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Business Statistics Plus Pearson Mylab Statistics With Pearson Etext 3rd Edition Norean R Sharpe ,Richard D De Veaux ,Paul Velleman - Solutions

=+Dependent variable is: Delay/person R-squared = 80.7% R-squared (adjusted) = 78.5%s = 6.316 with 68 - 8 = 60 degrees of freedom Source Sum of Squares df Mean Square F-ratio Regression 10013.0 7 1430.44 35.9 Residual 2393.82 60 39.8970 Variable Coeff SE(Coeff) t-ratio P-value Intercept 153.110
=+Here is another model that adds two new constructed variables to the model in Exercise 18. They are the product of ArterialMPH and Small and the product of ArterialMPH and VeryLarge.
=+a) The model in Exercise 18 includes indicators for city size. Considering this display, have these indicator variables accomplished what is needed for the regression model? Explain.
=+24. Traffic delays, part 3. Here’s a plot of the Studentized residuals from the regression model of Exercise 18 plotted against ArterialMPH. The plot is colored according to City Size (Small, Medium, Large, and Very Large), and regression lines are fit for each city size.–1.25 28 30 32 0.00
=+c) Is this a better regression model than the one in Exercises 17 and 19?
=+b) Interpret the coefficient of Type*Cals in this regression model.
=+a) What does this plot say about how the regression model deals with these two types of pizza?We constructed another variable consisting of the indicator variable Type multiplied by Calories. Here’s the resulting regression.Dependent variable is: Score R-squared = 73.1% R-squared (adjusted) =
=+A plot of the residuals against the predicted values for this regression looks like this. It has been colored according to the Type of pizza.–25 025 50 Residuals Predicted 25 50 75 100 Cheese Pepperoni
=+23. Pizza ratings, part 3. In Exercise 19, we raised questions about two gourmet pizzas. After removing them, the resulting regression looks like this.Dependent variable is: Score R-squared = 64.4% R-squared (adjusted) = 59.8%s = 14.41 with 27 - 4 = 23 degrees of freedom Source Sum of Squares df
=+d) Could Pedro’s agent claim, based on this regression, that his man attracts more fans to the ballpark? What statistics should he cite?
=+c) If we’re primarily interested in Pedro’s effect on attendance, why is it important to have the other variables in the model?
=+b) What is the interpretation of the coefficient for Pedro Start?
=+a) All of these predictors are of a special kind. What are they called?
=+Yankees 1 if game is against the Yankees(a hometown rivalry), 0 otherwise Rain Delay 1 if the game was delayed by rain(which might have depressed attendance), 0 otherwise Opening Day 1 for opening day, 0 for the others Pedro Start 1 if Pedro was the starting pitcher, 0 otherwise Here’s the
=+22. Baseball attendance. Pedro Martinez, who retired from Major League Baseball in 2012, had a stellar career, helping the Boston Red Sox to their first World Series title in 86 years in 2004. The next year he became a free agent and the New York Mets picked him up for $53 million for 4 years.
=+c) What additional assumption is required to include the variable December in this model? Is there reason to believe that it is satisfied?
=+b) What is the interpretation of the coefficient of the constructed variable December?
=+a) The points plotted with x are the December values. We can construct a variable that is “1” for those four values and“0” otherwise. What is such a variable called?Here’s the resulting regression.Dependent variable is: WM_Revenue R-squared = 80.3% R-squared (adjusted) = 79.2%s = 1.762
=+A scatterplot can give us some clues as to why they turned away from monthly reporting.16 20 24 28 WM_Revenue CPI 562.5 575.0 587.5 600.0
=+21. Walmart revenue. Each week about 100 million customers—nearly one-third of the U.S. population—visit one of Walmart’s U.S. stores. How does Walmart’s revenue relate to the state of the economy in general? Before 2009, Walmart reported sales each month, but since then it has switched
=+b) Is Los Angeles likely to be an influential point in this regression?
=+a) The point plotted with an x is Los Angeles. Read the graph and explain what it says about traffic delays in Los Angeles and about the regression model.
