- In a regression analysis involving observations, the following estimated regression equation was obtained. Enter negative values as negative numbers.
a. Interpret , , , and in this estimated regression equation. Assume that for each coefficient statement, the remaining three variables are held constant (to 1 decimal).
3.8 estimated change in per unit change in
-2.3 estimated change in per unit change in
7.6 estimated change in per unit change in
2.7. estimated change in per unit change in
b. Predict when , , , and . (to 1 decimal)
57.1
2. 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. Choose the correct scatter plot of selling price versus number of bathrooms.
graph c
graph A
graph B
Comment on the relationship between selling price and these three variables.
Square feet and number of bedrooms
number of bathrooms
b. Develop an estimated regression equation that can be used to predict the selling price given the three independent variables (number of baths, square footage, and number of bedrooms) (to decimals). Enter negative value as negative number.
-5531.01 -1386.21 60.28 54797.08
c. It is argued that we do not need both number of baths and number of bedrooms. Develop an estimated regression equation that can be used to predict selling price given square footage and the number of bedrooms (to decimals). Enter negative value as negative number.
-5882.76 59.73 54309.21
d. Suppose your house has four bedrooms and is square feet. What is the predicted selling price using the model developed in part (c). Use the regression coefficients rounded to decimals in your calculations. Round your answer to the nearest dollar.
369638.60
3. Consider the following estimated regression equation, based on observations.
The values of SST and SSR are and , respectively.
a. Find SSE (to 2 decimals).
507.75
b. Compute (to 3 decimals).
0.924
c. Compute (to 3 decimals).
0.902
d. Comment on the goodness of fit.
provided an excellent fit
4. 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
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 does provide a reasonable fit because the adjusted is 0.49 (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:
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 0.51 (to decimals) that is higher than the adjusted of the model in part a.
5. The following estimated regression equation is based on observations.
The values of SST and SSR are and , respectively.
a. Compute (to 3 decimals).
0.976
b. Compute (to 3 decimals).
0.972
c. Comment on the goodness of fit.
The estimated regression equation provided an excellent fit
6. The following estimated regression equation was developed for a model involving two independent variables.
After was dropped from the model, the least squares method was used to obtain an estimated regression equation involving only as an independent variable.
a. Give an interpretation of the coefficient of in both models.
Y
x1
x2
In the single independent variable case, the coefficient represents the expected change in
y
x1
Yes, because a change in x1 would be accompanied by a change in x2
7. 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.
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.
20385.250 -0.0375 -686.337
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 0.664
ii
c. Use the test to determine the overall significance of the relationship (to decimals). What is your conclusion at the level of significance? Use
290.85 less than 0.01 Significant
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.
-6.981 less than 0.01 Significant
-12.512 less than 0.01 Significant
8. Consider the following estimated regression equation based on observations.
a. Develop a point estimate of the mean value of when and (to 3 decimals)
289.815
b. Predict an individual value of when and (to 3 decimals).
289.815
9. 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.
16144
b. Develop a confidence interval for the selling price of a car with the data in part (a).
15829 16460
c. Develop a prediction interval for the selling price of a car with the data in part (a).
14727 17561
10. Consider a regression study involving a dependent variable , a quantitative independent variable , and a categorical independent variable with three possible levels (level 1, level 2, and level 3).
a. How many dummy variables are required to represent the categorical variable?
2
b. Write a multiple regression equation relating and the categorical variable to .
Option 5
Enter the values of dummy variables and that are used to indicate the three levels of the categorical variable.
0 0
1 0
0 1
c. Interpret the parameters in your regression equation.
E(y|level2) – E(y|level1)
E(y|level3) – E(y|level1)
is the change in for a unit change in x1 holding the categorical variable constant.
11. 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
| Repair Time | Months Since | ||||
| in Hours | Last Service | Type of Repair | Repairperson | ||
| 2.9 | 2 | Electrical | Dave Newton | ||
| 3.0 | 6 | Mechanical | Dave Newton | ||
| 4.8 | 8 | Electrical | Bob Jones | ||
| 1.8 | 3 | Mechanical | Dave Newton | ||
| 2.9 | 2 | Electrical | Dave Newton | ||
| 4.9 | 7 | Electrical | Bob Jones | ||
| 4.2 | 9 | Mechanical | Bob Jones | ||
| 4.8 | 8 | Mechanical | Bob Jones | ||
| 4.4 | 4 | Electrical | Bob Jones | ||
| 4.5 | 6 | Electrical | Dave Newton | ||
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).
