Question 1

In simple linear regression, the:

Accepted Answer

A) least squares line is used to predict values of the independent variable. 
B) residual plot will reveal information about the basic model assumptions. 
C) least square line will not pass through the point (average x, average y). 
D) value of r (correlation coefficient) cannot be 0. 
E) all of the above

Question 2

The manager of a local shopping mall uses simple linear regression to develop an equation that predicts the number of daily shoplifting incidents at the mall's stores based on the number of security guards employed.The manager uses the following data:  The slope of the regression line is b = -1.2; the intercept of the regression line is a = 14.5.Produce the 95% confidence interval for the estimate of the population slope, β, and use it to complete the following sentence:
With 95% confidence, the slope of the population regression line is between ______ and ______.

Accepted Answer

A) -3.8, 1.3 
B) -2.9, 31.9 
C) -2.06, 3.59 
D) -1.2, 14.5

Question 3

The computer output table below shows partial results for a linear regression analysis.Determine SSE, the Error Sum of Squares, that should be entered in the ANOVA table.

Accepted Answer

A) 12310 
B) 8480 
C) 18300 
D) 21210 
E) 19360

Question 4

You are attempting to link weekly hours of exercise (x) to blood pressure (y) using simple linear regression and the following data:  In applying the least squares criterion, the slope (b) and the intercept (a) for the best-fitting line are b = 90 and a = -4.Produce the 95% confidence interval estimate of the population intercept.Report the upper bound for your interval.

Accepted Answer

A) 162 
B) 154 
C) 204 
D) 168 
E) 177

Question 5

The manager of a local shopping mall uses simple linear regression to develop an equation that predicts the number of daily shoplifting incidents at the mall's stores based on the number of security guards employed.The manager uses the following data:  The slope of the regression line is b = -1.2; the intercept of the regression line is a = 14.5.
Use the results of the regression analysis to produce a 95% prediction interval for the expected number of shoplifting incidents on a particular day when there are 5 security guards on duty.Based on the prediction interval, complete the following sentence:
With 95% confidence, the predicted number of shoplifting incidents on a particular day when there are 5 security guards on duty is between ______ and ______.

Accepted Answer

A) -2.7, 19.4 
B) 2.3, 14.4 
C) 6.24, 10.36 
D) 7.7, 8.9

Question 6

Tennis coach Ben Gordon is trying to identify a linear relationship that can be used to link average first serve velocity to the percent of first serve points won for his junior tennis players.Below is a table showing velocity and percent of points won for a sample of five junior players.  The slope of the least squares line is .44.The intercept is 36.4.Determine the value of R, the correlation coefficient, that you would insert in the table below.

Accepted Answer

A) .719 
B) .926 
C) .773 
D) .848 
E) .874

Question 7

The computer output below shows partial results for a linear regression analysis.Determine the standard error (standard deviation) of the sampling distribution of the sample slope that should be entered in the indicated cell of the output table:

Accepted Answer

A) 86.2 
B) 123.7 
C) 79.4 
D) 164.6 
E) 143.5

Question 8

Partial regression results from a sample of 24 observations are shown below.Determine the standard error of estimate here.

Accepted Answer

A) 108 
B) 193 
C) 157 
D) 117 
E) 106

Question 9

A least squares line:

Accepted Answer

A) assumes a relationship between the slope of x and the intercept of y 
B) may be used to predict a value of y if the corresponding x value is given 
C) must be linear, upward-sloping and have a positive y-intercept 
D) minimizes the sum of the deviations between the observed value of y and the estimated value of y 
E) all of the above

Question 10

In simple linear regression, the difference between a predicted y value and an observed y value is commonly called the residual or error value.

Accepted Answer

A) True 
 B)False

Question 11

Home Products.com believes there is a linear connection between the number of service operators that it has available for its live customer chat option each work shift (x) and the percentage of items purchased by customers that are returned to the company each week (y).The following sample data were used to establish the relationship:  The computer output below shows partial results for the linear regression analysis.Determine the upper bound on the appropriate 95% confidence interval estimate of the population slope-a value that would be entered in the indicated cell below.

Accepted Answer

A) 3.8 
B) 6.8 
C) -4.3 
D) -2.7 
E) 4.6

Question 12

Residual analysis makes use of a plot of residuals (on the y axis) and the independent variable (on the x axis) to evaluate the assumptions about the error term in regression.

Accepted Answer

A) True 
 B)False

Question 13

Vicente Management is trying to identify a linear relationship that can be used to estimate the heating costs for its commercial properties.Below is a table showing heating costs and floor area for a sample of five buildings in the area.  The slope of the least squares line is 2.2.The intercept is 182.Construct a 95% confidence interval estimate of E(y200), the expected heating cost for the set of all buildings that have 200,000 square feet of floor space.Report the upper bound for the interval.

Accepted Answer

A) 754.3 
B) 836.5 
C) 678.1 
D) 792.8 
E) 906.9

Question 14

Home Products.com believes there is a linear connection between the number of service operators that it has available for its live customer chat option each work shift (x) and the percentage of items purchased by customers that are returned to the company each week (y).The following sample data were used to establish the relationship:  The computer output below shows partial results for the linear regression analysis done here.Determine the value of tstat that should be entered in the indicated cell below:

Accepted Answer

A) -3.22 
B) -4.28 
C) -1.60 
D) -2.47 
E) -1.96

Question 15

The following data have been collected for a simple linear regression analysis relating sales (y) to price (x):  In applying the least squares criterion, the slope (b) and the intercept (a) for the best-fitting line are b = -12 and a = 162.Compute the value of r2 here.

