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business
business statistics in practice
Business Statistics Plus Pearson Mylab Statistics With Pearson Etext 3rd Edition Norean R Sharpe ,Richard D De Veaux ,Paul Velleman - Solutions
=+a) The value of a beach front home decreases by $7500 every year.
=+23. Real estate prices. A regression was performed to predict selling Price of beach front vacation homes in dollars from their Area in square feet, Lotsize in square feet, and Age in years. The R2 is 90%. The equation from this regression is given here.Price = 159,228 + 85.3 Area + 1.78 Lotsize
=+Do you find that those conditions are met?
=+Which of the regression conditions can you check with these plots?
=+22. Ticket prices, part 6. Here are some plots of residuals for the regression of Exercise 14.–0.15 0.00 0.15 0.30 Residuals Predicted 15 18 21 510 15 20 25–0.08 0.12 0.32 Residuals–0.28–0.15 0.00 0.15 0.30 Residuals 2006 2007 Year 2008
=+Do you find that those conditions are met?
=+Which of the regression conditions can you check with these plots?
=+21. Police salaries, part 6. Here are some plots of residuals for the regression of Exercise 13. 7 Some values are rounded to simplify the exercises. If you recompute the analysis with your statistics software you may see slightly different numbers.M17_SHAR8696_03_SE_C17.indd 615 14/07/14 7:38 AM
=+20. Ticket prices, part 5. The investor in Exercise 18 now accepts your analysis but claims that it demonstrates that it doesn’t matter how many shows are playing on Broadway;receipts will be essentially the same. Explain why this interpretation is not a valid use of this regression model. Be
=+19. Police salaries, part 5. A Senate aide accepts your analysis in Exercise 17 but claims that it demonstrates that if the state pays police more, it will actually increase the rate of violent crime. Explain why this interpretation is not a valid use of this regression model. Offer some
=+c) A Broadway investor challenges your analysis. He points out that the scatterplot of Receipts vs. # Shows in Exercise 12 shows a strong linear relationship and claims that your result in part a can’t be correct. Explain to him why this is not a contradiction.
=+) Test the null hypothesis (at a = 0.05) and state your conclusion.
=+a) State the standard null and alternative hypotheses for the true coefficient of # Shows.
=+. Ticket prices, part 4. Consider the coefficient of # Shows in the regression table of Exercise 14.
=+b) Test the null hypothesis (at a = 0.05) and state your conclusion.
=+a) State the standard null and alternative hypotheses for the true coefficient of Police Officer Wage.
=+17. Police salaries, part 4. Consider the coefficient of Police Officer Wage in the regression table of Exercise 13.
=+c) The t-ratio for the intercept is negative. What does that mean?
=+b) How many weeks are included in this regression? How can you tell?
=+a) How was the t-ratio of 126.7 found for Paid Attendance?(Show what is computed using numbers found in the table.)
=+16. Ticket prices, part 3. Using the regression table in Exercise 14, answer the following questions.
=+c) The t-ratio for Graduation Rate is negative. What does that mean?
=+b) How many states are used in this model. How do you know?
=+a) How was the t-ratio of 0.221 found for Police Officer Wage? (Show what is computed using numbers from the table.)
=+15. Police salaries, part 3. Using the regression table in Exercise 13, answer the following questions.
=+d) Is this likely to be a good prediction? Why do you think that?
=+c) In a week in which the paid attendance was 200,000 customers attending 30 shows at an average ticket price of$70, what would you estimate the receipts would be?
=+b) What does the coefficient of Paid Attendance mean in this regression? Does that make sense?
=+a) Write the regression model.
=+14. Ticket prices, part 2. Here’s a multiple regression model for the variables considered in Exercise 12:7 Dependent variable is: Receipts($M)R squared = 99.9% R squared (adjusted) = 99.9%s = 0.0931 with 74 degrees of freedom Source Sum of Squares df Mean Square F-ratio Regression 484.789 3
=+d) Is this likely to be a good prediction? Why do you think that?
=+c) In a state in which the average police officer wage is $20/hour and the high school graduation rate is 70%, what does this model estimate the violent crime rate would be?
=+b) What does the coefficient of Police Officer Wage mean in the context of this regression model?
=+a) Write the regression model.
