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Business Statistics 10th Global Edition David Groebner, Patrick Shannon, Phillip Fry - Solutions
The publishing company recently came up with some additional data for the 15 books in the original sample.Two new variables, production expenditures 1x52 and number of prepublication reviewers 1x62, have been added. These additional data are as follows:Book x5 ($) x6 1 38,000 5 2 86,000 8 3 59,000
Develop a multiple regression model containing all four independent variables. Show clearly the regression coefficients. Write a short report discussing the model.In your report make sure you cover the following issues:a. How much of the total variation in book sales can be explained by these four
Develop the correlation matrix showing the correlation between all possible pairs of variables. Test statistically to determine which independent variables are significantly correlated with the dependent variable, book sales. Use a significance level of 0.05.
Amazon.com has become one of the most successful online merchants. Two measures of its success are sales and net income/loss figures. The data can be found in the file Amazon (source: Wikinvest, www.wikinvest.com).a. Produce a scatter plot for Amazon’s net income/loss and sales figures for the
Consider the following model:yn = 5 + 3x1 + 5x2a. Provide an interpretation of the coefficient of x1.b. Is the interpretation provided in part a true regardless of the value of x2? Explain.c. Now consider the model yn = 5 + 3x1 + 5x2 + 4x1x2. Let x2 = 1. Give an interpretation of the coefficient of
What does it mean if we have developed a multiple regression model and have concluded that the model is apt?
Go to the library or use the Internet to find three articles that make use of a regression model with more than one independent variable. For each article, write a short summary covering the following points:Purpose for using the model How the variables in the model were selected How the data in
Refer to Exercises 15-10 and 15-35. The file titled Flicks contains data on total U.S. box office grosses($billion), total number of admissions (billion), average U.S. ticket price ($), and number of movie screens for the years 1987–2015 (source: National Association of Theatre Owners,
In Exercise 15-47, you were asked to use best subsets stepwise regression to establish the relationship between body fat and the independent variables weight, abdomen circumference, and thigh circumference based on data in the file Bodyfat. This is an extension of that exercise.a. Construct an
Refer to Exercise 15-8 in which Paul Browning is interested in analyzing the effects of several variables on the weekly sales for his business. He has collected data for a sample of 20 weeks on the following variables:Sales ($000)Average weekly high temperature Advertising spending ($000)Number of
Examine the following data set:y x1 x2 25 5 25 35 5 5 14 5 5 45 25 40 52 25 5 41 25 25 65 30 30 63 30 30 68 30 25 75 40 30a. Determine the estimated regression equation for this data set.b. Calculate the residuals and the standardized residuals for this regression equation.c. Produce the
Examine the following data set:y x 25 10 35 10 14 10 45 20 52 20 41 20 65 30 63 30 68 30a. Determine the estimated regression equation for this data set.b. Calculate the residuals for this regression equation.c. Produce the appropriate residual plot to determine if the linear function is the
Referring to Exercise 15-48, develop a plot of the residuals against the x values. Discuss whether this plot implies that any of the regression assumptions have been violated.
