BA6933 Week(15 & 16)

 

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).    estimated change in  per  unit change in     estimated change in  per  unit change in     estimated change in  per  unit change in     estimated change in  per  unit change in  b. Predict  when , , , and . (to 1 decimal)

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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. A. B. C. The correct graph is  graph C -Select- graph A graph B graph C Item 1  . Choose the correct scatter plot of selling price versus square footage. A. B. C. The correct graph is  graph A -Select- graph A graph B graph C Item 2  . Choose the correct scatter plot of selling price versus number of bedrooms. A. B. C. The correct graph is  graph B -Select- graph A graph B graph C Item 3  . Comment on the relationship between selling price and these three variables. Square feet and number of bedrooms -Select- Square feet and number of bathrooms Square feet and number of bedrooms Number of bathrooms and number of bedrooms Item 4   show strong increasing relationships with selling price. The relationship between  number of bathrooms -Select- number of bathrooms number of bedrooms square feet Item 5   and selling price seems not as strong as the other two variables. 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.              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.           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. $

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Consider the following estimated regression equation, based on  observations. The values of SST and SSR are  and , respectively. a. Find SSE (to 2 decimals).   b. Compute  (to 3 decimals).   c. Compute  (to 3 decimals).   d. Comment on the goodness of fit. The estimated regression equation  provided an excellent fit - Select your answer - provided an excellent fit provided a moderately good fit did not provide a good fit Item 4  .

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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 Regression statistics Multiple R R Square Adjusted R Square Standard Error Observations ANOVA df SS MS F Significance F Regression Residual Total   Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept Baths Sq Ft 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  does - Select your answer - does does not Item 1   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 Regression statistics Multiple R R Square Adjusted R Square Standard Error Observations ANOVA df SS MS F Significance F Regression Residual Total   Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept Sq Ft 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  higher - Select your answer - lower higher Item 4   than the adjusted  of the model in part a.

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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  provided an excellent fit - Select your answer - provided an excellent fit provided a moderately good fit did not provide a good fit Item 3  . Hide Feedback Correct     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. In the two independent variable case, the coefficient  represents the expected change in  y - Select your answer -            x1            x2 y Item 1   corresponding to a one unit increase in  x1 - Select your answer -            x1            x2 y Item 2   when  x2 - Select your answer -            x1            x2 y Item 3   is held constant. In the single independent variable case, the coefficient  represents the expected change in  y - Select your answer -            x1            x2 y Item 4   corresponding to a one unit increase in  x1 - Select your answer -            x1            x2 y Item 5  . b. Could multicollinearity explain why the coefficient of  differs in the two models? If so, how? Assume that  and  are correlated. Yes, because a change in x1 would be accompanied by a change in x2 - Select your answer - Yes, because a change in x1 would be accompanied by a change in x2 Yes, because a change in x1 would not be accompanied by a change in x2 Item 6

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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  .        I.      Since the correlation between the independent variables is less than , we conclude that multicollinearity is an issue.      II.      Since the correlation between the independent variables is less than , we conclude that multicollinearity is not an issue.     III.      Since the correlation between the independent variables is greater than , we conclude that multicollinearity is an issue.     IV.      Since the correlation between the independent variables is greater than , we conclude that multicollinearity is not an issue. II - Select your answer - I II III IV Item 5   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. Significance  value -value at  Overall Model   less than 0.01 - Select your answer - less than 0.01 between 0.01 and 0.025 between 0.025 and 0.05 between 0.05 and 0.10 greater than 0.10 Item 7   significant - Select your answer - significant not significant Item 8   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. Significance  value -value at  Mileage   less than 0.01 - Select your answer - less than 0.01 between 0.01 and 0.025 between 0.025 and 0.05 between 0.05 and 0.10 greater than 0.10 Item 10   significant - Select your answer - significant not significant Item 11   Age   less than 0.01 - Select your answer - less than 0.01 between 0.01 and 0.025 between 0.025 and 0.05 between 0.05 and 0.10 greater than 0.10 Item 13   significant - Select your answer - significant not significant Item 14

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Consider the following estimated regression equation based on  observations. a. Develop a point estimate of the mean value of  when  and  (to 3 decimals).   b. Predict an individual value of  when  and  (to 3 decimals).