3.45 0.62
b. Does the equation that you developed in part (a) provide a good fit for the observed data? Explain. (to 4 decimals)
No 0.4077
not significant
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.
4.62 -1.60
d. Does the equation that you developed in part (c) provide a good fit for the observed data? Explain.
Repairperson Is a better predictor of repair time than the type of repair
12. a. Develop the estimated regression equation for these data (to 1 decimal).
0.2 2.6
b. Select the correct plot for the residuals against .
A
Does the residual plot support the assumptions about ε? Explain.
IS
c. Select the correct plot for the standardized residuals against .
C
Do any outliers appear in these data? Explain.
NO
Because None of the standard residuals is less than or greater than , we would conclude that there are no outliers in the data set.
13. The following data describes weekly gross revenue (), television advertising expenditures (), and newspaper advertising expenditures () for Showtime Movie Theaters.
a. Find an estimated regression equation relating weekly gross revenue to television advertising expenditures and newspaper advertising expenditures (to decimals).
81.73 2.85 1.29
graph B
Does the residual plot support the assumptions about ε? Explain.
No
With the relatively few observations, it Is difficult to determine if the model assumptions are violated.
c. Check for any outliers in these data. What are your conclusion?
Because none of the standard residuals are less than or greater than none of the observations can be classified as an outlier.
14. 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.
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 a decrease job satisfaction score by 8.69 units. If the length of service does not change, a dollar increase in wage results in an increase in job satisfaction score by 13.5 units.
b. Predict the job satisfaction test score for an employee who has four years of service and makes per hour.
67.39
15. 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. 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.
0.9681
0.9373
0.9194
0.1298
10
2 0.8810 52.4405 0.0001
7 0.1179 0.0168
-2.8987 0.0230
2.7078 0.0303
4.5125 0.0028
b. Using , test for overall significance.
there exists significant relationship
c. Did the estimated regression equation provide a good fit to the data? Explain.
Yes because the value is Greater
d. Use the test and to test and . Use t table.
between 0.025 and 0.05 , so reject
less than 0.01 , so reject
16. Consider the following data for two variables, and .
Excel File: data16-03.xls
| 2 | 3 | 4 | 5 | 7 | 7 | 7 | 8 | 9 | |
| 4 | 5 | 4 | 6 | 4 | 6 | 9 | 5 | 11 |
a. Choose the correct scatter diagram with and .
The correct scatter diagram is A
Does there appear to be a linear relationship between and ? Explain.
The scatter diagram shows some evidence of a possible linear relationship.
b. Develop the estimated regression equation relating and . Save “predicted” and “residuals” (to decimals).
[2.3220 , 0.6366]
c. Choose the correct scatter diagram of the standardized residuals versus for the estimated regression equation developed in part (b).
The correct scatter diagram is [B]
Do the model assumptions appear to be satisfied? Explain.
The standardized residual plot indicates that the constant variance assumption is not satisfied.
d. Perform a logarithmic transformation ( under Data/Transform Data/Log10) on the dependent variable . Develop an estimated regression equation using the transformed dependent variable (to decimals).
0.5134 0.0411
17. A highway department is studying the relationship between traffic flow and speed. The following model has been hypothesized.
where
traffic flow in vehicles per hour
vehicle speed in miles per hour
The following data were collected during rush hour for six highways leading out of the city.
| Traffic Flow () | Vehicle Speed () | |
| 1256 | 36 | |
| 1330 | 40 | |
| 1226 | 30 | |
| 1336 | 50 | |
| 1349 | 55 | |
| 1125 | 25 |
a. Use the data to compute the coefficients of this estimated regression equation (to decimals). Enter negative value as negative number. (Create the variable first using Data/Transform Data/Square.)
501.9340
33.4914
-0.3311
b. Using , test for a significant relationship.
38.6235
(to decimals)
-value 0.0072 (to decimals)
The relationship is significant.
c. Estimate the traffic flow in vehicles per hour at a speed of miles per hour (to decimals). 1296.43 vehicles per hour
18. Home Depot, a nationwide home improvement retailer, sells several brands of washing machines. A sample of models of full-size washing machines sold by Home Depot and corresponding capacity (in cubic feet) and list price (in ) follow (Home Depot website).
