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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
=+b) Check the assumptions and conditions for correlation.
=+44. Economic analysis 2012. An economics student is studying the American economy and finds that the correlation between the inflation-adjusted Dow Jones Industrial Average and the Gross Domestic Product(GDP) (also inflation adjusted) is 0.81 for the years 1946 to 2011. (www.measuringworth.com).
=+the two series and predicts that a drop in the GDP will make the stock market go down. Here is a scatterplot of the adjusted DJIA against the GDP (in the years 1946 to 2011). Describe the relationship and comment on the student’s conclusions.2,000 2.0e + 06 Inflation Adjusted Dow Jones Yearly
=+45. GDP growth 2012. Is economic growth in the developing world related to growth in the industrialized countries?Here’s a scatterplot of the growth (in % of Gross Domestic Product) of 180 developing countries vs. the growth of 33 developed countries as grouped by the World Bank
=+one of the years from 1970 to 2011. The output of a regression analysis follows Dependent variable: GDP Growth Developing Countries R2 = 31.64%s = 1.201 Variable Coefficient Intercept 3.38 GDP Growth Developed Countries 0.468a) Check the assumptions and conditions for the linear model.
=+b) Explain the meaning of R2 in this context.c) What are the cases in this model?
=+46. European GDP growth 2012. Is economic growth in Europe related to growth in the United States? Here’s a scatterplot of the average growth in 25 European countries(in % of Gross Domestic Product) vs. the growth in the United States. Each point represents one of the years from 1970 to
=+a) Check the assumptions and conditions for the linear model.
=+b) Explain the meaning of R2 in this context.
=+47. GDP growth 2012, part 2. From the linear model fit to the data on GDP growth in Exercise 45:
=+a) Write the equation of the regression line.
=+b) What is the meaning of the intercept? Does it make sense in this context?
=+c) Interpret the meaning of the slope.
=+d) In a year in which the developed countries grow 4%, what do you predict for the developing world?
=+e) In 2007, the developed countries experienced a 2.65%growth, while the developing countries grew at a rate of 6.09%. Is this more or less than you would have predicted?
=+f) What is the residual for this year?
=+48. European GDP growth 2012, part 2. From the linear model fit to the data on GDP growth of Exercise 46:
=+a) Write the equation of the regression line.
=+b) What is the meaning of the intercept? Does it make sense in this context?
=+c) Interpret the meaning of the slope.d) In a year in which the United States grows at 0%, what
=+do you predict for European growth?e) In 2010, the United States experienced a 3.00% growth, while Europe grew at a rate of 1.78%. Is this more or less than you would have predicted?
=+f) What is the residual for this year?
=+49. Attendance 2012. American League baseball games are played under the designated hitter rule, meaning that weak-hitting pitchers do not come to bat. Baseball owners believe that the designated hitter rule means more runs scored, which in turn means higher attendance. Is there evidence that
=+both major leagues during the 2012 season have a correlation of 0.477 between Runs Scored and the Home Attendance(espn.go.com/mlb/attendance).600 650 700 750 800 3,500,000 2,500,000 3,000,000 1,500,000 2,000,000 Runs Scored Attendance
=+a) Does the scatterplot indicate that it’s appropriate to calculate a correlation? Explain.
=+b) Describe the association between attendance and runs scored.
=+c) Does this association prove that the owners are right that more fans will come to games if the teams score more runs?
=+50. Attendance 2012, part 2. Perhaps fans are just more interested in teams that win. Here are displays of other variables in the dataset of exercise 49 (espn.go.com). Are the teams that win necessarily those that score the most runs?Correlation Wins Runs Attend Wins 1.000 Runs 0.437 1.000 Attend
=+a) Do winning teams generally enjoy greater attendance at their home games? Describe the association.
=+b) Is attendance more strongly associated with winning or scoring runs? Explain.
=+c) How strongly is scoring more runs associated with winning more games?
=+51. Mutual fund flows. As the nature of investing shifted in the 1990s (more day traders and faster flow of information using technology), the relationship between mutual fund monthly performance (Return) in percent and money flowing (Flow) into mutual funds ($ million) shifted. Using only the
=+a) Interpret the intercept in the linear model.b) Interpret the slope in the linear model.c) What is the predicted fund Flow for a month that had a market Return of 0%?
=+d) If during this month, the recorded fund Flow was$5 billion, what is the residual using this linear model? Did the model provide an underestimate or overestimate for this month?