You are given the following values for dependent and independent variables:y x 25 36 400 81 784 196 900 324 1,089 484 1,225 729 2,025 1,089a. Develop the linear regression model.b. Test to determine whether the regression model is statistically significant using alpha = 0.05.c. Calculate the
A variety of sources suggest that individuals assess their health, at least in part, by estimating their percentage of body fat. A widely accepted measure of body fat uses an underwater weighing technique. There are, however, more convenient methods that use only a scale and a measuring tape. An
An investment analyst collected data obtained from publicly available sources on 20 randomly chosen companies. The data consisted of the 52-week-high stock prices, PE ratios, and market values of the companies. These data are in the file titled Investment.The analyst wishes to produce a regression
Refer to Exercise 15-44.a. Develop the correlation matrix that includes all independent variables and the dependent variable.Predict the order that the variables will be selected into the model if forward selection stepwise regression is used.b. Use forward selection stepwise regression to develop
The White Cover Snowmobile Association gives out pamphlets, maps, and other tourist-related information to people who call a toll-free number and request the information. The association orders the packets of information from a document-printing company and likes to have enough available to meet
Consider the following data:y x1 x2 x3 x4 y x1 x2 x3 x4 61 37 18 2 13 69 35 21 2 20 37 25 5 4 10 24 23 7 6 9 22 23 12 7 4 68 35 15 3 14 48 12 6 2 15 65 37 19 2 19 66 34 14 3 25 45 30 12 3 12a. Use standard stepwise regression to produce an estimate of a multiple regression model to predict y.b. Use
The following data represent a dependent variable and four independent variables:y x1 x2 x3 x4 y x1 x2 x3 x4 61 37 13 10 21 68 35 17 3 33 69 35 19 9 23 48 12 8 8 30 37 25 7 11 32 65 37 11 17 19 24 23 14 7 31 66 34 15 2 33 22 23 6 7 18 45 30 9 24 31a. Use the standard stepwise regression to produce
You are given the following data:y x1 x2 x3 y x1 x2 x3 45 40 41 39 45 42 39 37 41 31 41 35 43 37 52 41 43 45 49 39 34 40 47 40 38 43 41 41 49 35 44 44 50 42 42 51 45 39 40 45 39 48 40 42 40 43 30 42 50 44 44 41 43 53 34 34a. Determine the appropriate correlation matrix and use it to predict which
Suppose you have four potential independent variables, x1, x2, x3, and x4, from which you want to develop a multiple regression model. Using stepwise regression, x2 and x4 entered the model.a. Why did only two variables enter the model?Discuss.b. Suppose a full regression with only variables x2 and
Recall from Exercise 15-7 that an investment analyst collected data obtained from publicly available sources on 20 randomly chosen companies. The data consisted of the 52-week-high stock prices, PE ratio, and market value of the company. These data are in the file titled Investment. The analyst
The Energy Information Administration (EIA), created by Congress in 1977, is a statistical agency of the U.S.Department of Energy. It provides data, forecasts, and analyses to promote sound policymaking and public understanding regarding energy and its interaction with the economy and the
The National Association of Theatre Owners is the largest exhibition trade organization in the world, representing more than 26,000 movie screens in all 50 states and in more than 20 countries worldwide.Its membership includes the largest cinema chains and hundreds of independent theater owners. It
The National Association of Realtors Existing-Home Sales Series provides measurements on the residential real estate market. One of the measurements is the Housing Affordability Index (HAI). It is a measure of the financial ability of U.S. families to buy a house:100 means that families earning the
McCullom’s International Grains is constantly searching out areas in which to expand its market.Such markets present different challenges, since tastes in the international market are often different from domestic tastes. India is one country on which McCullom’s has focused. Paddy is a grain
The Gilmore Accounting firm mentioned in Exercise 15-21, in an effort to explain variation in client profitability, collected the data in the file called Gilmore, where:y = Net profit earned from the client x1 = Number of hours spent working with the client x2 = Type of client:1, if manufacturing
In a bit of good news for male students, based on 2014 data, American men have closed the gap with women on life span, according to the Population Reference Bureau(source: “Life expectancy at birth, by gender, 1970 and 2014,” www.prb.org/DataFinder). Male life expectancy attained a record 76
A regression equation to be used to predict a dependent variable with four independent variables is developed from a sample of size 10. The resulting equation is yn = 32.8 + 0.470x1 + 0.554x2 - 4.77x3 + 0.929x4 Two other equations are developed from the sample:yn = 12.4 + 0.60x1 + 1.60x2 and yn =
Consider the following data:x 1 4 5 7 8 12 11 14 19 20 y 1 54 125 324 512 5,530 5,331 5,740 7,058 7,945a. Construct a scatter plot of the data. Determine the order of the polynomial that is represented by this data.b. Obtain an estimate of the model identified in part a.c. Conduct a test of
