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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
=+45. Burger King nutrition. Like many fast-food restaurant chains, Burger King (BK) provides data on the nutrition content of its menu items on its website. Here’s a multiple regression predicting calories for Burger King foods from Protein content (g), Total Fat (g), Carbohydrate (g), and
=+d) Be sure to check the conditions for multiple regression.What do you conclude?
=+c) Does this model mean that by changing the levels of the predictors in this equation, we could affect life expectancy in that state? Explain.
=+b) Would you leave all three predictors in this model?
=+a) Which model appears to do the best?
=+44. Demographics. The dataset corresponding to the exercise on the DVD holds various measures of the 50 United States. The Murder rate is per 100,000, HS Graduation rate is in %, Income is per capita income in dollars, Illiteracy rate is per 1000, and Life Expectancy is in years. Find a
=+b) The Suzuki DR650SE had an MSRP of $4999 and a 4-stroke engine, with a bore of 100 inches. Can you use this model to estimate its Clearance? Explain.
=+a) Would this be a good model to use to predict the price of an off-road motorcycle if you knew its bore, clearance, and engine strokes? Explain.
=+43. Motorcycles, part 3. Here’s another model for the MSRP of off-road motorcycles.Dependent variable is: MSRP R squared = 90.9% R squared (adjusted) = 90.6%s = 617.8 with 95 - 4 = 91 degrees of freedom Source Sum of Squares df Mean Square F-ratio Regression 346795061 3 115598354 303 Residual
=+b) Both of these predictors seem to be linearly related to MSRP. Explain what your result in part a means.
=+a) State and test the standard null hypothesis for the coefficient of Bore.
=+42. Motorcycles, part 2. In Exercise 41, we saw data on offroad motorcycles and examined scatterplots. Review those scatterplots. Here’s a regression of MSRP on both Displacement and Bore. Both of the predictors are measures of the size of the engine. The displacement is the total volume of
=+Lu, Joseph B. Kadane, and Peter Boatwright, server1.tepper.cmu.edu/gsiadoc/WP/2006-E57.pdf), but we can use these to predict msrp from other variables.Here are scatterplots of three potential predictors, Wheelbase (in), Displacement (cu in), and Bore (in).8000 6000 4000 2000 37.5 45.0 52.5 MSRP
=+41. Motorcycles. More than one million motorcycles are sold annually (www.webbikeworld.com). Off-road motorcycles(often called “dirt bikes”) are a market segment (about 18%) that is highly specialized and offers great variation in features. This makes it a good segment to study to learn about
=+c) Is the amount of money spent per student statistically significant in predicting whether or not the school is a university? Explain.
=+b) Is percent of students in the top 10% of their high school class statistically significant in predicting whether or not the school is a university? Explain.
=+a) Write out the estimated regression equation.
=+*40. Cost of higher education. Are there fundamental differences between liberal arts colleges and universities? In this case, we have information on the top 25 liberal arts colleges and the top 25 universities in the United States. We will consider the type of school as our response variable
=+e) What is the associated predicted probability?
=+d) What is the predicted log odds (logit) of the probability that a 60-year-old patient with an HDRS score of 8 will drop out of the study?
=+c) What is the predicted dropout probability of that patient?
=+b) What is the predicted log odds (logit) of the probability that a 30-year-old patient with an HDRS score of 30 will drop out of the study?
=+a) Write out the estimated regression equation.
=+Here is the output from a logistic regression model of Drop on HRDS and Age.Term Estimate Std Error z P-Value Intercept 0.441972938 0.488270354 0.9055 0.3654 AGE 0.037904831 0.011511729 3.292 0.001 HDRS -0.046817607 0.015903137 2.944 0.0032
=+* 39. Clinical trials. An important challenge in clinical trials is patients who drop out before the trial is completed.This can cost pharmaceutical companies millions of dollars because patients who have received a tested treatment for months must be combined with those who received it for a
=+c) Does it seem that Wal-Mart’s revenue is closely related to the general state of the economy?
=+b) Identify and remove the four cases corresponding to December revenue and find the regression with December results removed.
=+a) Plot the residuals against the predicted values and comment on what you see.M17_SHAR8696_03_SE_C17.indd 620 14/07/14 7:38 AM Exercises 621
=+38. Wal-Mart revenue, part 3. Consider the model you fit in Exercise 37 to predict Wal-Mart’s revenue from the Retail Index, CPI, and Personal Consumption index.
=+b) Does it seem that Wal-Mart’s revenue is closely related to the general state of the economy?
=+a) Using computer software, find the regression equation predicting Wal-Mart revenues from the Retail Index, the Consumer Price index (CPI), and Personal Consumption.
=+37. Wal-Mart revenue, part 2. Wal-Mart is the second largest retailer in the world. The data file on the disk holds monthly data on Wal-Mart’s revenue, along with several possibly related economic variables.
=+d) What effects do your observation in response to part b have on your test in part c?
=+c) State and test the standard null hypothesis for the coefficient of Expected Years of Schooling. Use the standard-level of a = 0.05 and state your conclusion.