Click on the datafile logo to reference the data.
a. Which of the following scatter diagrams represents the data, treating cubic feet as the independent variable?
Scatter diagram A
Does a simple linear regression model appear to be appropriate?
No
b. Use a simple regression model to develop an estimated regression equation to predict the list price given the cubic feet (to decimals). Enter negative value as negative number.
-513.573 308.3562
Choose a standardized residual plot.
A
Based upon the standardized residual plot, does a simple linear regression model appear to be appropriate?
No
c. Using a second-order model, develop an estimated regression equation to predict the list price given the cubic feet (to decimals). Enter negative value as negative number.
14218.55281 -5847.69976 638.2929
d. Do you prefer the estimated regression equation developed in part (b) or part (c)?
Part (c), because its R-squared is higher than the equation in part (b).
e. Are there other factors that should be considered for inclusion as independent variables in this regression?
All of the variants
19. As of September , , the film Suicide Squad had an average rating of out of based on viewer ratings (Rotten Tomatoes website). How are the viewer ratings of Suicide Squad related to the viewer age and the viewer ratings of The Secret Life of Pets? The file RottenTomatoes contains a sample of data containing viewer ages and their ratings of Suicide Squad and The Secret Life of Pets. Click on the datafile logo to reference the data.
1
Does a simple linear regression model appear to be appropriate?
No
b. Use the data provided to develop the regression equation for estimating the viewer ratings of Suicide Squad that is suggested by the scatter diagram in part (a) (to decimals).
7.3352 0.1637 0.0010
c. Include the viewer rating of The Secret Life of Pets as an independent variable in the regression model developed in part (b). Interpret the regression coefficient for the viewer rating of The Secret Life of Pets (to decimals). Enter negative values as negative numbers.
7.1856 -0.1264 0.0007 -0.1833
Holding the viewer’s age constant, a one point increase in the viewer’s rating of The Secret Life of Pets coincides with an estimated decrease of 0.1833
d. Is the regression equation developed in part (b) or the regression equation developed in part (c) superior? Use the equation that explains more variation.
Part b
e. Suppose a -year-old viewer gave The Secret Life of Pets a rating of . Use the model you selected in part (d) to predict that viewer’s rating of Suicide Squad (to decimals).
3.213
20. The Ladies Professional Golfers Association of America (LPGA) maintains statistics on performance and earnings for members of the LPGA Tour. Year-end performance statistics for golfers for appear in the file LPGA2014Stats (LPGA website). Earnings () is the total earnings in thousands of dollars; Scoring Avg. is the average score for all events; Greens in Reg. is the percentage of time a player is able to hit the greens in regulation; Putting Avg. is the average number of putts taken on greens hit in regulation; and Drive Accuracy is the percentage of times a tee shot comes to rest in the fairway. A green is considered hit in regulation if any part of the ball is touching the putting surface and the difference between the value of par for the hole and the number of strokes taken to hit the green is at least . Click on the datafile logo to reference the data.
a. Develop an estimated regression equation that can be used to predict the total earnings for all events given the average number of putts taken on greens hit in regulation.
1508009.831 -46708.61081
b. Develop an estimated regression equation that can be used to predict the total earnings for all events given the average number of putts taken on greens hit in regulation, the percentage of time a player is able to hit the greens in regulation, and the percentage of times a player’s tee shot comes to rest in the fairway.
961320.2337 -64259.42581 1748380.513 -179312.7192
c. At the level of significance, test whether the two independent variables added in part (b), the percentage of time a player is able to hit the greens in regulation and the percentage of times a player’s tee shot comes to rest in the fairway, contribute significantly to the estimated regression equation developed in part (a). Use Table 4 in Appendix B. 59.60 (to decimals)
The -value associated with is Less than 0.1 What is your conclusion?
The addition of the two independent variables Is statistically significant.
d. In general, lower scores should lead to higher earnings. To investigate this option for predicting total earnings, develop an estimated regression equation that can be used to predict total earnings for all events given the average score for all events.