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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). ( ,  )

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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?   b. Write a multiple regression equation relating  and the categorical variable to . 1.   2.   3.   4.   5.   Option 5 - Select your answer - Option 1 Option 2 Option 3 Option 4 Option 5 Item 2   Enter the values of dummy variables  and  that are used to indicate the three levels of the categorical variable. Level 0 - Select your answer - 1 0 Item 3   0 - Select your answer - 1 0 Item 4   1 - Select your answer - 1 0 Item 5   0 - Select your answer - 1 0 Item 6   0 - Select your answer - 1 0 Item 7   1 - Select your answer - 1 0 Item 8   c. Interpret the parameters in your regression equation.   E(y|level2) - E(y|level1) - Select your answer - E(y|level2) - E(y|level1) E(y|level1) - E(y|level2) E(y|level2) - E(y|level3) E(y|level3) - E(y|level2) Item 9     E(y|level3) - E(y|level1) - Select your answer - E(y|level3) - E(y|level1) E(y|level1) - E(y|level3) E(y|level3) - E(y|level2) E(y|level2) - E(y|level3) Item 10    is the change in  for a  unit change in  x1 - Select your answer - x2 x3 x1 Item 11   holding the categorical variable constant.

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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). Time =   +   Type b. Does the equation that you developed in part (a) provide a good fit for the observed data? Explain. (to 4 decimals) No - Select your answer - No Yes Item 3  , because the -value of   shows that the relationship is  not significant - Select your answer - significant not significant Item 5   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. Repairperson is a better predictor of repair time than the type of repair - Select your answer - Repairperson is a better predictor of repair time than the type of repair Both predictors are about the same Type of repair is a better predictor of repair time than the repairperson Item 8

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Data for two variables,  and , follow. Excel File: data15-39.xlsx a. Develop the estimated regression equation for these data (to 1 decimal).    +    b. Select the correct plot for the residuals against . A B C D A - Select your answer - A B C D Item 3   Does the residual plot support the assumptions about ε? Explain. With only  observations, it  is - Select your answer - is is not Item 4   difficult to determine if there are any violations in the assumptions. c. Select the correct plot for the standardized residuals against . A B C D C - Select your answer - A B C D Item 5   Do any outliers appear in these data? Explain. No - Select your answer - Yes No Item 6   Because  none - Select your answer - 1 value 2 values 3 or more values none Item 7   of the standard residuals is less than  or greater than , we would conclude that there  are no - Select your answer - are are no Item 8   outliers in the data set.

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The following data describes weekly gross revenue (), television advertising expenditures (), and newspaper advertising expenditures () for Showtime Movie Theaters. Weekly Gross Television Newspaper Revenue Advertising Advertising () () () 98 5.0 1.5 90 2.0 2.0 95 4.0 1.5 92 2.5 2.5 95 3.0 3.3 94 3.5 2.3 94 2.5 4.2 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 . A. B. C. D. Graph B - Select your answer - Graph A Graph B Graph C Graph D Item 4   Does the residual plot support the assumptions about ε? Explain. No - Select your answer - Yes No Item 5   With the relatively few observations, it  is - Select your answer - is is not Item 6   difficult to determine if the model assumptions are violated. c. Check for any outliers in these data. What are your conclusion? Because  none - Select your answer - 1 value 2 values 3 or more values none Item 7   of the standard residuals are less than  or greater than ,  none - Select your answer - 1 2 3 or more none Item 8   of the observations  can - Select your answer - can cannot Item 9   be classified as an outlier. Hide Feedback Correct     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 length of service (years) wage rate (dollars) job satisfaction test score (higher scores 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  a decrease - Select your answer - a decrease an increase Item 1   in job satisfaction score by   units. If the length of service does not change, a dollar increase in wage results in  an increase - Select your answer - a decrease an increase Item 3   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.