Accepted Answer

A) .66 
B) .72 
C) .54 
D) .77 
E) .81

Question 16

When the slope of a simple linear regression equation is a negative value, the correlation coefficient can be either positive or negative.

Accepted Answer

A) True 
 B)False

Question 17

A local shopping mall would like to better understand the effectiveness of its security guards in preventing shoplifting.The mall's operation manager uses simple linear regression to develop an equation that predicts the number of daily shoplifting incidents at the mall's stores based on the number of security guards employed.  The slope of the regression line is b = -1.2; the intercept of the regression line is a = 14.5.The value of r2 here is:

Accepted Answer

A) 0.52 
B) 0.68 
C) 0.82 
D) 2.15

Question 18

In a simple linear regression, the least squares line turns out to be y = 120 + 4x.The sum of the residuals (errors) around this line will be 0.

Accepted Answer

A) True 
 B)False

Question 19

Karina Burkholtz believes there is a linear connection between the hourly rate (x) that her company charges for its truck rentals and the number of weekly rental hours (y) that the company sells.The following data are available:  Determine the total sum of squares (SST) that should be entered in the indicated cell below.

Accepted Answer

A) 170000 
B) 164000 
C) 152000 
D) 198000 
E) 187000

Question 20

The regression printout below shows the results of a regression analysis intended to link variable x to variable y.A sample of 15 data points was used.  Can you use the sample results shown here to reject a β = 0 null hypothesis at the 5% significance level? Explain.

Accepted Answer

A) Yes, since the upper bound on the 95% interval estimate of β is greater than 0, we can reject the β = 0 null hypothesis. 
B) Yes, since the p-value for the coefficient of x is greater than the significance level of .05, we can reject the β = 0 null hypothesis. 
C) No, since the p-value for the coefficient of the x variable is greater than .05, we can't reject the β = 0 null hypothesis. 
D) No, since tstat for the x variable is outside ±2.160, we can't reject the β = 0 null hypothesis.

Exam 11: Basic Regression Analysis

In simple linear regression, the:

The computer output table below shows partial results for a linear regression analysis.Determine SSE, the Error Sum of Squares, that should be entered in the ANOVA table.

The computer output below shows partial results for a linear regression analysis.Determine the standard error (standard deviation) of the sampling distribution of the sample slope that should be entered in the indicated cell of the output table:

Partial regression results from a sample of 24 observations are shown below.Determine the standard error of estimate here.

A least squares line:

In simple linear regression, the difference between a predicted y value and an observed y value is commonly called the residual or error value.

Residual analysis makes use of a plot of residuals (on the y axis) and the independent variable (on the x axis) to evaluate the assumptions about the error term in regression.

The following data have been collected for a simple linear regression analysis relating sales (y) to price (x) : In applying the least squares criterion, the slope (b) and the intercept (a) for the best-fitting line are b = -12 and a = 162.Compute the value of r² here.

When the slope of a simple linear regression equation is a negative value, the correlation coefficient can be either positive or negative.

In a simple linear regression, the least squares line turns out to be y = 120 + 4x.The sum of the residuals (errors) around this line will be 0.

The regression printout below shows the results of a regression analysis intended to link variable x to variable y.A sample of 15 data points was used. Can you use the sample results shown here to reject a β = 0 null hypothesis at the 5% significance level? Explain.

Exam 11: Basic Regression Analysis

In simple linear regression, the:

The computer output table below shows partial results for a linear regression analysis.Determine SSE, the Error Sum of Squares, that should be entered in the ANOVA table.

The computer output below shows partial results for a linear regression analysis.Determine the standard error (standard deviation) of the sampling distribution of the sample slope that should be entered in the indicated cell of the output table:

Partial regression results from a sample of 24 observations are shown below.Determine the standard error of estimate here.

A least squares line:

In simple linear regression, the difference between a predicted y value and an observed y value is commonly called the residual or error value.

Residual analysis makes use of a plot of residuals (on the y axis) and the independent variable (on the x axis) to evaluate the assumptions about the error term in regression.

The following data have been collected for a simple linear regression analysis relating sales (y) to price (x) : In applying the least squares criterion, the slope (b) and the intercept (a) for the best-fitting line are b = -12 and a = 162.Compute the value of r2 here.

When the slope of a simple linear regression equation is a negative value, the correlation coefficient can be either positive or negative.

In a simple linear regression, the least squares line turns out to be y = 120 + 4x.The sum of the residuals (errors) around this line will be 0.

The regression printout below shows the results of a regression analysis intended to link variable x to variable y.A sample of 15 data points was used. Can you use the sample results shown here to reject a β = 0 null hypothesis at the 5% significance level? Explain.

The following data have been collected for a simple linear regression analysis relating sales (y) to price (x) : In applying the least squares criterion, the slope (b) and the intercept (a) for the best-fitting line are b = -12 and a = 162.Compute the value of r² here.