=+13. Police salaries, part 2. Here’s a multiple regression model for the variables considered in Exercise 11.Dependent variable is: Violent Crime R squared = 22.41% R squared (adjusted) = 19.10%s = 156.9 with 47 degrees of freedom Source Sum of Squares df Mean Square F-ratio Regression 334246 2
=+b) If we found a regression to predict Receipts only from Paid Attendance, what would the R2 of that regression be?
=+a) Name and check (to the extent possible) the regression assumptions and their corresponding conditions.M17_SHAR8696_03_SE_C17.indd 614 14/07/14 7:38 AM Exercises 615
=+Receipts ($M) 1.000 Paid Attendance 0.961 1.000# Shows 0.745 0.640 1.000 Average Ticket Price 0.258 0.331 -0.160 1.000
=+Paid Attendance (thousands)# Shows Average Ticket Price ($)Viewing this as a business, we’d like to model Receipts in terms of the other variables.First, here are plots and background information. Receipts ($M)180 210 240 270 Paid Attendance (000)21 18 15 Receipts ($M)20 24 28 32 36 Number of
=+12. Ticket prices. On a typical night in New York, about 25,000 people attend a Broadway show, paying an average price of more than $75 per ticket. Variety (www.variety.com), a news weekly that reports on the entertainment industry, publishes statistics about the Broadway show business. The
=+b) If we found a regression to predict Violent Crime just from Police Officer Wage, what would the R2 of that regression be?
=+a) Name and check (to the extent possible) the regression assumptions and their corresponding conditions.
=+First, here are plots and background information.HS Graduation Rate 65 70 75 80 85 200 100 400 300 500 600 700 Violent Crime per 100000 Police Officer Wage 15 20 25 30 35 40 200 100 400 300 500 600 700 Violent Crime Correlations Violent Crime Graduation Rate Police Officer Wage Violent Crime
=+11. Police salaries 2013. Is the amount of violent crime related to what police officers are paid? The U.S. Bureau of Labor Statistics publishes data on occupational employment and wage estimates (www.bls.gov/oes/) for each of the 50 states. Here are data released from 2011 to 2013.The
=+The next 12 exercises consist of two sets of 6 (one even-numbered, one odd-numbered). Each set guides you through a multiple regression analysis. We suggest that you do all 6 exercises in a set.Remember that the answers to the odd-numbered exercises can be found in the back of the book.
=+d) Would you reject that null hypothesis?M17_SHAR8696_03_SE_C17.indd 613 14/07/14 7:38 AM 614 CHAPTER 17 Multiple Regression Chapter Exercises
=+c) What null hypothesis can you test with it?
=+b) What is the F-statistic value for this regression?
=+a) Using the values from the table, show how the value of R2 could be computed. Don’t try to do the calculation, just show what is computed.
=+10. Here is another part of the regression output for the movies in Exercise 3:Source Sum of Squares df Mean Square F-ratio Regression 224995 3 74998.4 34.8 Residual 249799 116 2153.44
=+b) Why is the “Adjusted R Square” in the table different from the “R Square”?
=+a) What is the R2 for this regression? What does it mean?
=+9. In the regression model of Exercise 3,
=+e) Complete the hypothesis test. Do you reject the null hypothesis?Section 17.5
=+d) What is the P-value corresponding to this t-statistic?
=+c) Why is this t-statistic negative?
=+b) What is the t-statistic corresponding to this test?
=+8.a) What is the null hypothesis tested for the coefficient of Run Time in the regression of Exercise 3?
=+d) Complete the hypothesis test. Do you reject the null hypothesis?
=+c) What is the P-value corresponding to this t-statistic?
=+b) What is the t-statistic corresponding to this test?
=+a) What is the null hypothesis tested for the coefficient of Stars in this table?
=+7. In the regression output for the movies of Exercise 3,
=+6. For the movies regression, here is a histogram of the residuals. What does it tell us about these Assumptions and Conditions?50 10 20 30 40–150 –25 100 225 Residuals (U)a) Linearity conditionb) Nearly Normal conditionc) Equal Spread condition Section 17.4
=+a) Linearity conditionb) Equal Spread conditionc) Normality assumption
=+5. For the movies examined in Exercise 4, here is a scatterplot of USGross vs. Budget:300 200 100 U.S. Gross ($M)50 100 150 200 Budget ($M)What (if anything) does this scatterplot tell us about the following Assumptions and Conditions for the regression?