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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 high-school grade point average SAT mathemathics score 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. SUMMARY OUTPUT             Regression Statistics Multiple R   R Square   Adjusted R Square   Standard Error   Observations               ANOVA             df SS MS F Significance F Regression                  Residual           Total                                       Coefficients Standard Error t Stat P-value   Intercept                         X1                         X2                         b. Using , test for overall significance. There exists significant relationship. - Select your answer - There exists significant relationship. There exists no significant relationship. Item 19   c. Did the estimated regression equation provide a good fit to the data? Explain. Yes - Select your answer - Yes No Item 20  , because the  value is  greater - Select your answer - lower greater Item 21   than . d. Use the  test and  to test  and . Use t table. For , the -value is  between 0.02 and 0.05 - Select your answer - less than 0.01 between 0.01 and 0.02 between 0.02 and 0.05 between 0.05 and 0.10 between 0.10 and 0.20 between 0.20 and 0.40 greater than 0.40 Item 22  , so  reject - Select your answer - reject do not reject Item 23   . For , the -value is  less than 0.01 - Select your answer - less than 0.01 between 0.01 and 0.02 between 0.02 and 0.05 between 0.05 and 0.10 between 0.10 and 0.20 between 0.20 and 0.40 greater than 0.40 Item 24  , so  reject - Select your answer - reject do not reject Item 25   .

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                                                                         Week 16 Asst

 

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 . A. B. C. D. The correct scatter diagram is  - Select your answer - A B C D Item 1  . Does there appear to be a linear relationship between  and ? Explain. The scatter diagram  - Select your answer - does not show shows Item 2   some evidence of a possible linear relationship. b. Develop the estimated regression equation relating  and . Save "predicted" and "residuals" (to  decimals).        c. Choose the correct scatter diagram of the standardized residuals versus  for the estimated regression equation developed in part (b). A. B. C. D. The correct scatter diagram is  - Select your answer - A B C D Item 5  . Do the model assumptions appear to be satisfied? Explain. The standardized residual plot indicates that the constant variance assumption  - Select your answer - is not is Item 6   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).

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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.)          b. Using , test for a significant relationship.    (to  decimals) -value    (to  decimals) The relationship  - Select your answer - is not is Item 6   significant. c. Estimate the traffic flow in vehicles per hour at a speed of  miles per hour (to  decimals).   vehicles per hour

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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. Model Capacity List Price Maytag High-Efficiency Top Loading Washer with Steam 4.8 $749 Samsung High-Efficiency Top Loading Washer with ActiveWash and Integrated Touch Controls 5.0 $999 Whirlpool High-Efficiency Front Loading Washer with Steam 4.2 $1,299 Maytag High-Efficiency Top Loading Washer 4.3 $649 Whirlpool High-Efficiency Top Loading Washer 4.3 $599 Samsung High-Efficiency Front Loading Washer 4.2 $799 Samsung High Efficiency Front Loading Washer with AddWash Door 4.5 $999 Whirlpool High-Efficiency Front Loading Washer 4.5 $799 Whirlpool High-Efficiency Top Loading Washer with Steam 4.8 $799 Samsung High-Efficiency Top Loading Washer with ActiveWash 4.8 $899 Whirlpool High Efficiency Top Loading Washer 4.8 $699 Maytag High-Efficiency Front Loading Washer with Steam 4.3 $799 Whirlpool High-Efficiency Front Loading Washer with Steam 4.5 $1,099 Maytag High-Efficiency Top Loading Washer 5.3 $899 Samsung High-Efficiency Top Loading Washer 4.8 $799 Maytag High-Efficiency Front Loading Washer with Steam 4.5 $999 Samsung High-Efficiency Top Loading Washer with ActiveWash and Integrated Touch Controls 4.5 $849 Samsung High-Efficiency Top Loading Washer 4.5 $699 Samsung High-Efficiency Front Loading Washer with Steam 5.6 $1,599 Whirlpool High-Efficiency Front Loading Washer with Steam 4.5 $1,099 Whirlpool High Efficiency Front Loading Washer 4.2 $799 Samsung High-Efficiency Top Loading Washer with Activewash 5.2 $1,199 Maytag High-Efficiency Top Loading Washer with Steam 5.3 $1,099 Whirlpool High-Efficiency Top Loading Washer with Steam 5.3 $1,199 a. Which of the following scatter diagrams represents the data, treating cubic feet as the independent variable? A B C - Select your answer - Scatter diagram A Scatter diagram B Scatter diagram C None of these choices Item 1   Does a simple linear regression model appear to be appropriate? - Select your answer - Yes No Item 2   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.    +    Choose a standardized residual plot. A. B. C. D. - Select your answer - A B C D Item 5   Based upon the standardized residual plot, does a simple linear regression model appear to be appropriate? - Select your answer - Yes No Item 6   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.    +    +    d. Do you prefer the estimated regression equation developed in part (b) or part (c)? - Select your answer - Part (b), because its R-squared is lower than the equation in part (c). Part (c), because its R-squared is higher than the equation in part (b). Part (c), because its R-squared is lower than the equation in part (b). Part (b), because its R-squared is higher than the equation in part (c). Item 10   e. Are there other factors that should be considered for inclusion as independent variables in this regression? - Select your answer - Brand Top or Front Load Steam Other options such as the AddWash Door, ActiveWash, and Integrated Touch All of the variants Item 11

