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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
=+e) What is the equation of the regression line?
=+d) Is the association strong? Explain.
=+c) Is there evidence of a linear association between the highway mileage and the weight of the vehicle? Test an appropriate hypothesis and state your conclusion.
=+30. Automobiles. An editor for a major automobile magazine has collected data on the best-selling cars in the US.He is interested in the relationship between highway mileage and weight of the vehicles. Here are the regression and residual output, where the response variable is Mileage.Dependent
=+28. Assets and sales. A business analyst is looking at a company’s assets and sales to determine the relationship (if any)between the two measures. She has data (in $million) from a random sample of 79 Fortune 500 companies, and obtained the linear regression below:Predictor Coeff SE(Coeff)
=+27. Used cars, part 2. Based on the analysis of used car prices you did for Exercise 25, if appropriate, create a 95%confidence interval for the slope of the regression line and explain what your interval means in context.
=+f) The owner of a home measuring 2100 square feet files an appeal, claiming that the $270,000 assessed value is too high. Do you agree? Explain your reasoning.
=+e) From this analysis, can we conclude that adding a room to your house will increase its assessed value? Why or why not?
=+d) Give a 95% confidence interval for the slope of the true regression line, and explain its meaning in the proper context.
=+c) What percentage of the variability in assessed value is accounted for by this regression?
=+b) Is there a significant linear association between the Size of a home and its Assessment? Test an appropriate hypothesis and state your conclusion.
=+a) Explain why inference for linear regression is appropriate with these data.
=+26. Property assessments. The following software results provide information about the size (in square feet)of 12 homes in Montreal, Canada, and the city’s assessed value of those homes (in thousands of dollars), where the response variable is Assessment.Coefficients Standard Error t-Stat
=+d) Check the residuals to see if the conditions for inference are met.
=+c) Find the equation of the regression line.
=+b) Do you think a linear model is appropriate? Explain.
=+a) Make a scatterplot for these data.
=+b) Examine the residuals to determine if a linear regression is appropriate.M15_SHAR8696_03_SE_C15.indd 531 14/07/14 7:30 AM 532 CHAPTER 15 Inference for Regressionc) Test an appropriate hypothesis to determine if the association is significant.d) What percentage of the variability in
=+a) Find a regression model predicting unemployment from the inflation rate.
=+24. Unemployment. Using the unemployment data provided for this exercise on the website, investigate the association between unemployment and inflation rate for the 50 periods studied.
=+d) What percentage of the variability in the 2010 Index is accounted for by the regression model?
=+c) Test an appropriate hypothesis to determine if the association is significant.
=+b) Examine the residuals to determine if a linear regression is appropriate.
=+a) Find a regression model predicting the 2010 index from the index in 2007 for the sample of 43 countries provided by UNSD.
=+23. Retail trade index. The index of deflated turnover for retail trade shows the activity in volume of the retail trade sector. The United Nations Statistics Division reports Retail trade deflated sales/turnover (seasonally adjusted) with 2005 = 100. The datafile holds this index for 43
=+22. Mutual fund returns 2013. The brief case for Chapter 4 listed the rate of return for 92 mutual funds over the previous 3-year and 5-year periods. It’s common for advertisements to carry the disclaimer that “past returns may not be indicative of future performance.” Do these data
=+d) Interpret your interval in context.
=+c) Create a 95% confidence interval for the slope of the true line relating calcium concentration and mortality.
=+b) Assuming the assumptions for regression inference are met, what do you conclude?
=+a) Is there an association between the hardness of the water and the mortality rate? Write the appropriate hypothesis.
=+21. Water hardness. In an investigation of environmental causes of disease, data were collected on the annual mortality rate (deaths per 100,000) for males in 61 large towns in England and Wales. In addition, the water hardness was recorded as the calcium concentration (parts per million, or
=+b) Find a 95% confidence interval for the slope and interpret it.
=+a) Check the assumptions and conditions for inference.
=+20. House prices, part 2. Exercise 18 shows computer output examining the association between the sizes of houses and their sale prices.
=+b) Find a 95% confidence interval for the slope and interpret it.
=+a) Check the assumptions and conditions for inference.
=+19. Movie budgets, part 2. Exercise 17 shows computer output examining the association between the length of a movie and its cost.
=+e) Explain what that means in this context.
=+d) What’s the value of the standard error of the slope of the regression line?