Examine the following two sets of data:When x2 1 When x2 0 x1 y x1 y 1 2 2 3 4 15 3 9 5 23 6 5 7 52 7 10 8 60 9 48 12 154 10 50 11 122 14 87 14 200 13 51 19 381 16 63 20 392 21 202a. Produce a distinguishable scatter plot for each of the data sets on the same graph. Does it appear that there is
Examine the following data:x 2 8 9 12 15 22 21 25 37 39 y 4 75 175 415 620 7,830 7,551 7,850 11,112 11,617a. Construct a scatter plot of the data. Determine the order of the polynomial that is represented by the data.b. Obtain an estimate of the model identified in part a.c. Conduct a test of
Consider the following values for the dependent and independent variables:x y 6 5 9 20 14 28 18 30 22 33 27 35a. Develop a scatter plot of the data. Does the plot suggest a linear or nonlinear relationship between the dependent and independent variables?b. Develop an estimated linear regression
Consider the following values for the dependent and independent variables:x y 5 10 15 15 40 25 50 44 60 79 80 112a. Develop a scatter plot of the data. Does the plot suggest a linear or nonlinear relationship between the dependent and independent variables?b. Develop an estimated linear regression
There has been conjecture by high school administrators at a particular high school in Delaware about whether a relationship exists between the average math SAT score and the average verbal SAT score and the gender of the student taking the SAT examination. To help better understand the situation,
Refer again to the data from the Gilmore Accounting firm found in the data file Gilmore (see Exercise 15-21).a. Incorporate the client type into the regression analysis using dummy variables. Describe the resulting multiple regression estimate.b. Test to determine if this model is useful in
For years, import cars have held an advantage over domestic automobiles according to data collected by J.D. Power and Associates, which generates a widely respected report on initial quality. The 2015 data are in the file PP100. Initial quality is measured by the number of problems per 100 vehicles
A real estate agent wishes to determine the selling price of residences using the size (square feet) and whether the residence is a condominium or a singlefamily home. A sample of 20 residences was obtained with the following results:Price ($) Type Square Feet Price ($) Type Square Feet 199,700
A consumer association was interested in building a regression model to explain the variation in automobile highway mileage. At one stage of the analysis, the estimate of the model took the following form:yn = 34.20 - 0.003x1 + 4.56x2 where:x1 = Vehicle weight x2 = e 1, if standard transmission 0,
The Brentworth Utility Corporation is developing a multiple regression model that it plans to use to predict customers’ utility usage. The analyst currently has three quantitative variables 1x1, x2, and x32 in the model, but she is dissatisfied with the R-squared and the estimate of the standard
A real estate agent wishes to estimate the monthly rental for apartments based on the size (square feet)and the location of the apartments. She chose the following model:y = b0 + b1x1 + b2x2 + e where:x1 = Square footage of the apartment x2 = e 1 if located in town center 0 if not located in town
You are considering developing a regression equation relating a dependent variable to two independent variables. One of the variables can be measured on a ratio scale, but the other is a categorical variable with four possible levels.a. How many dummy variables do you need to represent the
Consider the following regression model:y = b0 + b1x1 + b2x2 + e where:x1 = A quantitative variable x2 = e 1 if x1 6 20 0 if x1 Ú 20 The following estimated regression equation was obtained from a sample of 30 observations:yn = 24.1 + 5.8x1 + 7.9x2a. Provide the estimated regression equation for
The National Association of Theatre Owners is the largest exhibition trade organization in the world, representing more than 26,000 movie screens in all 50 states and in more than 20 countries worldwide. Its membership includes the largest cinema chains and hundreds of independent theater owners.
Refer to Exercise 15-8 and the data file Browning.a. Produce a regression equation that will predict the sales as a function of the other four variables.b. Determine if the overall model is significant. Use a significance level of 0.05.c. Conduct a test of hypothesis to discover if any of the
An investment analyst collected data about 20 randomly chosen companies. The data obtained from publicly available sources consisted of the 52-weekhigh stock prices, the price-to-earnings (PE) ratio, and the market value of the company. These data are in the file titled Investment.a. Produce a
Consider the following set of data:x2 10 8 11 7 10 11 6 x1 50 45 37 32 44 51 42 y 103 85 115 73 97 102 65a. Obtain the estimated regression equation.b. Examine the coefficient of determination and the adjusted coefficient of determination. Does it seem that either of the independent
Consider the following set of data:x1 29 48 28 22 28 42 33 26 48 44 x2 15 37 24 32 47 13 43 12 58 19 y 16 46 34 26 49 11 41 13 47 16a. Obtain the estimated regression equation.b. Develop the correlation matrix for this set of data.Select the independent variable whose correlation magnitude is the
The following correlation matrix is associated with the same data used to build the regression model in Exercise 15-1:y x1 x2 x3 y 1 x1 -0.406 1 x2 0.459 0.051 1 x3 -0.244 0.504 0.272 1 Does this output indicate any potential multicollinearity problems with the analysis?