=+4. A middle manager at an entertainment company, upon seeing the analysis of Exercise 3, concludes that the longer you make a movie, the less money it will make. He argues that his company’s films should all be cut by 30 minutes to improve their gross. Explain the flaw in his interpretation of
=+b) What is the interpretation of the coefficient of Budget in this regression model?
=+a) Write the multiple regression equation.
=+We want a regression model to predict USGross. Parts of the regression output computed in Excel look like this:Dependent variable is: USGross($)R squared = 47.4% R squared (adjusted) = 46.0%s = 46.41 with 120 - 4 = 116 degrees of freedom Variable Coefficient SE(Coeff) t-ratio P-value Intercept
=+3. What can predict how much a motion picture will make? We have data on a number of recent releases that includes the USGross (in $M), the Budget ($M), the Run Time (minutes), and the average number of Stars awarded by reviewers. The first several entries in the data table look like this:Movie
=+c) What does that residual say about her candy?Exercises M17_SHAR8696_03_SE_C17.indd 612 14/07/14 7:38 AM Exercises 613 Section 17.2
=+b) In fact, a laboratory test shows that her candy has 227 calories per serving. Find the residual corresponding to this candy. (Be sure to include the units.)
=+a) The hand-crafted chocolate she makes has 15g of fat and 20g of sugar. How many calories does the model predict for a serving?
=+2. A candy maker surveyed chocolate bars available in a local supermarket and found the following least squares regression model:Calories = 28.4 + 11.37Fat1g2 + 2.91Sugar1g2.
=+c) What does that residual say about this transaction?
=+b) The house just sold for $135,000. Find the residual corresponding to this house.
=+a) Find the price that this model estimates.
=+1. A house in the upstate New York area from which the chapter data was drawn has 2 bedrooms and 1000 square feet of living area. Using the multiple regression model found in the chapter, Price = 20,986.09 - 7483.10Bedrooms + 93.84Living Area.
=+• Propose an ethical solution that considers the welfare of all stakeholders
=+• What are the undesirable consequences?
=+• Identify the ethical dilemma in this scenario.
=+recently purchased another item, or a 50-year-old customer who has not purchased in a year?
=+ Who would be more likely to respond, a 20-year-old customer who has
=+Interpret the model. Would you keep both predictor variables in the model? Why?
=+that is consistent with the decision we made to drop Age from the model.
=+The model for Respond Amount that included Age as a predictor (see For Example on page 598) had an adjusted R2 value of 0.9123 (or 91.23%) The original model (see For Example on page 586) had an adjusted R2 value of 0.9131. Explain how
=+Has the variable Age improved the model? Would you leave the term in? Comment
=+6 What role does the Normal model play in the construction, inference, and understanding of multiple regression models?
=+5 Give two ways that we use scatterplots to support the construction, inference, and understanding of multiple regression models.
=+4 Give two ways that we use histograms to support the construction, inference, and understanding of multiple regression models.
=+In the regression model of Respond Amount, interpret the intercept and the regression coefficients of the three predictors.
=+3 How can the coefficient of Height have such a small P-value in the multiple regression when the correlation between Height and Percent Body Fat was not statistically distinguishable from zero?
=+2 Interpret the coefficient of Age.
=+1 Interpret the R2 of this regression model.
=+How much of the variation in Respond Amount is explained by this model? What does the term s = 18.183 mean? Which variables seem important in the model?
=+66. Lobsters 2012, part 6. How has the price of a lobster changed? Here’s a plot tracking the price of lobster per pound in constant year 2000 dollars.2.25 3.00 3.75 1950.0 1962.5 1975.0 1987.5 2000.0 Year Price ($) / lb This plot is not straight. Would a transformation help? If so, which one?
=+58. GDP 2013, part 2. Consider again the post-1950 trend in U.S. GDP we examined in Exercise 57. Here are a regression and residual plot when we use the log of GDP in the model. Is this a better model for GDP? Explain.Dependent variable is: Log GDP R squared = 99.1% R squared (adjusted) = 99.1%s
=+b) Here’s a scatterplot of the residuals. Now do you think this is a good model for these data? Explain?0.75 0.00–0.75 Residual 3 6 9 12 Predicted GDP
=+a) Does the value 96.7% suggest that this is a good model?Explain.
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