=+c) The output reports s = 53.79. Explain what that means in this context.
=+b) The intercept is negative. Discuss its value, taking note of its P-value.
=+a) Explain in words and numbers what the regression says.
=+R-squared = 59.5%s = 53.79 with 1064 - 2 = 1062 degrees of freedom Variable Coefficient SE(Coeff) t-Ratio P-Value Intercept -3.1169 4.688 -0.665 0.5063 Size 94.4539 2.393 39.465 60.0001 M15_SHAR8696_03_SE_C15.indd 530 14/07/14 7:30 AM Exercises 531 300 150 0–150 125 250 375 500 Residuals
=+18. House prices. How does the price of a house depend on its size? Data from Saratoga, New York, on 1064 randomly selected houses that had been sold include data on price ($1000s) and size 11000 ft 22, producing the following graphs and computer output:800 600 400 200 1.25 2.50 3.75 5.00 Price
=+e) Explain what that means in this context.
=+d) What’s the value of the standard error of the slope of the regression line?
=+c) The output reports s = 32.95. Explain what that means in this context.
=+b) The intercept is negative. Discuss its value, taking note of the P-value.
=+a) Explain in words and numbers what the regression says.
=+17. Movie budgets. How does the cost of a movie depend on its length? Data on the cost (millions of dollars) and the running time (minutes) for major release films in one recent year are summarized in these plots and computer output:200 150 100 050 80 100 120 140 160 180 200 Budget ($M)Run Time
=+d) Do you think predictions made by this regression will be very accurate? Explain.
=+c) Find the t-value and P-value for the slope. Is there evidence of an association between CO2 level and global temperature? What do you know from the slope and t-test that you might not have known from the correlation?
=+b) Find the value of the correlation. Is there evidence of an association between CO2 level and global temperature?
=+a) Write the equation of the regression line.
=+16. Climate change. The Earth has been getting warmer.Most climate scientists agree that one important cause of the warming is the increase in atmospheric levels of carbon dioxide 1CO22, a greenhouse gas. Here is part of a regression analysis of the mean annual CO2 concentration in the
=+d) Check the residuals to see if the conditions for inference are met.
=+b) Do you think a linear model is appropriate? Explain.c) Find the equation of the regression line.
=+15. Family spending. A study would like to investigate the relationship between how much a family spends on recreation and its size. Do larger families spend more on recreation? Here are data showing the family size and the amount spent on recreation per week for a sample of 9 Canadian
=+c) Are these predictions likely to be useful? Explain.Chapter Exercises
=+b) Find a 95% prediction interval for the price of a 1 PB drive.
=+a) Disk drives keep growing in capacity. Some tech experts now talk about Petabyte 1PB = 1000 TB = 1,000,000 GB2 drives. What does this model predict that a Petabytecapacity drive will cost?
=+14. Look back at the prices for the external disk drives we saw in Exercise 10.The least squares line is Price = 15.112 + 62.417 Capacity.The assumptions and conditions for regression are met.SE1b12 = 11.328
=+c) Are these predictions likely to be useful? Explain.
=+b) Find a 95% prediction interval for the sales on a day with 500 employees working.
=+a) Find the predicted sales on a day with 500 employees working.
=+13. Recall the small bookstore we saw in Exercise 9.The regression line is:Sales = 8.10 + 0.9134 Number of Sales People Working and the assumptions and conditions for regression are met.Calculations with technology find that se = 1.477.
=+c) Which interval is of particular interest to the concessions manager? Which one is of particular interest to you, the moviegoer?Section 15.5
=+b) A 90% confidence interval for the mean of sales per person 10 minutes before the movie starts is ($6.65, $7.25).Explain how to interpret this interval.
=+a) A 90% prediction interval for sales to a concessions customer 10 minutes before the movie starts is ($4.60,$9.30). Explain how to interpret this interval.
=+12. In Exercise 5, we saw a regression to predict the sales per person at a movie theater in terms of the time (in minutes) before the show. The model was:Sales = 4.3 + 0.265 Minutes.
=+c) Now explain to her why these intervals are different.
=+a) A 95% prediction interval for a customer with a household income of $80,000 is ($35.60, $55.60). Explain to the restaurant owner how she should interpret this interval.b) A 95% confidence interval for the mean amount spent weekly to eat out by people with a household income of$80,000 is
=+11. A survey designed to study how much households spend on eating out finds the following regression model, EatOut $>wk = 17.28 + 0.354 HHIncome relating the amount respondents said they spent individually to eat out each week to their household income in$1000’s.
