David’s Landscaping has collected data on home values (in thousands of $) and expenditures (in thousands of $) on landscaping with the hope of developing a predictive model to help marketing to potential new clients. Data for 14 households may be found in the file Landscape.
a. Develop a scatter diagram with home value as the independent variable.
b. What does the scatter plot developed in part (a) indicate about the relationship between the two variables?
c. Use the least squares method to develop the estimated regression equation.
d. For every additional $1000 in home value, estimate how much additional will be spent on landscaping.
e. Use the equation estimated in part (c) to predict the landscaping expenditures for a home valued at $575,000.
> The owner of Showtime Movie Theaters, Inc., would like to predict weekly gross revenue as a function of advertising expenditures. Historical data for a sample of eight weeks follow. a. Develop an estimated regression equation with the amount of televis
> The Tire Rack maintains an independent consumer survey to help drivers help each other by sharing their long-term tire experiences. The data contained in the file named TireRatings show survey results for 68 all-season tires. Performance traits are rated
> Over the past few years the percentage of students who leave Lakeland College at the end of the first year has increased. Last year Lakeland started a voluntary one-week orientation program to help first-year students adjust to campus life. If Lakeland i
> Community Bank would like to increase the number of customers who use payroll direct deposit. Management is considering a new sales campaign that will require each branch manager to call each customer who does not currently use payroll direct deposit. As
> In Table 15.12 we provided estimates of the probability of using the coupon in the Simmons Stores catalog promotion. A different value is obtained for each combination of values for the independent variables. a. Compute the odds in favor of using the cou
> A poll for the presidential campaign sampled 491 potential voters in June. A primary purpose of the poll was to obtain an estimate of the proportion of potential voters who favored each candidate. Assume a planning value of p* = .50 and a 95% confidence
> Refer to the Simmons Stores example introduced in this section. The dependent variable is coded as y = 1 if the customer used the coupon and 0 if not. Suppose that the only information available to help predict whether the customer will use the coupon is
> The Ladies Professional Golfers Association (LPGA) maintains statistics on performance and earnings for members of the LPGA Tour. Year-end performance statistics for 134 golfers for 2014 appear in the file named LPGA2014 (LPGA website, April 2015). Earn
> The following data show the curb weight, horsepower, and ¼-mile speed for 16 popular sports and GT cars. Suppose that the price of each sports and GT car is also available. The complete data set is as follows: a. Find the estimated regres
> Exercise 5 gave the following data on weekly gross revenue, television advertising, and newspaper advertising for Showtime Movie Theaters. a. Find an estimated regression equation relating weekly gross revenue to television and newspaper advertising. b
> Data for two variables, x and y, follow. a. Develop the estimated regression equation for these data. b. Compute the studentized deleted residuals for these data. At the .05 level of significance, can any of these observations be classified as an outli
> A shoe store developed the following estimated regression equation relating sales to inventory investment and advertising expenditures. ŷ = 25 + 10 x1 + 8 x2 where x1 = inventory investment ($1000s) x2 = advertising expenditures ($1000s) y = sales ($100
> Data for two variables, x and y, follow. a. Develop the estimated regression equation for these data. b. Plot the standardized residuals versus yˆ. Do there appear to be any outliers in these data? Explain. c. Compute the studentized deleted
> A 10-year study conducted by the American Heart Association provided data on how age, blood pressure, and smoking relate to the risk of strokes. Assume that the following data are from a portion of this study. Risk is interpreted as the probability (time
> Best Buy, a nationwide retailer of electronics, computers, and appliances, sells several brands of refrigerators. A random sample of models of full size refrigerators prices sold by Best Buy and the corresponding cubic feet (cu. ft.) and list price follo
> This problem is an extension of the situation described in exercise 35. a. Develop the estimated regression equation to predict the repair time given the number of months since the last maintenance service, the type of repair, and the repairperson who pe
> Fewer young people are driving. In 1995, 63.9% of people under 20 years old who were eligible had a driver’s license. Bloomberg reported that percentage had dropped to 41.7% in 2016. Suppose these results are based on a random sample of 1200 people under