4998308.184 -67764.73307
Would you prefer to use this equation to predict total earnings, or would you prefer to use the estimated regression equation developed in part (b)? Explain.
I. Although the equation developed in part (b) provides a better fit, the equation developed in part (d) is a simpler model. Therefore, we cannot determine which equation is better.
II. Because the equation developed in part (b) provides a better fit, it is preferred over the equation developed in part (d).
III. Because the equation developed in part (d) provides a better fit and is a simpler model, it is preferred over the equation developed in part (b).
21. The average monthly residential gas bill for Black Hills Energy customers in Cheyenne, Wyoming is (Wyoming Public Service Commission website). How is the average monthly gas bill for a Cheyenne residence related to the square footage, number of rooms, and age of the residence? The following data show the average monthly gas bill for last year, square footage, number of rooms, and age for typical Cheyenne residences
a. Develop an estimated regression equation that can be used to predict a residence’s average monthly gas bill for last year given its age. Round your answers to four decimals.
60.9908 0.1243
b. Develop an estimated regression equation that can be used to predict a residence’s average monthly gas bill for last year given its age, square footage, and number of rooms. Round your answers to four decimals. Enter negative value as negative number.
-5.3932 0.1053 0.0067 8.5267
c. At the level of significance, test whether the two independent variables added in part (b), the square footage and the number of rooms, contribute significantly to the estimated regression equation developed in part (a). If not stated otherwise, round your answers to four decimals. Use Table 4 from Appendix B.
8996.3689
1231.2755
76.9547
33.74 (to decimals)
The p-value associated with F is less than 0.01 Therefore, the addition of the two independent variables is statistically significant.
22. Consider a completely randomized design involving four treatments: , , , and . Select a correct multiple regression equation that can be used to analyze these data. Define all variables.
iii
23. Select a correct multiple regression equation that can be used to analyze the data for a two-factorial design with two levels for factor and three levels for factor . Define all variables.
iii
24. Four different paints are advertised as having the same drying time. To check the manufacturers’ claims, five samples were tested for each of the paints. The time in minutes until the paint was dry enough for a second coat to be applied was recorded for each sample. The data obtained follow.
| Paint 1 | Paint 2 | Paint 3 | Paint 4 |
| 128 | 144 | 133 | 150 |
| 137 | 133 | 143 | 142 |
| 135 | 142 | 137 | 135 |
| 124 | 146 | 136 | 140 |
| 141 | 130 | 131 | 153 |
a. Use to test for any significant differences in mean drying time among the paints. If your answer is zero, enter “0”.
Lets define the dummy variables as follows:
| Multiple R (to decimals) | 0.5682 |
| R Square (to decimals) | 0.3229 |
| Adjusted R Square (to decimals) | 0.1959 |
| Standard Error (to decimals) | 6.5765 |
| Observations (to whole number) | 20 |
3 330 110.00 2.5434 0.0928
16 692 43.25
19 1022
| Intercept | 133 | 2.9411 | 2.9411 | 0 | |
| D1 | 6 | 4.1593 | 1.4425 | 0.1684 | |
| D2 | 3 | 4.1593 | 0.7213 | 0.4812 | |
| D3 | 11 | 4.1593 | 4.1593 | 0.0177 |
At the level of significance, do not reject
b. What is your estimate of mean drying time for paint (to whole number)?
139
25. Mbuy is a media consulting firm that provides advice to companies on how to allocate their advertising budgets. Mbuy designed a factorial experiment to test the effect of the size of a banner ad on a website and the ad design on the number (in thousands) of product inquiries received. Three advertising designs and two sizes of advertisements were considered. The following data were obtained. Test for any significant effects due to type of design, size of advertisement, or interaction. Use . If your answer is zero enter “”. Excel File: data16-23.xls
| 8 (A, Small) | 0 | 0 | 0 | 0 | 0 |
| 12 (A, Small) | 0 | 0 | 0 | 0 | 0 |
| 12 (A, Large) | 1 | 0 | 0 | 0 | 0 |
| 8 (A, Large) | 1 | 0 | 0 | 0 | 0 |
| 22 (B, Small) | 0 | 1 | 0 | 0 | 0 |
| 14 (B, Small) | 0 | 1 | 0 | 0 | 0 |
| 26 (B, Large) | 1 | 1 | 0 | 1 | 0 |
| 30 (B, Large) | 1 | 1 | 0 | 1 | 0 |
| 10 (C, Small) | 0 | 0 | 1 | 0 | 0 |
| 18 (C, Small) | 0 | 0 | 1 | 0 | 0 |
| 18 (C, Large) | 1 | 0 | 1 | 0 | 1 |
| 14 (C, Large) | 1 | 0 | 1 | 0 | 1 |
0.9075
0.8235
0.6765
4
12
5 448 89.6 5.6 0.0292
6 96 16
11 544
10 2.8284 3.5355 0.0123
0 4.0000 0.0000 1.0000
8 4.0000 2.0000 0.0924
4 4.0000 1.0000 0.3559
10 5.6569 1.7678 0.1275
2 5.6569 0.3536 0.7358
The analysis shows that type of design has a significant effect.