=+52. Online clothing purchases. An online clothing retailer examined their transactional database to see if total yearly Purchases ($) were related to customers’ Incomes ($). (You may assume that the assumptions and conditions for regression are met.)The least squares linear regression
=+a) Interpret the intercept in the linear model.b) Interpret the slope in the linear model.c) If a customer has an Income of $20,000, what is his predicted total yearly Purchases?d) This customer’s yearly Purchases were actually $100.What
=+is the residual using this linear model? Did the model provide an underestimate or overestimate for this customer?
=+53. Residual plots. Tell what each of the following residual plots indicates about the appropriateness of the linear model that was fit to the data.
=+a)b) c)
=+54. Residual plots, again. Tell what each of the following residual plots indicates about the appropriateness of the linear model that was fit to the data.a)b) c)
=+55. Consumer spending. An analyst at a large credit card bank is looking at the relationship between customers’ charges to the bank’s card in two successive months. He selects 150 customers at random, regresses charges in March ($) on charges in February ($), and finds an R2 of 79%. The
=+56. Insurance policies. An actuary at a mid-sized insurance company is examining the sales performance of the company’s sales force. She has data on the average size of the policy ($) written in two consecutive years by 200 salespeople. She fits a linear model and finds the slope to be 3.00
=+ is 99.92%. She concludes that the predictions for next year’s policy size will be very accurate. Examine the data on the CD and comment on her conclusions.
=+57. What slope? If you create a regression model for predicting the sales ($ million) from money spent on advertising the prior month ($ thousand), is the slope most likely to be closer to 0.03, 300, or 3000? Explain.
=+58. What slope, part 2? If you create a regression model for estimating a student’s business school GPA (on a scale of 1–5) based on his math SAT (on a scale of 200–800), is the slope most likely to be closer to 0.01, 1, or 10? Explain.
=+59. Misinterpretations. An advertising agent who created a regression model using amount spent on Advertising to predict annual Sales for a company made these two statements. Assuming the calculations were done correctly, explain what is wrong with each interpretation.a) My R2 of 93% shows that
=+b) If this company spends $1.5 million on advertising, then annual sales will be $10 million.
=+60. More misinterpretations. An economist investigated the association between a country’s Literacy Rate and Gross Domestic Product (GDP) and used the association to draw the following conclusions. Explain why each statement is incorrect. (Assume that all the calculations were done properly.)
=+a) The Literacy Rate determines 64% of the GDP for a country.b) The slope of the line shows that an increase of 5% in Literacy Rate will produce a $1 billion improvement in GDP.
=+61. Business admissions. An analyst at a business school’s admissions office claims to have developed a valid linear model predicting success (measured by starting salary ($) at time of graduation) from a student’s undergraduate performance (measured by GPA). Describe how you would check
=+62. School rankings. A popular magazine annually publishes rankings of both U.S. business programs and international business programs. The latest issue claims to have developed a linear model predicting the school’s ranking (with
=+“1” being the highest ranked school) from its financial resources (as measured by size of the school’s endowment).Describe how you would apply each of the four regression conditions in this context.
=+63. Rooms per person. Personal earnings and favorable living conditions are both among contributors to well-being.The numbers of rooms per person is one of these living conditions. But in order to allow oneself a spacious house, adequate personal earnings are needed. These two variables thus
=+34 OECD countries, Russia, and Brazil.a) Make a scatterplot relating the number of rooms per person to personal earnings.
=+b) Describe the association between the two variables.c) Do you think a linear model is appropriate?d) Computer software says that R2 = 58.1%. What is the correlation between number of rooms per person and personals earnings?
=+e) Explain the meaning of R2 in this context.
=+f) Why doesn’t this model explain 100% of the variability in number of rooms per person?
=+64. Rooms per person, part 2. Use the OECD data on number of rooms per person and personals earnings to create a linear model for the relationship between Rooms per person and Personals earnings.
=+a) Find the equation of the regression line.
=+b) Explain the meaning of the slope of the line.
=+c) Explain the meaning of the intercept of the line.
=+d) Amongst all OECD countries, what living conditions may
=+a household expect with personal earnings equal to $45,000?
=+e) Would you prefer to live in a country having a positive residual in this regression equation, or a country with a negative residual, if other circumstances are comparable?