> A simple random sample with n = 54 provided a sample mean of 22.5 and a sample standard deviation of 4.4. a. Develop a 90% confidence interval for the population mean. b. Develop a 95% confidence interval for the population mean. c. Develop a 99% confide
> Refer to the Johnson Filtration problem introduced in this section. Suppose that in addition to information on the number of months since the machine was serviced and whether a mechanical or an electrical repair was necessary, the managers obtained a lis
> Management proposed the following regression model to predict sales at a fast-food outlet. y = β0 + β1x1 + β2x2 + β3x3 + e where x1 = number of competitors within one mile x2 = population within one mile (1000s) x3 = { 51 if drive-up window present
> Consider a regression study involving a dependent variable y, a quantitative independent variable x1, and a categorical independent variable with three possible levels (level 1, level 2, and level 3). a. How many dummy variables are required to represent
> Consider a regression study involving a dependent variable y, a quantitative independent variable x1, and a categorical independent variable with two levels (level 1 and level 2). a. Write a multiple regression equation relating x1 and the categorical va
> Refer to Problem 25. Use the estimated regression equation from part (a) to answer the following questions. a. Estimate the selling price of a four-year-old Honda Accord with mileage of 40,000 miles. b. Develop a 95% confidence interval for the selling p
> In exercise 24, an estimated regression equation was developed relating the percentage of games won by a team in the National Football League for the 2011 season given the average number of passing yards obtained per game on offense and the average numbe
> In a regression analysis involving 30 observations, the following estimated regression equation was obtained. ŷ = 17.6 + 3.8 x1 - 2.3 x2 + 7.6x3 + 2.7 x4 a. Interpret b1, b2, b3, and b4 in this estimated regression equation. b. Predict y when x1 = 10, x
> In exercise 5, the owner of Showtime Movie Theaters, Inc., used multiple regression analysis to predict gross revenue (y) as a function of television advertising (x1) and newspaper advertising (x2). The estimated regression equation was ŷ = 83.23 + 2.29
> Refer to the data in exercise 2. The estimated regression equation for those data is ŷ = 218.4 + 2.01x1 + 4.74x2 a. Develop a 95% confidence interval for the mean value of y when x1 = 47 and x2 = 10. b. Develop a 95% prediction interval for y when x1 =
> In exercise 1, the following estimated regression equation based on 10 observations was presented. ŷ = 29.1270 + .5906x1 + .4980x2 a. Develop a point estimate of the mean value of y when x1 = 180 and x2 = 310. b. Develop a point estimate for an individu
> For many years businesses have struggled with the rising cost of health care. But recently, the increases have slowed due to less inflation in health care prices and employees paying for a larger portion of health care benefits. A recent survey showed th
> In exercise 10, data showing the values of several pitching statistics for a random sample of 20 pitchers from the American League of Major League Baseball were provided. In part (c) of this exercise an estimated regression equation was developed to pred
> The Honda Accord was named the best midsized car for resale value for 2018 by the Kelley Blue Book (Kelley Blue Book website). The file AutoResale contains mileage, age, and selling price for a sample of 33 Honda Accords. a. Develop an estimated regressi
> The National Football League (NFL) records a variety of performance data for individuals and teams. A portion of the data showing the average number of passing yards obtained per game on offense (Off-PassYds/G), the average number of yards given up per g
> Refer to exercise 5. Use α = .01 to test the hypotheses H0: β 1 = β 2 = 0 Ha: β 1 and/or β2 is not equal to zero for the model y = β0 + β1x1 + β2x2 + e, wh
> In exercise 4, the following estimated regression equation relating sales to inventory investment and advertising expenditures was given. ŷ = 25 + 10x1 + 8x2 The data used to develop the model came from a survey of 10 stores; for these data SST = 16,000
> The following estimated regression equation was developed for a model involving two independent variables. ŷ = 40.7 1+ 8.63x1 + 2.71x2 After x2 was dropped from the model, the least squares method was used to obtain an estimated regression equation invo
> Refer to the data presented in exercise 2. The estimated regression equation for these data is ŷ = 218.37 + 2.01x1 + 4.74x2 Here SST = 15,182.9, SSR = 14,052.2, sb1 = .2471, and sb2 = .9484. a. Test for a significant relationship among x1,
> Consider the following data for a dependent variable y and two independent variables, x1 and x2. a. Develop an estimated regression equation relating y to x1. Predict y if x1 = 47. b. Develop an estimated regression equation relating y to x2. Predict y
> In exercise 1, the following estimated regression equation based on 10 observations was presented. ŷ = 29.1270 + .5906x1 + .4980x2 Here SST = 6724.125, SSR = 6216.375, sb1 = .0813, and sb2 = .0567. a. Compute MSR and MSE. b. Compute F and perform the ap
