independent variable and one dependent variable. The independent variable is used to predict or explain the changes in the dependent variable. Therefore, the correct answer is 2.

Explanation

In a simple regression equation, there are two variables involved: one independent variable and one dependent variable. The independent variable is used to predict or explain the changes in the dependent variable. Therefore, the correct answer is 2.

3. If the value of any regression coefficient is zero, then two variables are:

Qualitative

Correlation

Dependent

Independent

If the value of any regression coefficient is zero, it indicates that there is no relationship or association between the independent variable and the dependent variable. In other words, the independent variable does not have any effect on the dependent variable. Therefore, the two variables are considered independent of each other.

Explanation

If the value of any regression coefficient is zero, it indicates that there is no relationship or association between the independent variable and the dependent variable. In other words, the independent variable does not have any effect on the dependent variable. Therefore, the two variables are considered independent of each other.

4. The straight line graph of the linear equation Y = a + bX, slope will be upward If:

B = 0

B < 0

B > 0

B ≠ 0

The slope of a straight line graph represents the rate of change between the variables. In the equation Y = a + bX, the slope is represented by the coefficient b. If b > 0, it means that as X increases, Y also increases. This indicates a positive relationship between the variables, resulting in an upward slope on the graph.

Explanation

The slope of a straight line graph represents the rate of change between the variables. In the equation Y = a + bX, the slope is represented by the coefficient b. If b > 0, it means that as X increases, Y also increases. This indicates a positive relationship between the variables, resulting in an upward slope on the graph.

5. In simple linear regression model Y = α + βX + ε where α and β are called:

Estimates

Parameters

Random errors

Variables

In a simple linear regression model, the variables Y and X represent the dependent and independent variables, respectively. The parameters α and β are the coefficients that determine the intercept and slope of the regression line, respectively. These parameters are estimated from the data and represent the true population values. Therefore, the correct answer is "Parameters".

Explanation

In a simple linear regression model, the variables Y and X represent the dependent and independent variables, respectively. The parameters α and β are the coefficients that determine the intercept and slope of the regression line, respectively. These parameters are estimated from the data and represent the true population values. Therefore, the correct answer is "Parameters".

6. In simple linear regression, the numbers of unknown constants are:

One

Two

Three

Four

In simple linear regression, there are two unknown constants: the slope (represented by the letter "m") and the y-intercept (represented by the letter "b"). These constants are determined by fitting a straight line to a set of data points in order to model the relationship between a dependent variable (y) and an independent variable (x). The slope represents the rate of change of the dependent variable with respect to the independent variable, while the y-intercept represents the value of the dependent variable when the independent variable is zero.

Explanation

In simple linear regression, there are two unknown constants: the slope (represented by the letter "m") and the y-intercept (represented by the letter "b"). These constants are determined by fitting a straight line to a set of data points in order to model the relationship between a dependent variable (y) and an independent variable (x). The slope represents the rate of change of the dependent variable with respect to the independent variable, while the y-intercept represents the value of the dependent variable when the independent variable is zero.

7. The slope of the regression line of Y on X is also called the:

Correlation coefficient of X on Y

Correlation coefficient of Y on X

Regression coefficient of X on Y

Regression coefficient of Y on X

The slope of the regression line of Y on X represents the change in the dependent variable Y for a unit change in the independent variable X. Therefore, it is the regression coefficient of Y on X.

Explanation

The slope of the regression line of Y on X represents the change in the dependent variable Y for a unit change in the independent variable X. Therefore, it is the regression coefficient of Y on X.

8. Regression coefficient is independent of:

Units of measurement

Scale and origin

Both (a) and (b)

None of them

The regression coefficient is a measure of the relationship between the independent variable and the dependent variable in a regression analysis. It represents the change in the dependent variable for a one-unit change in the independent variable. The coefficient is independent of the units of measurement because it is a standardized measure that takes into account the scale and origin of the variables. Therefore, the correct answer is both (a) and (b) - the regression coefficient is independent of both the units of measurement and the scale and origin of the variables.

Explanation

The regression coefficient is a measure of the relationship between the independent variable and the dependent variable in a regression analysis. It represents the change in the dependent variable for a one-unit change in the independent variable. The coefficient is independent of the units of measurement because it is a standardized measure that takes into account the scale and origin of the variables. Therefore, the correct answer is both (a) and (b) - the regression coefficient is independent of both the units of measurement and the scale and origin of the variables.

9. The purpose of simple linear regression analysis is to:

Predict one variable from another variable

Replace points on a scatter diagram by a straight-line

Measure the degree to which two variables are linearly associated

Obtain the expected value of the independent random variable for a given value of the dependent variable

Simple linear regression analysis is a statistical method used to predict or estimate the value of one variable based on the value of another variable. It involves fitting a straight line to a scatter diagram of the data points, with the goal of understanding the linear relationship between the two variables. By using this analysis, we can make predictions about the value of the dependent variable based on the known value of the independent variable. Therefore, the purpose of simple linear regression analysis is to predict one variable from another variable.

Explanation

Simple linear regression analysis is a statistical method used to predict or estimate the value of one variable based on the value of another variable. It involves fitting a straight line to a scatter diagram of the data points, with the goal of understanding the linear relationship between the two variables. By using this analysis, we can make predictions about the value of the dependent variable based on the known value of the independent variable. Therefore, the purpose of simple linear regression analysis is to predict one variable from another variable.

10. If the points on the scatter diagram indicate that as one variable increases the other variable tends to decrease the value of r will be:

Perfect positive

Perfect negative

Negative

Zero

If the points on the scatter diagram indicate that as one variable increases, the other variable tends to decrease, the value of r will be negative. This is because a negative correlation exists between the two variables, meaning that as one variable increases, the other variable decreases. The correlation coefficient, r, measures the strength and direction of the linear relationship between the variables. In this case, the negative correlation indicates that as one variable increases, the other variable tends to decrease, resulting in a negative value for r.

Explanation

If the points on the scatter diagram indicate that as one variable increases, the other variable tends to decrease, the value of r will be negative. This is because a negative correlation exists between the two variables, meaning that as one variable increases, the other variable decreases. The correlation coefficient, r, measures the strength and direction of the linear relationship between the variables. In this case, the negative correlation indicates that as one variable increases, the other variable tends to decrease, resulting in a negative value for r.