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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. a. Select a scatter diagram for these data with the viewers' ages as the independent variable and their rating of Suicide Squad as the dependent variable. 1.  2.  3.  4.  - Select your answer - 1 2 3 4 Item 1   Does a simple linear regression model appear to be appropriate? - Select your answer - No Yes Item 2   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).          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.              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   Select increase decrease Item 10   of   points in the viewer's rating of Suicide Squad. 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. - Select your answer - part (c) part (b) Item 12   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).

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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. If not otherwise stated, round your answers to the nearest whole number. Enter negative values as negative numbers. 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.        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.                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.     (to  decimals) The -value associated with  is  - Select your answer - less than 0.01 between 0.01 and 0.025 between 0.025 and 0.05 between 0.05 and 0.10 greater than 0.10 Item 8  . What is your conclusion? The addition of the two independent variables  - Select your answer - is is not Item 9   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.        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). - Select your answer - I II III Item 12

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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. Average Monthly Gas Number of Bill for Last Year Age Square Footage Rooms $70.20 16 2537 6 $81.33 2 3437 8 $45.86 27 976 6 $59.21 11 1713 7 $117.88 16 3979 11 $57.78 2 1328 7 $47.01 27 1251 6 $52.89 4 827 5 $32.90 12 645 4 $67.04 29 2849 5 $76.76 1 2392 7 $60.40 26 900 5 $44.07 14 1386 5 $26.68 20 1299 4 $62.70 17 1441 6 $45.37 13 562 4 $38.09 10 2140 4 $45.31 22 908 6 $52.45 24 1568 5 $96.11 27 1140 10 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.        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.           +    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.         (to  decimals) The p-value associated with F is  - Select your answer - less than 0.01 between 0.01 and 0.025 between 0.025 and 0.05 between 0.05 and 0.10 greater than 0.10 Item 11  . Therefore, the addition of the two independent variables  - Select your answer - is is not Item 12   statistically significant.

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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.        I.      , where  if treatment ,  , otherwise;  if treatment ,  , otherwise;  if treatment ,  , otherwise;  if treatment ,  , otherwise.      II.      , where  if treatment ,  , otherwise;  if treatment ,  , otherwise;  if treatment ,  , otherwise;  if treatment ,  , otherwise.     III.      , where  if treatment ,  , otherwise;  if treatment ,  , otherwise;  if treatment ,  , otherwise. - Select your answer - I II III Item 1

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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.        I.      , where  if level  for factor ,  , if level  for factor ;  if level  for factor ,  , otherwise;  if level  for factor ,  , otherwise.      II.      , where  if level  for factor ,  , if level  for factor ;  if level  for factor ,  , otherwise;  if level  for factor ,  , otherwise.     III.      , where  if level  for factor ,  , if level  for factor ;  if level  for factor ,  , otherwise;  if level  for factor ,  , otherwise.     IV.      , where  if level  for factor ,  , if level  for factor ;  if level  for factor ,  , otherwise;  if level  for factor ,  , otherwise.       V.      , where  if level  for factor ,  , if level  for factor ;  if level  for factor ,  , if level  for factor ;  if level  for factor ,  , otherwise;  if level  for factor ,  , otherwise;  if level  for factor ,  , if otherwise. - Select your answer - I II III IV V Item 1