> Refer to exercise 10, where Major League Baseball (MLB) pitching statistics were reported for a random sample of 20 pitchers from the American League for one full season. a. In part (c) of exercise 10, an estimated regression equation was developed rela
> In June 2014, Pew Research reported that in 16% of all homes with a stay-at-home parent, the father is the stay-at-home parent. An independent research firm has been charged with conducting a sample survey to obtain more current information. a. What samp
> Revisit exercise 9, where we develop an estimated regression equation that can be used to predict the selling price given the number of bathrooms, square footage, and number of bedrooms in the house. a. Does the estimated regression equation provide a go
> In exercise 6, data were given on the average number of passing yards per attempt (Yds/Att), the number of interceptions thrown per attempt (Int/Att), and the percentage of games won (Win%) for a random sample of 16 National Football League (NFL) teams f
> In exercise 5, the owner of Showtime Movie Theaters, Inc., used multiple regression analysis to predict gross revenue (y) as a function of television advertising (x1) and newspaper advertising (x2). The estimated regression equation was ŷ = 83.2 + 2.29
> In exercise 4, the following estimated regression equation relating sales to inventory investment and advertising expenditures was given. ŷ = 25 + 10 x1 + 8x2 The data used to develop the model came from a survey of 10 stores; for those data, SST = 16,0
> In exercise 3, the following estimated regression equation based on 30 observations was presented. ŷ = 17.6 + 3.8 x1 - 2.3 x2 + 7.6 x3 + 2.7x4 The values of SST and SSR are 1805 and 1760, respectively. a. Compute R2. b. Compute R2a. c. Comment on the g
> In exercise 2, 10 observations were provided for a dependent variable y and two independent variables x1 and x2; for these data SST = 15,182.9, and SSR = 14,052.2. a. Compute R2. b. Compute R2a. c. Does the estimated regression equation explain a large a
> In exercise 1, the following estimated regression equation based on 10 observations was presented. ŷ = 29.1270 + .5906 x1 + .4980 x2 The values of SST and SSR are 6724.125 and 6216.375, respectively. a. Find SSE. b. Compute R2. c. Compute R2a. d. Commen
> Major League Baseball (MLB) consists of teams that play in the American League and the National League. MLB collects a wide variety of team and player statistics. Some of the statistics often used to evaluate pitching performance are as follows: ERA: The
> The estimated regression equation for a model involving two independent variables and 10 observations follows. ŷ = 29.1270 + .5906 x1 + .4980 x2 a. Interpret b1 and b2 in this estimated regression equation. b. Predict y when x1 = 180 and x2 = 310.
> According to Franchise Business Review, over 50% of all food franchises earn a profit of less than $50,000 a year. In a sample of 142 casual dining restaurants, 81 earned a profit of less than $50,000 last year. a. What is the point estimate of the propo
> The American Association of Individual Investors (AAII) On-Line Discount Broker Survey polls members on their experiences with discount brokers. As part of the survey, members were asked to rate the quality of the speed of execution with their broker as
> A sales manager collected the following data on annual sales for new customer accounts and the number of years of experience for a sample of 10 salespersons. a. Develop a scatter diagram for these data with years of experience as the independent variab
> The National Football League (NFL) records a variety of performance data for individuals and teams. To investigate the importance of passing on the percentage of games won by a team, the following data show the average number of passing yards per attempt
> The following data show the annual revenue ($ millions) and the estimated team value ($ millions) for 30 Major League Baseball teams (Forbes website). // a. Develop a scatter diagram with Revenue on the horizontal axis and Value on the vertical axis. L
> Retail chain Kroger has more than 2700 locations and is the largest supermarket in the United States based on revenue. Kroger has invested heavily in data, technology, and analytics. Feeding predictive models with data from an infrared sensor system call
> Charity Navigator is America’s leading independent charity evaluator. The following data show the total expenses ($), the percentage of the total budget spent on administrative expenses, the percentage spent on fundraising, and the perc
> Consider the following data for two variables, x and y. a. Compute the standardized residuals for these data. Do the data include any outliers? Explain. b. Compute the leverage values for these data. Do there appear to be any influential observations i
> Consider the following data for two variables, x and y. a. Compute the standardized residuals for these data. Do the data include any outliers? Explain. b. Plot the standardized residuals against yˆ. Does this plot reveal any outliers? c. De
