Question 1
The estimated regression equation for a model involving two independent variables and observations follows.
a. Interpret and in this estimated regression equation (to 4 decimals).
b. Estimate when and (to 3 decimals).
ANSWER
Question 2
The following estimated regression equation is based on observations.
The values of SST and SSR are and , respectively.
a. Compute (to 3 decimals).
b. Compute (to 3 decimals).
c. Comment on the goodness of fit.
The estimated regression equation
.ANSWER
Question 3
Spring is a peak time for selling houses. The file SpringHouses contains the selling price, number of bathrooms, square footage, and number of bedrooms of homes sold in Ft. Thomas, Kentucky, in spring (realtor.com website)
Click on the datafile logo to reference the data.
a. The Excel output for the estimated regression equation that can be used to predict the selling price given the number of bathrooms, square footage, and number of bedrooms in the house:
SUMMARY OUTPUT
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Regression statistics |
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Multiple R |
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R Square |
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Adjusted R Square |
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Standard Error |
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Observations |
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ANOVA
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df |
SS |
MS |
F |
Significance F |
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Regression |
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Residual |
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Total |
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Coefficients |
Standard Error |
t Stat |
P-value |
Lower 95% |
Upper 95% |
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Intercept |
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Baths |
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Sq Ft |
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Beds |
Does the estimated regression equation provide a good fit to the data? Explain. Hint: If is greater than , the estimated regression equation provides a good fit.
The estimated regression equation
provide a reasonable fit because the adjusted is (to decimals).
b. The Excel output for the estimated regression equation that can be used to predict selling price given square footage and the number of bedrooms:
SUMMARY OUTPUT
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Regression statistics |
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Multiple R |
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R Square |
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Adjusted R Square |
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Standard Error |
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Observations |
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ANOVA
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df |
SS |
MS |
F |
Significance F |
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Regression |
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Residual |
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Total |
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Coefficients |
Standard Error |
t Stat |
P-value |
Lower 95% |
Upper 95% |
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Intercept |
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Sq Ft |
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Beds |
Compare the fit for this simpler model to that of the model that also includes number of bathrooms as an independent variable.
The adjusted for the simpler model is (to decimals) that is
than the adjusted of the model in part a.
ANSWER
Question 4
The Honda Accord was named the best midsized car for resale value for by the Kelley Blue Book (Kelley Blue Book website). The file AutoResale contains mileage, age, and selling price for a sample of Honda Accords.
Click on the datafile logo to reference the data.
a. Develop an estimated regression equation that predicts the selling price of a used Honda Accord given the mileage and age of the car (to decimals). Enter negative value as negative number.
b. Is multicollinearity an issue for this model? Find the correlation between the independent variables to answer this question (to decimals).
The correlation between age and mileage is .
- Since the correlation between the independent variables is less than , we conclude that multicollinearity is an issue.
- Since the correlation between the independent variables is less than , we conclude that multicollinearity is not an issue.
- Since the correlation between the independent variables is greater than , we conclude that multicollinearity is an issue.
- Since the correlation between the independent variables is greater than , we conclude that multicollinearity is not an issue.
c. Use the test to determine the overall significance of the relationship (to decimals). What is your conclusion at the level of significance? Use F table.
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Significance |
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value |
-value |
at |
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Overall Model |
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d. Use the test to determine the significance of each independent variable (to decimals). What is your conclusion at the level of significance? Use t table. Enter negative value as negative number.
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Significance |
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value |
-value |
at |
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Mileage |
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Age |
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ANSWER
Question 5
The Honda Accord was named the best midsized car for resale value for by the Kelley Blue Book (Kelley Blue Book website). The file AutoResale contains mileage, age, and selling price for a sample of Honda Accords.
Click on the datafile logo to reference the data.
The estimated regression equation is
Round your answers to the nearest dollar.
a. Estimate the selling price of a four-year-old Honda Accord with mileage of miles.
$
b. Develop a confidence interval for the selling price of a car with the data in part (a).
( , )
c. Develop a prediction interval for the selling price of a car with the data in part (a).
( , )
ANSWER
Question 6
Johnson Filtration, Inc. provides maintenance service for water-filtration systems. Suppose that in addition to information on the number of months since the machine was serviced and whether a mechanical or an electrical repair was necessary, the managers obtained a list showing which repairperson performed the service. The revised data follow.
Click on the datafile logo to reference the data.
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Repair Time |
Months Since |
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in Hours |
Last Service |
Type of Repair |
Repairperson |
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2.9 |
2 |
Electrical |
Dave Newton |
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3.0 |
6 |
Mechanical |
Dave Newton |
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4.8 |
8 |
Electrical |
Bob Jones |
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1.8 |
3 |
Mechanical |
Dave Newton |
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2.9 |
2 |
Electrical |
Dave Newton |
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4.9 |
7 |
Electrical |
Bob Jones |
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4.2 |
9 |
Mechanical |
Bob Jones |
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4.8 |
8 |
Mechanical |
Bob Jones |
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4.4 |
4 |
Electrical |
Bob Jones |
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4.5 |
6 |
Electrical |
Dave Newton |
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a. Ignore for now the months since the last maintenance service ( ) and the repairperson who performed the service. Develop the estimated simple linear regression equation to predict the repair time ( ) given the type of repair ( ). Recall that if the type of repair is mechanical and if the type of repair is electrical (to 2 decimals).