=+20. Traffic delays, part 2. Here’s a scatterplot of the residuals from the regression in Exercise 18 plotted against mean Highway mph.–7.5 0.0 7.5 Residuals Highway mph 35 40 45 50 55
=+b) Do you think these two pizzas are likely to be influential in the regression. Would setting them aside be likely to change the coefficients? What other statistics might help you decide?
=+a) The two extraordinary points in the lower right are Reggio’s and Michelina’s, two gourmet brands. Interpret these points.
=+19. Pizza ratings, part 2. Here’s a scatterplot of the residuals against predicted values for the regression model found in Exercise 17.–30–15 015 Residuals Predicted 50.0 62.5 75.0
=+b) Explain how the coefficients of Small, Large, and Very Large account for the size of the city in this model.
=+a) Why is there no coefficient for Medium?
=+Regression 9808.23 5 1961.65 46.8 Residual 2598.64 62 41.9135 Variable Coeff SE(Coeff) t-ratio P-value Intercept 139.104 16.69 8.33 60.0001 HiWay MPH -1.07347 0.2474 -4.34 60.0001 Arterial MPH -2.04836 0.6672 -3.07 0.0032 Small -3.58970 2.953 -1.22 0.2287 Large 5.00967 2.104 2.38 0.0203 Very
=+by traffic), the Average Arterial Road Speed (mph), the Average Highway Road Speed (mph), and the Size of the city(small, medium, large, very large). The regression model based on these variables looks like this. The variables Small, M18_SHAR8696_03_SE_C18.indd 663 14/07/14 7:37 AM 664 CHAPTER
=+18. Traffic delays. The Texas Transportation Institute(tti.tamu.edu) studies traffic delays. They estimate that in the year 2011, 498 urban areas experienced 5.5 billion vehicle hours of delay, resulting in 2.9 billion gallons of wasted fuel and $121 billion in lost productivity and fuel
=+b) What displays would you like to see to check assumptions and conditions for this model?
=+a) What is the interpretation of the coefficient of Type in this regression? According to these results, what type would you expect to sell better—cheese or pepperoni?
=+to 2012 (www.companiesandmarkets.com). The prestigious Consumer’s Union rated frozen pizzas for flavor and quality, assigning an overall score to each brand tested. A regression model to predict the Consumer’s Union score from Calories, Type (1 = cheese, 0 = pepperoni), and fat content gives
=+17. Pizza ratings. Manufacturers of frozen foods often reformulate their products to maintain and increase customer satisfaction and sales. So they pay particular attention to evaluations of their products in comparison to their competitors’ products. Frozen pizzas are a major sector of the
=+b) Why did the model subtract 38.5122 from Age in the quadratic term?Chapter Exercises
=+a) The slope of Age is negative. Does this indicate that older houses cost less, on average? Explain.
=+16. A regression model from the collection of houses in Exercise 15 shows the following:Variable Coeff SE(Coeff) t-ratio P-value Intercept 217854.85 4197.417 51.90 60.0001 Age -1754.254 127.3356 -13.78 60.0001 1Age@38.512222 20.401223 1.327713 15.37 60.0001
=+c) What might you do instead?
=+b) A linear regression of Price on Age shows that the slope for Age is not statistically significant. Is Price unrelated to Age? Explain.
=+a) Describe the relationship between Price and Age. Explain what this says in terms of house prices.
=+15. A collection of recreational boats in Kuwait shows the following relationship between Price and Age of the boat: Price 0 20 40 60 80 100 Age 200,000 250,000 300,000 350,000
=+14. If the VIF for Networth in the regression of Exercise 11 was 20.83, what would the R2 be from the regression of Networth on Age, Income, and Past Spending?Section 18.6
=+What is the VIF for Age?