> Production Line Speed and Quality Control. Brawdy Plastics, Inc., produces plastic seat belt retainers for General Motors at the Brawdy Plastics plant in Buffalo, New York. After final assembly and painting, the parts are placed on a conveyor belt that m
> Occasionally, it has been the case that home prices and mortgage rates dropped so low that in a number of cities the monthly cost of owning a home was less expensive than renting. The following data show the average asking rent for 10 markets and the mon
> One of the questions Rasmussen Reports included on a 2018 survey of 2.500 likely voters asked if the country is headed in the right direction. Representative data are shown in the file RightDirection. A response of Yes indicates that the respondent does
> Refer to exercise 7, where an estimated regression equation relating years of experience and annual sales was developed. a. Compute the residuals and construct a residual plot for this problem. b. Do the assumptions about the error terms seem reasonable
> Data on advertising expenditures and revenue (in thousands of dollars) for the Four Seasons Restaurant follow. Advertising Expenditures ……………………………………………………………. Revenue 1 …………………………………………………………………………………………………………. 19 2 ……………………………………………………………………………………………
> The following data were used in a regression study. a. Develop an estimated regression equation for these data. b. Construct a plot of the residuals. Do the assumptions about the error term seem to be satisfied?
> Given are data for two variables, x and y. a. Develop an estimated regression equation for these data. b. Compute the residuals. c. Develop a plot of the residuals against the independent variable x. Do the assumptions about the error terms seem to be
> Automobile racing, high-performance driving schools, and driver education programs run by automobile clubs continue to grow in popularity. All these activities require the participant to wear a helmet that is certified by the Snell Memorial Foundation, a
> Sherry is a production manager for a small manufacturing shop and is interested in developing a predictive model to estimate the time to produce an order of a given size—that is, the total time to produce a certain quantity of the product. She has collec
> A regression model relating x, number of salespersons at a branch office, to y, annual sales at the office (in thousands of dollars) provided the following computer output from a regression analysis of the data. a. Write the estimated regression equati
> Following is a portion of the computer output for a regression analysis relating y = maintenance expense (dollars per month) to x = usage (hours per week) of a particular brand of computer. a. Write the estimated regression equation. b. Use a t test to
> The commercial division of a real estate firm is conducting a regression analysis of the relationship between x, annual gross rents (in thousands of dollars), and y, selling price (in thousands of dollars) for apartment buildings. Data were collected on
> The following data give the percentage of women working in five companies in the retail and trade industry. The percentage of management jobs held by women in each company is also shown. a. Develop a scatter diagram for these data with the percentage o
> According to statistics reported on CNBC, a surprising number of motor vehicles are not covered by insurance. Sample results, consistent with the CNBC report, showed 46 of 200 vehicles were not covered by insurance. a. What is the point estimate of the p
> The Wall Street Journal asked Concur Technologies, Inc., an expense-management company, to examine data from 8.3 million expense reports to provide insights regarding business travel expenses. Their analysis of the data showed that New York was the most
> Refer to exercise 21, where data on the production volume x and total cost y for a particular manufacturing operation were used to develop the estimated regression equation ŷ = 1246.67 + 7.6x. a. The company’s production schedule shows that 500 units mu
> In exercise 13, data were given on the adjusted gross income x and the amount of itemized deductions taken by taxpayers. Data were reported in thousands of dollars. With the estimated regression equation ŷ = 4.68 + .16x, the point estimate of a reasonab
> In exercise 7, the data on y = annual sales ($1000s) for new customer accounts and x = number of years of experience for a sample of 10 salespersons provided the estimated regression equation ŷ = 80 + 4x. For these data x̅ = 7, ∑(xi − x̅)2 = 142, and s
> Many small restaurants in Portland, Oregon, and other cities across the United States do not take reservations. Owners say that with smaller capacity, no-shows are costly, and they would rather have their staff focused on customer service rather than mai
> The data from exercise 3 follow. Develop the 95% confidence and prediction intervals when x = 12. Explain why these two intervals are different.
> The data from exercise 2 follow. a. Estimate the standard deviation of ŷ* when x = 8. b. Develop a 95% confidence interval for the expected value of y when x = 8. c. Estimate the standard deviation of an individual value of y when x = 8.