=+b) Are the assumptions and conditions met?
=+a) Write the regression model.
=+live births) -0.000120 0.0000254 -4.74 60.0001 Mean years of schooling of adults(years) 0.01686 0.00166 10.19 60.0001 Population urban (%) 0.000745 0.000181 4.13 60.0001 GDP Per Capita 0.0000008020.000000263 3.05 0.003 Cell phones/100 people 0.000460 0.000141 3.26 0.0016–0.06 Residuals
=+36. HDI. In 1990, the United Nations created a single statistic, the Human Development Index or HDI, to summarize the health, education, and economic status of countries.Using data from 96 countries, here is a multiple regression model trying to predict HDI.Dependent variable is: HDI R squared =
=+e) This model has an adjusted R2 of 93.8%. The previous model of Chapter 16, Exercise 56, had an adjusted R2 of 91.6%. What does adjusted R2 say about the two models?
=+d) Does the coefficient of Pounds/Trap mean that when the pounds per trap declines the price will increase?
=+c) State and test the standard null hypothesis for the coefficient of Pounds/Trap. Use the standard a-level of .05 and state your conclusion.
=+b) Are the assumptions and conditions met?
=+a) Write the regression model.
=+35. Lobster industry 2012, revisited, part 2. In Chapter 16, Exercise 54 predicted the price ($/lb) of lobster harvested in the Maine lobster fishing industry. Here’s a multiple regression to predict the Price from the number of Traps(millions), the number of Fishers, and Pounds/Trap during the
=+d) State and test the standard null hypothesis for the coefficient of Pounds/Trap. Scientists claim that this is an important predictor of the harvest. Do you agree?
=+c) Interpret the coefficient of Fishers. Would you expect that restricting the number of lobstering licenses to even fewer fishers would increase the value of the harvest?
=+b) Are the assumptions and conditions met?
=+a) Write the regression model.
=+logarithms. Here’s a more sophisticated multiple regression to predict the logValue from other variables published by the Maine Department of Marine Resources (maine.gov/dmr). The predictors are number of Traps (millions), number of licensed Fishers, and Pounds/Trap during the years 1957 to
=+34. Lobster industry 2012, revisited. In Chapter 16, Exercise 53 predicted the annual value of the Maine lobster industry catch from the number of licensed lobser fishers. The lobster industry is an important one in Maine, with annual landings worth about $300,000,000 and employment
=+c) Explain how the slope of Primary completion rate can now be negative.
=+b) Explain why you are not surprised that the sign of the slope is positive.The researcher adds two variables to the regression and finds:Dependent variable is: GDP per Capita R squared = 80.00%s = 7327.65 with 96 - 4 = 92 df Term Estimate SE(Coeff) t-Ratio P-value Intercept 2775.98251 2803.32606
=+a) Explain to the researcher why, on the basis of the regression summary, she might want to consider other predictor variables in the model.
=+. Gross domestic product. The gross domestic product(GDP) is an important measure of the overall economic strength of a country. GDP per capita makes comparisons between different size countries more meaningful. A researcher looking at GDP, fit the following model based on an educational
=+c) Test the standard null hypothesis for the coefficient of CPI and state your conclusions.
=+b) Interpret the coefficient of the Consumer Price Index(CPI). Does it surprise you that the sign of this coefficient is negative? Explain.
=+a) Write the regression model.
=+. Wal-Mart revenue. Here’s a regression of monthly revenue of Wal-Mart Corp, relating that revenue to the Total U.S. Retail Sales, the Personal Consumption Index, and the Consumer Price Index.Dependent variable is: Wal-Mart_Revenue R squared = 66.7% R squared (adjusted) = 63.8%s = 2.327 with
=+e) A correlation of age with salary finds r = 0.682, and the scatterplot shows a moderately strong positive linear association. However, if X6 = Age is added to the multiple regression, the estimated coefficient of age turns out to be b6 = -0.154. Explain some possible causes for this apparent
=+d) How might this model be improved?
=+c) Test whether the coefficient for words per minute of typing speed (X4) is significantly different from zero at a = 0.05.
=+b) From this model, what is the predicted salary (in thousands of dollars) of a secretary with 10 years (120 months)of experience, 9th grade education (9 years of education), 50 on the standardized test, 60 wpm typing speed, and the ability to take 30 wpm dictation?
=+a) What is the regression equation?
=+Assume that the residual plots show no violations of the conditions for using a linear regression model.
=+A multiple regression model with all five variables was run on a computer package, resulting in the following output.Variable Coeff Std. Error t-value Intercept 9.788 0.377 25.960 X1 0.110 0.019 5.178 X2 0.053 0.038 1.369 X3 0.071 0.064 1.119 X4 0.004 0.0307 0.013 X5 0.065 0.038 1.734 s = 0.430
=+31. Secretary performance. The AFL-CIO has undertaken a study of 30 secretaries’ yearly salaries (in thousands of dollars). The organization wants to predict salaries from several other variables. The variables to be considered potential predictors of salary are:X1 = months of service X2 =
=+30. Home prices, part 2. Here are some diagnostic plots for the home prices data from Exercise 29. These were generated by a computer package and may look different from the plots generated by the packages you use. (In particular, note that the axes of the Normal probability plot are swapped
=+Is it true that the number of bathrooms is unrelated to house price? (Hint: Do you think bigger houses have more bathrooms?)