26. Refer to the following Cravens data set. Click on the datafile logo to reference the data.
| The Cravens Data | |||||||||||||||
| Sales | Time | Poten | AdvExp | Share | Change | Accounts | Work | Rating | |||||||
| 3,669.88 | 43.1 | 74,065.1 | 4,582.9 | 2.51 | 0.34 | 74.86 | 15.05 | 4.9 | |||||||
| 3,473.95 | 108.13 | 58,117.3 | 5,539.8 | 5.51 | 0.15 | 107.32 | 19.97 | 5.1 | |||||||
| 2,295.1 | 13.82 | 21,118.5 | 2,950.4 | 10.91 | -0.72 | 96.75 | 17.34 | 2.9 | |||||||
| 4,675.56 | 186.18 | 68,521.3 | 2,243.1 | 8.27 | 0.17 | 195.12 | 13.4 | 3.4 | |||||||
| 6,125.96 | 161.79 | 57,805.1 | 7,747.1 | 9.15 | 0.5 | 180.44 | 17.64 | 4.6 | |||||||
| 2,134.94 | 8.94 | 37,806.9 | 402.4 | 5.51 | 0.15 | 104.88 | 16.22 | 4.5 | |||||||
| 5,031.66 | 365.04 | 50,935.3 | 3,140.6 | 8.54 | 0.55 | 256.1 | 18.8 | 4.6 | |||||||
| 3,367.45 | 220.32 | 35,602.1 | 2,086.2 | 7.07 | -0.49 | 126.83 | 19.86 | 2.3 | |||||||
| 6,519.45 | 127.64 | 46,176.8 | 8,846.2 | 12.54 | 1.24 | 203.25 | 17.42 | 4.9 | |||||||
| 4,876.37 | 105.69 | 42,053.2 | 5,673.1 | 8.85 | 0.31 | 119.51 | 21.41 | 2.8 | |||||||
| 2,468.27 | 57.72 | 36,829.7 | 2,761.8 | 5.38 | 0.37 | 116.26 | 16.32 | 3.1 | |||||||
| 2,533.31 | 23.58 | 33,612.7 | 1,991.8 | 5.43 | -0.65 | 142.28 | 14.51 | 4.2 | |||||||
| 2,408.11 | 13.82 | 21,412.8 | 1,971.5 | 8.48 | 0.64 | 89.43 | 19.35 | 4.3 | |||||||
| 2,337.38 | 13.82 | 20,416.9 | 1,737.4 | 7.8 | 1.01 | 84.55 | 20.02 | 4.2 | |||||||
| 4,586.95 | 86.99 | 36,272 | 10,694.2 | 10.34 | 0.11 | 119.51 | 15.26 | 5.5 | |||||||
| 2,729.24 | 165.85 | 23,093.3 | 8,618.6 | 5.15 | 0.04 | 80.49 | 15.87 | 3.6 | |||||||
| 3,289.4 | 116.26 | 26,878.6 | 7,747.9 | 6.64 | 0.68 | 136.58 | 7.81 | 3.4 | |||||||
| 2,800.78 | 42.28 | 39,572 | 4,565.8 | 5.45 | 0.66 | 78.86 | 16 | 4.2 | |||||||
| 3,264.2 | 52.84 | 51,866.1 | 6,022.7 | 6.31 | -0.1 | 136.58 | 17.44 | 3.6 | |||||||
| 3,453.62 | 165.04 | 58,749.8 | 3,721.1 | 6.35 | -0.03 | 138.21 | 17.98 | 3.1 | |||||||
| 1,741.45 | 10.57 | 23,990.8 | 861 | 7.37 | -1.63 | 75.61 | 20.99 | 1.6 | |||||||
| 2,035.75 | 13.82 | 25,694.9 | 3,571.5 | 8.39 | -0.43 | 102.44 | 21.66 | 3.4 | |||||||
| 1,578 | 8.13 | 23,736.3 | 2,845.5 | 5.15 | 0.04 | 76.42 | 21.46 | 2.7 | |||||||
| 4,167.44 | 58.44 | 34,314.3 | 5,060.1 | 12.88 | 0.22 | 136.58 | 24.78 | 2.8 | |||||||
| 2,799.97 | 21.14 | 22,809.5 | 3,552 | 9.14 | -0.74 | 88.62 | 24.96 | 3.9 | |||||||
The estimated regression equation involving Accounts, AdvExp, Poten, and Share had an adjusted coefficient of determination of . Use the level of significance and apply the Durbin-Watson test to determine whether positive autocorrelation is present. Use Table 16.10.