=+Past Spending 3.339e - 04 1.828e - 04 1.826 0.0681 Income 3.811e - 04 7.610e - 06 50.079 60.0001 Networth 2.420e - 05 1.455e - 06 16.628 60.0001
=+13. The analyst from Exercise 11, worried about collinearity, regresses Age against Past Spending, Income, and Networth. The output shows:Response Variable: Age R2 = 98.75% Adjusted R2 = 98.74%s = 2.112 with 908 - 4 = 904 degrees of freedom Variable Coeff SE(Coeff) t-ratio P-value(Intercept)
=+Spending 1.063e - 01 4.203e - 03 25.292 60.0001 Income 1.902e - 03 3.392e - 04 5.606 60.0001 Networth 2.900e - 05 3.815e - 05 0.760 0.447 Age 6.065e - 01 7.631e - 01 0.795 0.427a) How many observations were used in the regression?b) What might you do next?c) Is it clear that Income is more
=+12. The analyst in Exercise 11 fits the model with the four predictor variables. The regression output shows:Response Variable: Spending R2 = 84.92% Adjusted R2 = 84.85%s = 48.45 with 908 - 5 = 903 degrees of freedom Variable Coeff SE(Coeff) t-ratio P-value Intercept -3.738e + 00 1.564e + 01
=+Why might a stepwise regression search not find the same model as an “all subsets” regression?M18_SHAR8696_03_SE_C18.indd 662 14/07/14 7:37 AM Exercises 663
=+11. An analyst wants to build a regression model to predict spending from the following four predictor variables: Past Spending, Income, Net Worth and Age. A correlation matrix of the four predictors shows:Income Net Worth Age Past Spending 0.442 0.433 0.446 Income 0.968 0.992 Net Worth 0.976
=+b) Which model do you prefer? Explain briefly.Section 18.4
=+a) What are the main differences between this model with John Carter removed and the model from Exercise 7 with it included?
=+Dependent variable is: USGross($M)R-squared = 0.4635, Adjusted R-squared: 0.4478 s = 53.89 with 106 - 3 = 103 degrees of freedom Variable Coefficient SE(Coeff) t-ratio P-value Intercept 21.6562 10.2755 2.108 0.0375 Budget 1.0224 0.1188 8.607 60.0001 R Rating 22.2916 17.6941 1.260 0.2106 Budget*R
=+The outlier, once again, is John Carter, whose budget was more than $200M more than its gross revenue in the U.S.Setting this movie aside and rerunning the regression from Exercise 8, we find:
=+10. For the same regression as in Exercise 9, the Cook’s Distances look like this:0.00 Number of Movies Cook’s Distance 0.2 0.4 0.6 0.8 1.0 1.2 20 40 60 80 100
=+If the budget for John Carter had been $1M higher than it was (and everything else remained the same), how much would the model’s prediction of John Carter’s U.S. gross revenue change?
=+The movie with the highest leverage of 0.219 is Walt Disney’s John Carter, which grossed $66M but had a budget of $300M.
=+9. For the regression model in Exercise 8, the leverage values look like this:0.00 Number of movies Leverage 0.05 0.10 0.15 0.20 60 50 40 30 20 10
=+d) Would you reject that hypothesis at 0.05? What do you conclude?Section 18.3
=+c) What null hypothesis can we test with the t-ratio for Budget*R Rating?
=+b) In this regression, the variable Budget*R Rating is an interaction term. How would you interpret its coefficient?
=+8. Here is the scatterplot of the variables in Exercise 7 with regression lines added for each kind of movie:300 50 100 150 200 250 300 Budget ($M)200 US Gross ($M)100 The regression model is:Dependent variable is: USGross($M)R-squared = 0.3674, Adjusted R-squared: 0.3491 s = 58.24 with 107 - 3 =
=+b) How would you construct the interaction term variable?Exercises M18_SHAR8696_03_SE_C18.indd 661 14/07/14 7:37 AM 662 CHAPTER 18 Building Multiple Regression Models
=+a) How would you code the indicator variable? (Use PG-13 as the base level.)