=+d) The owner of a construction firm, upon seeing this model, objects because the model says that the number of bathrooms has no effect on the price of the home. He says that when he adds another bathroom, it increases the value.
=+c) Explain in context what the coefficient of Area means.
=+b) How much of the variation in home asking prices is accounted for by the model?
=+a) Write the regression equation.
=+Dependent Variable is: Asking Price s = 67013 R-Sq = 71.1% R-Sq(adj) = 64.6%Predictor Coeff SE(Coeff) t-ratio P-value Intercept -152037 85619 -1.78 0.110 Baths 9530 40826 0.23 0.821 Area 139.87 46.67 3.00 0.015 Analysis of Variance Source DF SS MS F P-value Regression 2 99303550067 49651775033
=+29. Home prices. Many variables have an impact on determining the price of a house. A few of these are size of the house (square feet), lot size, and number of bathrooms.Information for a random sample of homes for sale in the Statesboro, Georgia, area was obtained from the Internet.Regression
=+c) If GDP/Capita(1988) is removed as a predictor, then the F-statistic drops to 0.694 and none of the t-statistics is significant (all P-values 7 0.22). Reconsider your interpretation in part a.
=+b) The F-statistic for this model is 129.61 (5, 17 df). What do you conclude about the model?
=+) The researchers hoped to show that more regulation leads to lower GDP/Capita. Does the coefficient of the OECD Economic Regulation Index demonstrate that? Explain.
=+GDP>Capita11998920022 = 10487 - 1343 OECD Economic Regulation Index + 1.078 GDP>Capita119882- 69.99 Ethno@linguistic Diversity Index+ 44.71 Trade as share of GDP 11998920022- 58.4 Primary Education1%Eligible Population2 All t-statistics on the individual coefficients have P-values 6 0.05, except
=+28. OECD economic regulations. A study by the U.S. Small Business Administration used historical data to model the GDP per capita of 24 of the countries in the Organization for Economic Cooperation and Development (OECD)(Crain, M. W., The Impact of Regulatory Costs on Small Firms, available at
=+) The model uses the (natural) logarithms of the two predictors. What does the use of this transformation say about their effects on pollution abatement costs?
=+) The coefficient of ln(Number of Employees) is negative.What does that mean in the context of this model? What does it mean that the coefficient of ln(Sales) is positive?
=+27. Cost of pollution. What is the financial impact of pollution abatement on small firms? The U.S. government’s Small Business Administration studied this and reported the following model.Pollution abatement>employee = -2.494 - 0.431 ln1Number of Employees2 + 0.698 ln1Sales2 Pollution
=+d) Each dollar increase in the price of wine increases its tasting score by 1.22.
=+c) Each year a bottle of wine ages, its tasting score increases by 1.22.
=+b) The price for a bottle of wine increases on average about$.55 for each year it ages, after allowing for the effects of tasting score.
=+a) The minimum price for a bottle of wine that has not aged is $6.25.
=+. Wine prices, part 2. Here are some more interpretations of the regression model to predict the price of wine developed in Exercise 24. One of these interpretations is correct. Which is it? Explain what is wrong with the others.
=+d) Every million dollars spent on TV advertising increases sales by $6.75 million, after allowing for the effects of other kinds of advertising.M17_SHAR8696_03_SE_C17.indd 616 14/07/14 7:38 AM Exercises 617
=+c) Every million dollars spent on radio advertising increases sales by $2.5 million.
=+b) Every million dollars spent on internet advertising increases sales by $2.3 million.
=+a) If the company did no advertising at all, then income would be $150 million.
=+25. Advertising and sales. A local dairy product company wants to know the correlation between the amount of money spent on advertising (Internet, TV, radio) and their sales (in millions of $). They found the following regression equation.Sales = 150 + 6.75 TV + 2.5 Radio + 2.3 Internet One of
=+d) After allowing for the age of a bottle of wine, a wine with a one unit higher tasting score can be expected to cost about $1.22 more.
=+c) For a unit increase in tasting score, the price of a bottle of wine increases about $1.22.
=+b) This model fits 65% of the points exactly.
=+a) Each year a bottle of wine ages, its price increases about$.55.
=+24. Wine prices. Many factors affect the price of wine, including such qualitative characteristics as the variety of grape, location of winery, and label. Researchers developed a regression model considering two quantitative variables:the tasting score of the wine and the age of the wine (in
=+d) This model fits 90% of the data points exactly.
=+c) Every additional dollar in price means lot size increases.
=+b) For a home with a given lot size and age, the expected extra price of the home for every additional square foot is$85.3.
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