the test is inconclusive
27. Consumer Reports tested different brands and models of road, fitness, and comfort bikes. Road bikes are designed for long road trips; fitness bikes are designed for regular workouts or daily commutes; and comfort bikes are designed for leisure rides on typically flat roads. The following data show the type, weight (), and price () for the bicycles tested. Click on the datafile logo to reference the data
a. Select an appropriate scatter diagram with weight as the independent variable and price as the dependent variable.
4
Does a simple linear regression model appear to be appropriate?
A simple linear regression model does not appear to be appropriate.
Round your answers to four decimal places.
b. Develop an estimated multiple regression equation with and as the two independent variables.
11375.99884 728.3345472 11.97373749
c. Use the following dummy variables to develop an estimated regression equation that can be used to predict the price given the type of bike: if the bike is a fitness bike, otherwise; and if the bike is a comfort bike; otherwise. Compare the results obtained to the results obtained in part (b).
1283.75 571.75 907.0833333
Type of bike appears to be a(n) significant factor in predicting price. But, the estimated regression equation developed in part (b) appears to provide a slightly better fit.
d. To account for possible interaction between the type of bike and the weight of the bike, develop a new estimated regression equation that can be used to predict the price of the bike given the type, the weight of the bike, and any interaction between weight and each of the dummy variables defined in part (c). What estimated regression equation appears to be the best predictor of price? Please round to four decimal places.
5923.544304 214.556962 6343.250186 7232.062822 261.3216679 266.4088139
28. A study investigated the relationship between audit delay and variables that describe the client and the auditor. The file Audit contains data from a sample of companies on the following set of variables:DelayThe length of time from a company’s fiscal year-end to the date of the auditor’s report.IndustryA dummy variable coded if the firm was an industrial company or if the firm was a bank, savings and loan, or insurance company.PublicA dummy variable coded if the company was traded on an organized exchange or over the counter; otherwise coded .QualityA measure of overall quality of internal controls, as judged by the auditor, on a five-point scale ranging from “virtually none” () to “excellent” ().FinishedA measure ranging from to , as judged by the auditor, where indicates “all work performed subsequent to year-end” and indicates “most work performed prior to year-end.”Click on the datafile logo to reference the data.Error! Filename not specified.Consider a model in which only Industry is used to predict Delay. At a level of significance, test for any positive autocorrelation in the data. Use Table 16.10.
No significant positive autocorrelation
29. A study was conducted to investigate browsing activity by shoppers. Shoppers were classified as nonbrowsers, light browsers, and heavy browsers. For each shopper in the study a measure was obtained to determine how comfortable the shopper was in the store. Higher scores indicated greater comfort . Assume that the following data are from this study.
| Nonbrowser | Light Browser | Heavy Browser |
| 4 | 5 | 5 |
| 5 | 6 | 7 |
| 6 | 5 | 5 |
| 3 | 4 | 7 |
| 3 | 7 | 4 |
| 4 | 4 | 6 |
| 5 | 6 | 5 |
| 4 | 5 | 7 |
Use a level of significance to test for differences in comfort levels among the three types of browsers.
there are significant difference between comfort levels for the three types of browsers
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