1.
Load Data Set 111
I run a linear regression and find the equation for the line, then use it to predict the value for y when x = 12.
Which of the following features would be a concern in terms of accuracy?
Correct Answer(s)
A. Least squares regression line
B. Extrapolation
F. Pattern in the residual plot
Explanation
The least squares regression line is a concern in terms of accuracy because it assumes a linear relationship between the independent variable (x) and the dependent variable (y), which may not always be the case. Extrapolation is also a concern as it involves predicting values outside the range of the data, which can be unreliable. A pattern in the residual plot indicates that the model may not be capturing all the underlying patterns in the data, suggesting a lack of accuracy.
2.
I have the equation for the best transformation for a set of data :
y = 27 - 3.4 * log(x)
To predict the value of y when x = 12, which App should I use?
Correct Answer(s)
bivartranspredct
bivartranspredict
Explanation
The correct answer is "bivartranspredct" or "bivartranspredict" because both options refer to an app that can be used to predict the value of y when x = 12. The equation provided in the question represents a logarithmic transformation, and the app mentioned in the options is likely designed specifically for predicting values based on this type of transformation.
3.
Load Data Set 111
What is the equation for the least squares linear regression? (2 decimal places, no spaces)
Correct Answer(s)
y=62.43-8.14x
Explanation
The equation for the least squares linear regression is y=62.43-8.14x. This equation represents the line that best fits the given data points, minimizing the sum of the squared differences between the observed and predicted values of y. The coefficient -8.14 represents the slope of the line, indicating the rate of change in y for each unit change in x. The constant term 62.43 represents the y-intercept, indicating the value of y when x is 0.
4.
Load Data Set 111
Which quadrant does the shape of the data fit?
Correct Answer(s)
1
q1
quadrant 1
Explanation
The correct answer is quadrant 1. This suggests that the shape of the data fits in the first quadrant of a coordinate plane. In a coordinate plane, the first quadrant is the top right section where both the x and y coordinates are positive. This means that the data points are located in the upper right area of the graph, indicating a positive relationship between the variables being measured.
5.
Load Data Set 111
Which transformations apply to this data set?
Correct Answer(s)
A. X squared
B. Y squared
Explanation
The given transformations that apply to the data set are squaring the x-values and squaring the y-values. This means that each x-value in the data set is multiplied by itself, and each y-value is multiplied by itself. This transformation helps to analyze the relationship between the variables and can be useful in certain statistical analyses.
6.
Load Data Set 111
I run a linear regression and find the equation for the line, then use it to predict the value for y when x = 12.
Which of the following features would be a concern in terms of accuracy?
Correct Answer(s)
A. Least squares regression line
B. Extrapolation
F. Pattern in the residual plot
Explanation
The least squares regression line is a concern in terms of accuracy because it assumes a linear relationship between the variables, which may not always be the case. Extrapolation is also a concern because it involves predicting values outside of the range of the observed data, which can be unreliable. Additionally, a pattern in the residual plot suggests that the assumptions of the linear regression model may not be met, indicating potential inaccuracies in the predictions.
7.
The accuracy of any prediction using least squares regression, including transformations, is dependent on :
Correct Answer(s)
A. The regression line or transformation being linear
B. Residual plot being random
C. High r value
D. Interpolation
Explanation
The accuracy of any prediction using least squares regression is dependent on several factors. Firstly, the regression line or transformation being linear ensures that the relationship between the variables is adequately represented. Secondly, a random residual plot indicates that the model's errors are distributed evenly, suggesting a good fit. A high r-value signifies a strong correlation between the variables, which improves the accuracy of the predictions. Interpolation, which involves predicting within the range of the observed data, is generally more accurate than extrapolation, which predicts outside the observed range. Therefore, these factors contribute to the accuracy of predictions using least squares regression.
8.
The two main ways to indicate a predictions from a linear regression line or transformation will be accurate are:
Correct Answer
D. Interpolation and linearity
Explanation
The explanation for the correct answer is that interpolation and linearity are the main ways to indicate that a prediction from a linear regression line or transformation will be accurate. Interpolation refers to making predictions within the range of the observed data, while linearity refers to the relationship between the independent and dependent variables being linear. By using interpolation and ensuring linearity, we can have confidence in the accuracy of the predictions made using the linear regression line or transformation.
9.
In any linear regression equation, the value of b represents
Correct Answer
B. The rate of change in the relationship
Explanation
The value of b in a linear regression equation represents the rate of change in the relationship between the independent variable and the dependent variable. This means that for every one unit increase in the independent variable, the dependent variable is expected to change by the value of b.
10.
In any linear regression equation, the value of a represents
Correct Answer
C. The y intercept
Explanation
In any linear regression equation, the value of a represents the y intercept. The y intercept is the point where the regression line intersects the y-axis. It indicates the value of the dependent variable when the independent variable is equal to zero.
11.
Enter Data Set 111
Using the equation of the regression line to two decimal places, what is the value of y when x is 3.5?
Correct Answer
33.94
Explanation
The value of y when x is 3.5 can be determined by using the equation of the regression line. Since the equation is not provided, we cannot calculate the exact value.
12.
Enter Data Set 111
The data represents the migration of birds over the winter. The y values show the number of birds nesting in a cave. The x values indicate the number of weeks into winter the sample was taken.
birds in cave = 62.43 - 8.14 * weeks into winter
What is the prediction for the 10th week.
Correct Answer
0
0 Birds
13.
Enter Data Set 131
The data represents the sales of properties in a housing development by JCon Developers. Properties are developed and sold in stages of 10 houses. JCon decide to promote the properties for a month before putting them on sale. After the extensive advertising blitz for a month, JCon Developers have a total of 70 properties. The x values represent the number of months since the start of the advertising blitz. The y values represent the number of houses remaining.
number of house remaining = 67.62 - 63.37 * log(months since advertising blitz)
How many months will it take to sell out the development?
Correct Answer
12 months
11.67 months
12
11.67
Explanation
The given equation represents the relationship between the number of months since the start of the advertising blitz and the number of houses remaining. By substituting the value of the number of houses remaining as 0, we can solve for the number of months it will take to sell out the development. In this case, the answer is 11.67 months, which can be rounded up to 12 months.
14.
Enter Data Set 131
The data represents the sales of properties in a housing development by JCon Developers. Properties are developed and sold in stages of 10 houses. JCon decide to promote the properties for a month before putting them on sale. After the extensive advertising blitz for a month, JCon Developers have a total of 70 properties. The x values represent the number of months since the start of the advertising blitz. The y values represent the number of houses remaining.
number of house remaining = 67.62 - 63.37 * log(months since advertising blitz)
How many houses would remain to be sold four months after the advertising blitz?
Correct Answer
30 houses
30
Explanation
The equation provided gives the number of houses remaining as a function of the number of months since the start of the advertising blitz. To find the number of houses remaining four months after the blitz, we substitute 4 into the equation:
number of houses remaining = 67.62 - 63.37 * log(4)
Calculating this expression gives us the result of 30 houses remaining.
15.
Enter Data Set 131
The data represents the sales of properties in a housing development by JCon Constructions. Properties are developed and sold in stages of 10 houses, with seven stages planned. JCon decide to promote the properties for a month before putting them on sale. After the extensive advertising blitz for a month, JCon Developers have a total of 70 properties. The x values represent the number of months since the start of the advertising blitz. The y values represent the number of houses remaining.
number of house remaining = 67.62 - 63.37 * log(months since advertising blitz)
Using the transformation equation, predict how many houses have been sold 6 months after the advertising blitz?
Correct Answer
51 houses
51