> The data from exercise 1 follow. a. Use equation (14.23) to estimate the standard deviation of ŷ* when x = 4. b. Use expression (14.24) to develop a 95% confidence interval for the expected value of y when x = 4. c. Use equation (14.26) to
> In exercise 20, data on x = weight (pounds) and y = price ($) for 10 road-racing bikes provided the estimated regression equation ŷ = 28,574 − 1439x. (Bicycling website). For these data SSE = 7,102,922.54 and SST = 52,120,800. Use the F test to determin
> Companies in the U.S. car rental market vary greatly in terms of the size of the fleet, the number of locations, and annual revenue. The following data were used to investigate the relationship between the number of cars in service (1000s) and the annual
> In the spring of 2017, the Consumer Reports National Research Center conducted a survey of 1007 adults to learn about their major health-care concerns. The survey results showed that 574 of the respondents lack confidence they will be able to afford heal
> Given are five observations collected in a regression study on two variables. a. Develop a scatter diagram for these data. b. Develop the estimated regression equation for these data. c. Use the estimated regression equation to predict the value of y w
> Refer to exercise 21, where data on production volume and cost were used to develop an estimated regression equation relating production volume and cost for a particular manufacturing operation. Use α = .05 to test whether the production volume is signif
> In exercise 8, ratings data on x = the quality of the speed of execution and y = overall satisfaction with electronic trades provided the estimated regression equation ŷ = .2046 + .9077x. At the .05 level of significance, test whether speed of execution
> Do students with higher college grade point averages (GPAs) earn more than those graduates with lower GPAs (CivicScience)? Consider the college GPA and salary data (10 years after graduation) provided in the file GPASalary. a. Develop a scatter diagram f
> In exercise 18, the data on price ($) and the overall score for six stereo headphones tested by Consumer Reports were as follows (Consumer Reports website). a. Does the t test indicate a significant relationship between price and the overall score? Wha
> The data from exercise 3 follow. a. What is the value of the standard error of the estimate? b. Test for a significant relationship by using the t test. Use α = .05. c. Use the F test to test for a significant relationship. Use Î&pl
> The data from exercise 2 follow. a. Compute the mean square error using equation (14.15). b. Compute the standard error of the estimate using equation (14.16). c. Compute the estimated standard deviation of b1 using equation (14.18). d. Use the t test
> The data from exercise 1 follow. a. Compute the mean square error using equation (14.15). b. Compute the standard error of the estimate using equation (14.16). c. Compute the estimated standard deviation of b1 using equation (14.18). d. Use the t test
> The following data were used to investigate the relationship between the number of cars in service (1000s) and the annual revenue ($millions) for six smaller car rental companies (Auto Rental News website). With x = cars in service (1000s) and y = annu
> An important application of regression analysis in accounting is in the estimation of cost. By collecting data on volume and cost and using the least squares method to develop an estimated regression equation relating volume and cost, an accountant can e
> At 95% confidence, how large a sample should be taken to obtain a margin of error of .03 for the estimation of a population proportion? Assume that past data are not available for developing a planning value for p*.
> Bicycling, the world’s leading cycling magazine, reviews hundreds of bicycles throughout the year. Their “Road-Race” category contains reviews of bikes used by riders primarily interested in racing. O
> Given are five observations for two variables, x and y. a. Develop a scatter diagram for these data. b. What does the scatter diagram developed in part (a) indicate about the relationship between the two variables? c. Try to approximate the relationshi
> In exercise 7 a sales manager collected the following data on x = annual sales and y = years of experience. The estimated regression equation for these data is ŷ = 80 + 4x. a. Compute SST, SSR, and SSE. b. Compute the coefficient of deter
> The following data show the brand, price ($), and the overall score for six stereo headphones that were tested by Consumer Reports (Consumer Reports website). The overall score is based on sound quality and effectiveness of ambient noise reduction. Score
> The data from exercise 3 follow. The estimated regression equation for these data is ŷ = 7.6 + .9x. What percentage of the total sum of squares can be accounted for by the estimated regression equation? What is the value of the sample cor
> The data from exercise 2 follow. The estimated regression equation for these data is ŷ = 68 − 3x. a. Compute SSE, SST, and SSR. b. Compute the coefficient of determination r2. Comment on the goodness of fit. c. Compute t