=+7. Are R rated movies as profitable as those rated PG-13?Here’s scatterplot of USGross ($M) vs. Budget ($M) for PG-13 (green) and R (purple) rated movies 300 50 100 150 200 250 300 Budget ($M)200 US Gross ($M)100
=+c) Do you think a regression with the indicator variables would model jacket sales better than one without those predictors?Section 18.2
=+a) How would you code the variables? (How many dummy variables do you need? What values would they have?)
=+6. A marketing manager has developed a regression model to predict quarterly sales of his company’s mid-weight microfiber jackets based on price and amount spent on advertising. An intern suggests that he include indicator(dummy) variables for each quarter.
=+a) Type of residence (Apartment, Condominium, Townhouse, Single family home)b) Employment status (Full-time, Part-time, Unemployed)
=+5. For each of the following, show how you would code dummy (indicator) variables to include in a regression model.
=+d) Can you reject the null hypothesis of part c? Explain.
=+c) What null hypothesis can we test with the t-ratio for R Rating?
=+b) In this regression, the variable R Rating is an indicator variable that is 1 for movies that have an R rating. How would you interpret the coefficient of R Rating?
=+4. Here is the regression for Exercise 3 with an indicator variable:150 50 100 150 Budget ($M)100 50 US Gross ($M)Dependent variable is: USGross($M)R-squared = 0.193, Adjusted R-squared: 0.166 s = 37.01 with 62 - 3 = 59 degrees of freedom Variable Coefficient SE(Coeff) t-ratio P-value Intercept
=+b) What would the data values in such an indicator variable be?
=+a) Why might a researcher want to use an indicator variable for the MPAA Rating?
=+3. Do movies of different types have different rates of return on their budgets? Here’s a scatterplot of Gross Revenue in US ($M) vs. Budget ($M) for recent movies whose MPAA Rating is either PG (blue) or R (red):150 0 50 100 150 Budget ($M)100 50 0US Gross ($M)
=+c) Do you think a regression with the indicator variable for Fall would model down jacket sales better than one without that predictor?
=+b) Why does the intern’s suggestion make sense?
=+a) How would you code such a variable? (What values would it have for each quarter?)
=+2. A marketing manager has developed a regression model to predict quarterly sales of his company’s down jackets based on price and amount spent on advertising. An intern suggests that he include an indicator (dummy) variable for the Fall quarter.
=+a) Company unionization status (Unionized, No Union)b) Gender (Female, Male)c) Account Status (Paid on time, Past Due)d) Political party affiliation (Democrat, Republican, Other)
=+1. For each of the following, show how you would code dummy (or indicator) variables to include in a regression model.
=+• Propose an ethical solution that considers the welfare of all stakeholders.
=+• What are the undesirable consequences?
=+• Identify the ethical dilemma in this scenario.
=+Experience for different Education levels, how many indicator variables will she need for Education?
=+2 If she wants to study the differences in the relationship between Salary and Years
=+Experience for men and women, what terms should she enter in the regression?
=+1 If she wants to account for differences in the relationship between Salary and Years
=+Based on this, what model might you use to predict Log10Price?
=+For the three colors of diamonds, what are the models that predict Log10Price? Does the addition of the indicator variables for the colors seem like a good idea? Why are there only two indicator variables?
=+d) Does the coefficient of Internet Users/100 people mean that when Internet use increases, the expenditures on public health will increase as well?
=+c) State and test the standard null hypothesis for the coefficient of Expected Years of Schooling. Use the standard a-level of a = 0.05 and state your conclusion.
=+b) Are the assumptions and conditions met?
=+a) Write the regression model.
=+46. Health expenditures. Can the amount of money that a country spends on health (as % of GDP) be predicted by other economic indicators? Here’s a regression predicting Expenditures on Public Health (as % of GDP) from Expected Years of Schooling and Internet Users (per 100 people):Dependent
=+c) Does the R2 value of 100.0% mean that the residuals are all actually equal to zero?
=+b) The mean of Calories is 455.5 with a standard deviation of 217.5. Discuss what the value of s in the regression means about how well the model fits the data.
=+a) Do you think this model would do a good job of predicting calories for a new BK menu item? Why or why not?

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