=+65. Expensive cities. The Worldwide Cost of Living Survey City Rankings determine the cost of living in the most expensive cities in the world as an index. This index scales New York City as 100 and expresses the cost of living in other cities as a percentage of the New York cost. For example,
=+a) Describe the association between cost of living indices in 2007 and 2013.b) The R2 for the regression equation is 0.070. Interpret the value of R2.c) Find the correlation.d) Using the data provided, find the least squares fit of the 2013 index to the 2007 index.
=+e) Predict the 2013 cost of living index of Moscow and find its residual.
=+66. Lobster prices 2012. The demand for lobster has grown steadily for several decades. The Maine lobster fishery is carefully controlled to protect the lobster population from over-fishing. The number of fishing licenses and the number of traps are both limited. During the years from 1974 to
=+The years from 2007 to 2012 have seen a change in this pattern. Here is the scatterplot.2 34 5Price/lb 1980 1990 2000 2010 Yeare) How would you suggest dealing with these new cases to model the change in prices?
=+67. El Niño. Concern over the weather associated with El Niño has increased interest in the possibility that the climate on Earth is getting warmer. The most common theory relates an increase in atmospheric levels of carbon dioxide 1CO22, a greenhouse gas, to increases in temperature. Here is a
=+A regression predicting Mean Temperature from CO2 produces the following output table (in part).Dependent variable: Temperature R-squared = 33.4%Variable Coefficient Intercept 15.3066 CO2 0.004
=+a) What is the correlation between CO2 and Mean Temperature?
=+b) Explain the meaning of R-squared in this context.
=+c) Give the regression equation.
=+d) What is the meaning of the slope in this equation?
=+e) What is the meaning of the intercept of this equation?
=+f) Here is a scatterplot of the residuals vs. CO2. Does this plot show evidence of the violations of any of the assumptions of the regression model? If so, which ones?–0.075 0.000 0.075 325.0 337.5 350.0 CO2(ppm)Residuals g) CO2 levels may reach 364 ppm in the near future. What Mean
=+68. U.S. birthrates. The table shows the number of live births per 1000 women aged 15–44 years in the United States, starting in 1965. (National Center for Health Statistics, www.cdc.gov/nchs/)Year 1965 1970 1975 1980 1985 Rate 19.4 18.4 14.8 15.9 15.6 Year 1990 1995 2000 2005 2010 Rate 16.4
=+a) Make a scatterplot and describe the general trend in Birthrates. (Enter Year as years since 1900: 65, 70, 75, etc.)
=+b) Find the equation of the regression line.c) Check to see if the line is an appropriate model. Explain.
=+d) Interpret the slope of the line.e) The table gives rates only at 5-year intervals. Estimate
=+what the rate was in 1978.
=+f) In 1978, the birthrate was actually 15.0. What was the residual?
=+g) Predict what the Birthrate will be in 2012. Comment on your faith in this prediction.
=+h) Predict the Birthrate for 2050. Comment on your faith in this prediction.
=+• Is the age distribution of the clients a typical one found in most businesses?
=+ • Do people who give more often make smaller gifts on average?
=+ • Do people who give to other organizations tend to give to this organization?
=+Describe the relationship between the Income and Wealth rankings. How do you explain this relationship (or lack of one)? (Hint: Look at the age distribution.)
=+What variables (if any) seem to have an association with the Current Gift? Do you think the
=+organization can use any of these variables to predict the gift for the next campaign?
=+Optional: This file includes people who did not give to the current campaign. Do your answers to any of the questions above change if you consider only those who gave to this campaign?
=+1 It has been shown that the stock market fluctuates randomly. Nevertheless, some investors believe that they should buy right after a day when the market goes down because it is bound to go up soon. Explain why this is faulty reasoning.
=+What is the probability that a customer who enters the store will not make a purchase at all?
=+If we can assume that customers behave independently, what is the probability that the next two customers entering Lee’s Lights both make purchases?
=+When two customers enter the store together, what is the probability that at least one of them makes a purchase?
=+2 Even successful companies sometimes make products with high failure rates. One (in)famous example is the Apple 40GB click wheel iPod, which used a tiny disk drive for storage. According to Macintouch.com, 30% of those devices eventually failed. It is reasonable to assume that the failures were
=+a) What is the probability that a particular 40GB click wheel iPod failed?
=+b) What is the probability that two 40GB click wheel iPods sold together both failed?
=+c) What is the probability that the store’s first failure problem was the third one they sold?
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