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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) Some of the residuals from a least squares linear model will be positive and some will be negative.b) Least Squares means that some of the squares of the residuals are minimized.
=+c) We write yn to denote the predicted values and y to denote the observed values.Section 4.6
=+11. For the bookstore sales data in Exercise 1, the correlation of number of sales people and sales is 0.965.
=+a) If the number of people working is 2 standard deviations above the mean, how many standard deviations above or below the mean do you expect sales to be?
=+b) What value of sales does that correspond to?c) If the number of people working is 1 standard deviation below the mean, how many standard deviations above or below the mean do you expect sales to be?
=+d) What value of sales does that correspond to?
=+12. For the hard drive data in Exercise 2, some research on the prices discovered that the 200 GB hard drive was a special “hardened” drive designed to resist physical shocks and work under water. Because it is completely different from the other drives, it was removed from the data. For the
=+a) If a drive has a capacity of 3.046 TB (or 1 SD above the mean of 1.531 TB), how many standard deviations above or below the mean price of $110.70 do you expect the drive to cost?
=+b) What price does that correspond to?
=+13. For the bookstore of Exercise 1, the manager wants to predict Sales from Number of Sales People Working.a) Find the slope estimate, b1.
=+b) What does it mean, in this context?
=+c) Find the intercept, b0.
=+d) What does it mean, in this context? Is it meaningful?e) Write down the equation that predicts Sales from Number of Sales People Working.
=+f) If 18 people are working, what Sales do you predict?
=+g) If sales are actually $25,000 when 18 people are working, what is the value of the residual?h) Have we overestimated or underestimated the sales?
=+14. For the disk drives in Exercise 2 (as corrected in Exercise 12), we want to predict Price from Capacity.
=+a) Find the slope estimate, b1.b) What does it mean, in this context?c) Find the intercept, b0.d) What does it mean, in this context? Is it meaningful?
=+e) Write down the equation that predicts Price from Capacity.
=+f) What would you predict for the price of a 3.0 TB disk?g) You have found a 3.0 TB drive for $175. Is this a good
=+buy? How much would you save compared to what you expected to pay?h) Did the model overestimate or underestimate the pricing?Section 4.7
=+16. An online investment blogger advises investing in mutual funds that have performed badly the past year because“regression to the mean tells us that they will do well next year.” Is he correct?Section 4.8
=+17. Here are the residuals for a regression of Sales on Number of Sales People Working for the bookstore of Exercise 1:Sales People Working Residual 2 0.07 3 0.16 7 -1.49 9 -2.32 10 0.77 10 2.77 12 0.94 15 0.20 16 -0.72 20 -0.37
=+a) What are the units of the residuals?
=+b) Which residual contributes the most to the sum that was
=+minimized according to the Least Squares Criterion to find this regression?
=+c) Which residual contributes least to that sum?
=+18. Here are residual plots (residuals plotted against predicted values) for three linear regression models. Indicate which condition appears to be violated (linearity, outlier, or equal spread) in each case.a)–10 0 10 20 30 40 50 60 70 15 10 50–5–10 Predicted Value Residual b)15.0 17.5
=+c)100 200 300 400 500 600 700 200 100 0–100–200 Predicted Value Residual Section 4.9
=+19. For the regression model for the bookstore of Exercise 1,
=+what is the value of R2 and what does it mean?
=+20. For the disk drive data of Exercise 2 (as corrected in Exercise 12), find and interpret the value of R2.Section 4.11
=+21. When analyzing data on the number of employees in small companies in one town, a researcher took square roots of the counts. Some of the resulting values, which are reasonably symmetric were:4, 4, 6, 7, 7, 8, 10
=+What were the original values, and how are they distributed?
=+22. You wish to explain to your boss what effect taking the base-10 logarithm of the salary values in the company’s database will have on the data. As simple, example values you compare a salary of $10,000 earned by a part-time
=+shipping clerk, a salary of $100,000 earned by a manager, and the CEO’s $1,000,000 compensation package. Why might the average of these values be a misleading summary? What would the logarithms of these three values be?Chapter Exercises
=+23. Association. Suppose you were to collect data for each
=+pair of variables.You want to make a scatterplot.Which variable would you use as the explanatory variable and which as the response variable? Why? What would you expect to see in the scatterplot? Discuss the likely direction and form.