Time = + Type
b. Does the equation that you developed in part (a) provide a good fit for the observed data? Explain. (to 4 decimals)
, because the -value of shows that the relationship is
for any reasonable value of α.
c. Ignore for now the months since the last maintenance service and the type of repair associated with the machine. Develop the estimated simple linear regression equation to predict the repair time given the repairperson who performed the service. Let if Bob Jones performed the service and if Dave Newton performed the service (to 2 decimals). Enter negative value as negative number.
Time = + Person
d. Does the equation that you developed in part (c) provide a
good fit for the observed data? Explain.
ANSWER
Question 7
Johnson Filtration, Inc., provides maintenance service for water-filtration systems throughout southern Florida. Suppose that in addition to information on the number of months since the machine was serviced and whether a mechanical or an electrical repair was necessary, the managers obtained a list showing which repairperson performed the service. The revised data follow.
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Repair Time |
Months Since |
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in Hours |
Last Service |
Type of Repair |
Repairperson |
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2.8 |
2 |
Electrical |
Dave Newton |
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3.0 |
6 |
Mechanical |
Dave Newton |
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4.8 |
8 |
Electrical |
Bob Jones |
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1.8 |
3 |
Mechanical |
Dave Newton |
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3.0 |
2 |
Electrical |
Dave Newton |
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4.9 |
7 |
Electrical |
Bob Jones |
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4.3 |
9 |
Mechanical |
Bob Jones |
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4.9 |
8 |
Mechanical |
Bob Jones |
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4.5 |
4 |
Electrical |
Bob Jones |
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4.5 |
6 |
Electrical |
Dave Newton |
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a. Develop the estimated regression equation to predict the repair time given the number of months since the last maintenance service, the type of repair, and the repairperson who performed the service. Assume that if the type of repair is electrical and if Dave Newton performed the service. Enter negative value as negative number.
Round your answers to three decimal places.
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b. At the level of significance, test whether the estimated regression equation developed in part (a) represents a significant relationship between the independent variables and the dependent variable.
Compute test statistic (to 2 decimals).
Use Table 4 from Appendix B to determine the -value.
The -value is
What is your conclusion?
c. Is the addition of the independent variable , the repairperson who performed the service, statistically significant? Use .
Compute the test statistic for the significance of (to 2 decimals). Enter negative value as negative number.
Use Table 2 from Appendix B to determine the -value.
The -value is
What is your conclusion?
The addition of Person
statistically significant.
What explanation can you give for the results observed?
Person is highly correlated with
, so once the effect of that is accounted for the addition of person will not add much.
ANSWER
Question 8
The following data describes weekly gross revenue ( ), television advertising expenditures ( ), and newspaper advertising expenditures ( ) for Showtime Movie Theaters.
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Weekly Gross |
Television |
Newspaper |
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Revenue |
Advertising |
Advertising |
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( ) |
( ) |
( ) |
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99 |
5.0 |
1.5 |
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90 |
2.0 |
2.0 |
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95 |
4.0 |
1.5 |
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92 |
2.5 |
2.5 |
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95 |
3.0 |
3.3 |
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94 |
3.5 |
2.3 |
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94 |
2.5 |
4.2 |
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94 |
3.0 |
2.5 |
a. Find an estimated regression equation relating weekly gross revenue to television advertising expenditures and newspaper advertising expenditures (to decimals).
+ +
b. Choose the correct plot of the standardized residuals against .
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A. |
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B. |
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C. |
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D. |
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Does the residual plot support the assumptions about ε? Explain.
With the relatively few observations, it
difficult to determine if the model assumptions are violated.
c. Check for any outliers in these data. What are your conclusion?
Because
of the standard residuals are less than or greater than , of the observations be classified as an outlier.
ANSWER
Question 9
The personnel director for Electronics Associates developed the following estimated regression equation relating an employee's score on a job satisfaction test to his or her length of service and wage rate.
where
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length of service (years) |
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wage rate (dollars) |
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job satisfaction test score (higher scores |
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indicate greater job satisfaction) |
Round your answers to 2 decimal places.
a. Interpret the coefficients in this estimated regression equation.
If the wage rate does not change, a one year increase in length of service is associated with
in job satisfaction score by units. If the length of service does not change, a dollar increase in wage results in
in job satisfaction score by units.
b. Predict the job satisfaction test score for an employee who has four years of service and makes per hour.
ANSWER
Question 10
The admissions officer for Clearwater College developed the following estimated regression equation relating the final college GPA to the student's SAT mathematics score and high-school GPA.
where
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high-school grade point average |
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SAT mathemathics score |
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final college grade point average |
Round test statistic values to 2 decimal places and all other values to 4 decimal places. Do not round your intermediate calculations.
a. Complete the missing entries in this Excel Regression tool output. Enter negative values as negative numbers.
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SUMMARY OUTPUT |
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Regression Statistics |
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Multiple R |
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R Square |
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Adjusted R Square |
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Standard Error |
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Observations |
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ANOVA |
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df |
SS |
MS |
F |
Significance F |
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Regression |
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Residual |
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Total |
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Coefficients |
Standard Error |
t Stat |
P-value |
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Intercept |
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X1 |
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X2 |
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b. Using , test for overall significance.
c. Did the estimated regression equation provide a good fit to the
data? Explain.
, because the value is
than .
d. Use the test and to test and . Use t table.
For , the -value is
, so
.
For , the -value is
, so .
ANSWER
Correct Significance F is 0.0001
Please see below.