In working for a local retail store, you have developed the following estimated regression equation:yn = 22,167 - 412x1 + 818x2 - 93x3 - 71x4 where:y = Weekly sales x1 = Local unemployment rate x2 = Weekly average high temperature x3 = Number of activities in the local community x4 = Average price
You are given the following estimated regression equation involving a dependent and two independent variables:yn = 12.67 + 4.14x1 + 8.72x2a. Interpret the values of the slope coefficients in the equation.b. Estimate the value of the dependent variable when x1 = 4 and x2 = 9.
The following output is associated with a multiple regression model with three independent variables:df SS MS F Significance F Regression 3 16,646.091 5,548.697 5.328 0.007 Residual 21 21,871.669 1,041.508 Total 24 38,517.760 Coefficients Standard Error t Stat p-value Intercept 87.790 25.468 3.447
Refer to the Grinfield Service Company discussed in Exercise 14-69.a. Develop the least squares regression equation for these variables. Plot the regression line on the scatter plot.b. Develop a 95% confidence interval estimate for the increase in sales resulting from increasing the advertising
Living donor kidney transplants are becoming more prevalent with the advent of kidney exchanges such as the National Kidney Registry (NKR). In order for a transplant to take place, there needs to be a good match between a willing donor and the recipient. Many factors must be considered in an effort
Exercise 14-13 involved a file called Breakcue, which contains data on pool cue weights and the speed of pool balls struck with various cues. In that problem you were asked to calculate the correlation coefficient, and to test whether the two variables are significantly correlated.The next step is
Terry Downes owns a commercial cleaning company.He has conducted a survey of customers to determine how satisfied they are with the work performed. He devised a rating scale between 0 and 100, with 0 being poor and 100 being excellent service. He selected a random sample of 14 customers and asked
The board of directors for a small regional bank has decided to look into all aspects of revenues and costs.One service the bank offers is free checking, and the board is interested in whether the costs of this service are offset by revenues from interest earned on the deposits. One aspect in
A company is considering recruiting new employees from a particular college and plans to place a great deal of emphasis on the student’s college GPA. However, the company is aware that not all schools have the same grading standards, so it is possible that a student at this school might have a
One of the advances that have helped to alleviate carpal tunnel syndrome is ergonomic keyboards. The ergonomic keyboards may also increase typing speed.Ten administrative assistants were chosen to type on both standard and ergonomic keyboards. The resulting typing speeds follow:Ergonomic 69 80 60
A regional airline company recently performed a customer survey in which it asked a random sample of 100 passengers to indicate their income and the total cost of the airfares they purchased for pleasure trips during the past year. A regression model was developed for the purpose of determining
Referring to Exercise 14-58, suppose a student has an SAT score of 400. What is her estimate GPA at State University? Discuss the ramifications of using the model developed in Exercise 14-58 to estimate this student’s GPA.
Susan decides to run a pizza franchise in her hometown.To determine the cost of the initial investment for her startup, she hired an analyst to help her to analyze the startup cost (all figures in $thousands) and the annual franchise fee ($ 000) for the pizza shop. The analyst collected data from
At State University, a study was done to establish whether a relationship exists between students’graduating grade point average (GPA) and the SAT verbal score when the student originally entered the university. The sample data are reported as follows:GPA 2.5 3.2 3.5 2.8 3.0 2.4 3.4 2.9 2.7 3.8
Go to the library and locate an article in a journal related to your major (Journal of Marketing, Journal of Finance, etc.) that uses linear regression. Discuss the following:a. How the author chose the dependent and independent variablesb. How the data were gatheredc. What statistical tests the
Consider the following set of data:x 48 27 34 24 49 29 39 38 46 32 y 47 23 31 20 50 48 47 47 42 47a. Calculate the correlation coefficient of these two variables.b. Multiply each value of the variable x by 5 and add 10 to the resulting products. Now multiply each value of the variable y by 3 and
Discuss why prediction intervals that attempt to predict a particular y value are less precise than confidence intervals for predicting an average y value.