=+a) Cell phone bills: number of text messages, cost.b) Automobiles: Fuel efficiency (mpg), sales volume(number of autos).c) For each week: Ice cream cone sales, air conditioner sales.d) Product: Price ($), demand (number sold per day).
=+24. Association, part 2. Suppose you were to collect data for each pair of variables. You want to make a scatterplot.Which variable would you use as the explanatory variable and which as the response variable? Why? What would you expect to see in the scatterplot? Discuss the likely direction and
=+b) Real estate: house price, house size (square footage).c) Economics: Interest rates, number of mortgage applications.d) Employees: Salary, years of experience.25. Scatterplots. Which of the scatterplots show:a) Little or no association?b) A negative association?c) A linear association?d) A
=+26. Scatterplots, part 2. Which of the scatterplots show:a) Little or no association?b) A negative association?c) A linear association?d) A moderately strong association?e) A very strong association?(1) (2)(3) (4)
=+27. Manufacturing. A ceramics factory can fire eight large batches of pottery a day. Sometimes a few of the pieces break in the process. In order to understand the problem better, the factory records the number of broken pieces in each batch for three days and then creates the scatterplot shown.
=+a) Make a histogram showing the distribution of the number of broken pieces in the 24 batches of pottery examined.
=+b) Describe the distribution as shown in the histogram.
=+What feature of the problem is more apparent in the histogram than in the scatterplot?
=+c) What aspect of the company’s problem is more apparent in the scatterplot?
=+28. Coffee sales. Owners of a new coffee shop tracked sales for the first 20 days and displayed the data in a scatterplot(by day).a) Make a histogram of the daily sales since the shop has been in business.
=+b) State one fact that is obvious from the scatterplot, but not from the histogram.c) State one fact that is obvious from the histogram, but not from the scatterplot.
=+29. Matching. Here are several scatterplots. The calculated correlations are -0.923, -0.487, 0.006, and 0.777. Which is which?(a) (b)(c) (d)
=+30. Matching, part 2. Here are several scatterplots. The calculated correlations are -0.977, -0.021, 0.736, and 0.951.Which is which?(a) (b)(c) (d)
=+31. Pizza sales and price. A linear model fit to predict weekly Sales of frozen pizza (in pounds) from the average Price($/unit) charged by a sample of stores in the city of Dallas in 39 recent weeks is:Sales = 141,865.53 - 24,369.49 Price.a) What is the explanatory variable?
=+b) What is the response variable?c) What does the slope mean in this context?
=+d) What does the y-intercept mean in this context? Is it meaningful?
=+e) What do you predict the sales to be if the average price charged was $3.50 for a pizza?
=+f) If the sales for a price of $3.50 turned out to be 60,000 pounds, what would the residual be?
=+32. Student skills surplus. According to the OECD’s How’s life? 2013 study, the dimension of education and skills consists of three different indicators: ‘Educational attainment’,‘Student skills’, and ‘Years in education’. A linear model to predict Student skills from Years in
=+a) What is the explanatory variable?
=+b) What is the response variable?
=+c) What does the slope mean in this context?
=+d) What does the y-intercept mean in this context? Is it meaningful?
=+e) What do you predict average student skills to be for South Korea, with on average 17.7 years of education?
=+f) In fact, South Korea students achieve an average student skills score of 541 after staying on average 17.7 years in education. What is the residual?
=+g) How would you judge the quality of the South Korean educational system in preparing its students for the labor market, in comparison to other OECD countries? Explain.
=+33. Football salaries 2013. Is there a relationship between total team salary and the performance of teams in the National Football League (NFL)? For the 2012–2013 season, a linear model predicting Wins (out of 16 regular season games) from the total team Salary ($M) for the 32 teams in the
=+a) What is the explanatory variable?
=+b) What is the response variable?
=+c) What does the slope mean in this context?
=+d) What does the y-intercept mean in this context? Is it meaningful?
=+e) If one team spends $10 million more than another on salary, how many more games on average would you predict them to win?
=+f) If a team spent $120 million on salaries and won 8 games, would they have done better or worse than predicted?
=+g) What would the residual of the team in part f be?
=+h) The residual standard deviation is 2.78 games.What does that tell you about the likely practical use of this model for predicting wins?