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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. Excel File: data16-21.xls 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:   Regression Statistics Multiple R (to  decimals)   R Square (to  decimals)   Adjusted R Square (to  decimals)   Standard Error (to  decimals)   Observations (to whole number)     ANOVA             df (to whole number) SS (to whole number) MS (to  decimals) F (to  decimals) Significance F (to  decimals) Regression           Residual           Total                         Coefficients (to whole number) Standard Error (to  decimals) t Stat (to  decimals) P-value (to  decimals)   Intercept           D1           D2           D3           At the  level of significance,  - Select your answer - do not reject reject Item 32   . b. What is your estimate of mean drying time for paint  (to whole number)?

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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 Size of Advertisement Small Large A 8 12 12 8 Design B 22 26 14 30 C 10 18 18 14 Let define:   if a small advertisement and  if a large advertisement   8 (A, Small)           12 (A, Small)           12 (A, Large)           8 (A, Large)           22 (B, Small)           14 (B, Small)           26 (B, Large)           30 (B, Large)           10 (C, Small)           18 (C, Small)           18 (C, Large)           14 (C, Large)             Regression Statistics Multiple R (to  decimals)   R Square (to  decimals)   Adjusted R Square (to  decimals)   Standard Error (to whole number)   Observations (to whole number)     ANOVA             df (to whole number) SS (to whole number) MS (to  decimals) F (to  decimals) Significance F (to  decimals) Regression           Residual           Total                         Coefficients (to whole number) Standard Error (to  decimals) t Stat (to  decimals) P-value (to  decimals)   Intercept                                                             The analysis shows that  - Select your answer - size of advertisement interaction type of design Item 100   has a significant effect.

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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. - Select your answer - There is positive autocorrelation present. There is not positive autocorrelation present. The test is inconclusive. Item 1

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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. Brand and Model Type Weight Price Klein Reve V Road 20 1800 Giant OCR Composite 3 Road 22 1800 Giant OCR 1 Road 22 1000 Specialized Roubaix Road 21 1300 Trek Pilot 2.1 Road 21 1320 Cannondale Synapse 4 Road 21 1050 LeMond Poprad Road 22 1350 Raleigh Cadent 1.0 Road 24 650 Giant FCR3 Fitness 23 630 Schwinn Super Sport GS Fitness 23 700 Fuji Absolute 2.0 Fitness 24 700 Jamis Coda Comp Fitness 26 830 Cannondale Road Warrior 400 Fitness 25 700 Schwinn Sierra GS Comfort 31 340 Mongoose Switchback SX Comfort 32 280 Giant Sedona DX Comfort 32 360 Jamis Explorer 4.0 Comfort 35 600 Diamondback Wildwood Deluxe Comfort 34 350 Specialized Crossroads Sport Comfort 31 330 a. Select an appropriate scatter diagram with weight as the independent variable and price as the dependent variable. 1. 2. 3. 4. Select the correct scatter diagram from the options above. - Select your answer - 1 2 3 4 Item 1   Does a simple linear regression model appear to be appropriate? - Select your answer - A simple linear regression model appears to be appropriate. A simple linear regression model does not appear to be appropriate. Item 2   Round your answers to four decimal places. b. Develop an estimated multiple regression equation with  and  as the two independent variables.           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).           Type of bike appears to be a(n)  - Select your answer - significant insignificant Item 9   factor in predicting price. But, the estimated regression equation developed in part (b) appears to provide a slightly  - Select your answer - better worse Item 10   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.

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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: Delay The length of time from a company's fiscal year-end to the date of the auditor's report. Industry A dummy variable coded  if the firm was an industrial company or  if the firm was a bank, savings and loan, or insurance company. Public A dummy variable coded  if the company was traded on an organized exchange or over the counter; otherwise coded . Quality A measure of overall quality of internal controls, as judged by the auditor, on a five-point scale ranging from "virtually none" () to "excellent" (). Finished A 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. 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. - Select your answer - No significant positive autocorrelation No conclusion can be drawn Significant positive autocorrelation occurs Item 1

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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. - Select your answer - There are significant differences between comfort levels for the three types of browsers. There are not significant differences between comfort levels for the three types of browsers. Item 1

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