=+c) Find the 95% prediction interval for the Price of a 2 TB hard drive.Section 15.4
=+a) Find the predicted Price of a 2 TB hard drive.M15_SHAR8696_03_SE_C15.indd 528 14/07/14 7:30 AM Exercises 529b) Find a 95% confidence interval for the mean Price of 2 TB disk drives.
=+The least squares line was found to be: Price = 15.112 +62.417 Capacity with se = 42.037 and SE1b12 = 11.328.
=+10. The study of external disk drives from Chapter 4, exercise 2 (with the outlier removed) finds the following:Capacity (TB) Price ($)0.15 35 0.25 39.95 0.32 49.95 1 75 2 110 3 140 4 325 Mean 1.53 110.7 SD 1.51 102.05
=+b) Find a 95% confidence interval for the mean Sales on days that have 12 employees working.
=+a) Find the predicted Sales on a day with 12 employees working.
=+The regression line is:Sales = 8.10 + 0.9134 Number of Salespeople Working.The assumptions and conditions for regression are met, and from technology we learn that SE1b12 = 0.0873 se = 1.477
=+9. Here are data from a small bookstore.Number of Salespeople Working Sales (in $1000’s)2 10 3 11 7 13 9 14 10 18 10 20 12 20 15 22 16 22 20 26 x = 10.4 y = 17.6 SD1x2 = 5.64 SD1y2 = 5.34
=+For each of the regression assumptions, state whether it is satisfied, not satisfied, or can’t be determined from this plot.a) Linearityb) Independencec) Equal spreadd) Normal population Section 15.3
=+8. Here’s a scatterplot of the % of income spent on food versus household income for respondents to the Cornell National Social Survey:30 60 90 120 40 80 120 160 Household Income ($000)% Income Spent on Food
=+7. For the data from Exercise 1, which of the following conditions can you check from the scatterplot? Are satisfied?a) Linearityb) Independencec) Equal spreadd) Normal population
=+a) The standard deviation of the residualsb) The slope of the regression linec) The standard error of b1d) The P-value appropriate for testing H0: b1 = 0 versus HA: b1 ≠ 0e) Is the null hypothesis rejected at a = 0.05?Section 15.2
=+6. A soap manufacturer tested a standard bar of soap to see how long it would last. A test subject showered with the soap each day for 15 days and recorded the Weight (in grams) of the soap after the shower. The resulting regression computer output looks, in part, like this:Dependent variable
=+d) At a = 0.05, can the standard null hypothesis be rejected for the slope. Comment
=+) What is the p-value associated with t-statistic?
=+) What are the degrees of freedom associated with the t-statistic?
=+a) Compute the value of the t-statistic to test if there is a significant relationship between Sales and Minutes.
=+5. A set of 5 data observations for Sales per person ($) at a rodeo show gave the following estimated regression model Minutes before the show:Sales = 3.3 + 0.165 Minutes The standard error of the regression slope is 0.0345
=+4. For the regression of Exercise 2, find the standard error of the regression slope. Show all three values that go into the calculation.Exercises Nenana Fairbanks Tanana River M15_SHAR8696_03_SE_C15.indd 527 14/07/14 7:30 AM 528 CHAPTER 15 Inference for Regression
=+3. For the regression of Exercise 1, find the standard error of the regression slope. Show all three values that go into the calculation.
=+) Calculate the residual standard deviation, se.
=+a) Use the model to predict the correct responses for each number of training days.b) Find the residuals, ei.
=+2. A training center, wishing to demonstrate the effectiveness of their methods, tests some of their clients after different numbers of days of training, recording their scores on a sample test. Their data are:Training Days Correct Responses 1 4 4 6 8 7 10 9 12 10 The regression model they
=+c) Calculate the residual standard deviation, se.
=+a) Use the estimated regression equation to predict Rentals for all six values of Age.b) Find the residuals ei.
=+Make a scatterplot for these data. What does it tell you about the relationship between these two variables? From computer output, the regression line has b0 = 18.9 and b1 = -0.260.
=+1. A website that rents movies online recorded the age and the number of movies rented during the past month for some of their customers. Here are their data:Age Rentals 35 9 40 8 50 4 65 3 40 10 30 12
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