=+34. Baseball salaries 2012. In 2012, the New York Yankees won 95 games and spent $198 million on salaries for their players (USA Today). Is there a relationship between salary and team performance in Major League Baseball? For the 2012 season, a linear model fit to the number of Wins (out of 162
=+a) What is the explanatory variable?
=+b) What is the response variable?
=+c) What does the slope mean in this context?
=+d) What does the y-intercept mean in this context? Is it meaningful?
=+e) If one team spends $10 million more than another on salaries, how many more games on average would you predict them to win?
=+f) If a team spent $110 million on salaries and won half (81)of their games, would they have done better or worse than predicted?
=+g) What would the residual of the team in part f be?h) The R2
=+ for this model is 2.05% and the residual standard deviation is 12.0 games. How useful is this model likely to be for predicting the number of wins?
=+35. Pizza sales and price, part 2. For the data in Exercise
=+31, the average Sales was 52,697 pounds (SD = 10,261 pounds), and the correlation between Price and Sales was= -0.547. If the Price in a particular week was one SD higher than the mean Price, how much pizza would you predict was sold that week?
=+36. Student skills surplus, part 2. The 36 countries in Exercise 32 had an average score for ‘Student skills’ of 493.25(SD = 30.285), and the correlation between ‘Student skills’and ‘Years in education’ was 0.633. In Chile, students stay an average of 16.2 years in education, which
=+37. Packaging. A CEO announces at the annual shareholders meeting that the new see-through packaging for the company’s flagship product has been a success. In fact, he says, “There is a strong correlation between packaging and sales.” Criticize this statement on statistical grounds.
=+38. Insurance. Insurance companies carefully track claims histories so that they can assess risk and set rates appropriately. The National Insurance Crime Bureau reports that Honda Accords, Honda Civics, and Toyota Camrys are the cars most frequently reported stolen, while Ford Tauruses, Pontiac
=+39. Sales by region. A sales manager for a major pharmaceutical company analyzes last year’s sales data for her 96 sales representatives, grouping them by region (1 = East Coast United States; 2 = Mid West United States; 3 = West United States; 4 = South United States; 5 = Canada;6 = Rest of
=+200 1 2 3 4 5 6 400 600 800 1000 Total Sales 2008 ($ 1000)Region She fits a regression to the data and finds:Sales = 1002.5 - 102.7 Region The R2 is 70.5%.
=+Write a few sentences interpreting this model and describing what she can conclude from this analysis.
=+40. Salary by job type. At a small company, the head of human resources wants to examine salary to prepare annual reviews. He selects 28 employees at random with job types ranging from 01 = Stocking clerk to 99 = President. He plots Salary ($) against Job Type and finds a strong linear
=+20 40 60 80 100 Salary Job Type The regression output gives:Salary = 15827.9 + 1939.1 Job Type Write a few sentences interpreting this model and describing what he can conclude from this analysis.
=+41. Carbon footprint 2013. The scatterplot shows, for 2013 cars, the carbon footprint (tons of CO2 per mile) vs. the new Environmental Protection Agency (EPA) highway mileage for 76 family sedans as reported by the U.S.
=+government (www.fueleconomy.gov/feg/byclass.htm).There are seven cars (two points in the scatterplot are pairs of overlapping cars) with high highway mpg and low carbon footprint. They are all hybrids.Highway mpg 25 30 35 40 45 225 300 375 450 Carbon Footprint
=+a) The correlation is -0.959. Describe the association.
=+b) Are the assumptions and conditions met for computing correlation?
=+c) Using technology, find the correlation of the data when the hybrid cards are not included with the others. Can you explain why it changes in that way?
=+42. EPA mpg 2013. In 2008, the EPA revised their methods for estimating the fuel efficiency (mpg) of cars—a factor that plays an increasingly important role in car sales. How do the new highway and city estimated mpg values relate to each other? Here’s a scatterplot for 76 family sedans as
=+a) The correlation of these two variables is 0.896. Describe the association.
=+b) If the hybrids were removed from the data, what would you expect to happen to the slope (increase, decrease, or stay pretty much the same) and to the correlation (increase, decrease, the same)? Try it using technology. Report and discuss what you find.
=+43. Real estate. Is the number of total rooms in the house associated with the price of a house? Here is the scatterplot of a random sample of homes for sale:6 54 32 10 Homes for Sale Rooms 5.0 10.0 15.0 Price ($000,000)a) Is there an association?
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