Referring to Exercise 14-50, another student in the same class computed a regression equation relating the same two variables. The slope of the equation was found to be-0.735. After trying several times and always coming up with the same result, she felt that she must have been doing something
A regional retailer would like to determine if the variation in average monthly store sales can, in part, be explained by the size of the store measured in square feet. A random sample of 21 stores was selected and the store size and average monthly sales were computed. The following results are
An engineering firm is interested in investigating whether the variability in the cost of small projects(defined as projects under $10 million) can be accounted for, in part, by differences in the number of direct engineering consulting hours billed. A random sample of 24 small projects was
A study was conducted to determine the effect of the geographical distance to a city center on the selling price of a residential property. The following data cover a random sample of new residential housings sold from July 2014 to June 2016 with their respective distances (miles) from the city
The following data have been collected by an accountant who is performing an audit of account balances for a major city billing department. The population from which the data were collected is the accounts for which the customer had indicated the balance was incorrect.The dependent variable, y, is
A sample of ten yields the following data:x 10 8 11 7 10 11 6 7 15 9 y 103 85 115 73 97 102 65 75 155 95a. Provide a 95% confidence interval for the average y when xp = 9.4.b. Provide a 95% confidence interval for the average y when xp = 10.c. Obtain the margin of errors for both part a and partb.
The sales manager at City Real Estate Company is interested in describing the relationship between condo sales prices and the number of weeks the condo is on the market before it sells. He has collected a random sample of 17 low-end condos that have sold within the past three months. These data are
You are given the following summary statistics from a regression analysis:yn = 200 + 150x SSE = 25.25 SSX = Sum of square X = (x - x)2 = 99,645 n = 18 x = 52.0a. Determine the point estimate for y if xp = 48 is used.b. Provide a 95% confidence interval estimate for the average y, given xp = 48.
Construct and interpret a 90% confidence interval estimate for the regression slope coefficient.
Referring to the displayed regression model, what percentage of the variation in the y variable is explained by the x variable in the model?
You are given the following sample data:x y 10 3 6 7 9 3 x y 3 8 2 9 8 5 3 7a. Develop a scatter plot for these data.b. Determine the regression equation for the data.c. Develop a 95% confidence interval estimate for the true regression slope and interpret this interval estimate.d. Provide a 95%
The following data have been collected by an accountant who is performing an audit of paper products at a large office supply company. The dependent variable, y, is the time (in minutes) the accountant takes to count the units.The independent variable, x, is the number of units on the computer
The file called Vehicles contains data for a sample of motor vehicles that are owned by an insurance company. Data are available for two variables: highway mileage and curb weight.a. Develop a scatter plot for these data. Discuss what the plot implies about the relationship between the two
The National Football League (NFL) commissioner’s office staff wants you to developed a simple linear regression model with 2015 average home attendance used as the dependent variable and the total number of games won during the season as the independent variable. The staff is interested in
An engineering firm is interested in investigating whether the variability in the cost of small projects(defined as projects under $10 million) can be accounted for, in part, by differences in the number of direct engineering consulting hours billed. A sample of 24 small projects was randomly
A company that makes designer sandals has tracked the production volume over the past six months.Because of the company’s focus on quality, some sandals need to be reworked before they are fit to be shipped to customers. The number of pairs of sandals produced and the number of pairs that require
A shipping company believes that the variation in the cost of a customer’s shipment can be explained by differences in the weight of the package being shipped.To investigate whether this relationship is useful, a random sample of 20 customer shipments was selected, and the weight (in lb) and the
The Skelton Manufacturing Company recently did a study of its customers. A random sample of 50 customer accounts was pulled from the computer records. Two variables were observed:y = Total dollar volume of business this year x = Miles customer is from corporate headquarters The following statistics
Examine the following sample data for the variables y and x:x 1 2 3 4 5 y 4 2 5 8 9a. Construct a scatter plot of these data. Describe the relationship between x and y.b. Calculate the sum of squares error for the following equations: (1) yn = 0.8 + 1.60x, (2) yn = 1 + 1.50x, and (3) yn = 0.7 +
Consider the following sample data for the variables y and x:x 30.3 4.8 15.2 24.9 8.6 20.1 9.3 11.2 y 14.6 27.9 17.6 15.3 19.8 13.2 25.6 19.4a. Calculate the linear regression equation for these data.b. Determine the predicted y value when x = 10.c. Estimate the change in the y variable resulting
You are given the following sample data for variables x and y:x(independent)y(dependent)1 16 7 50 3 22 8 59 11 63 5 46 4 43a. Construct a scatter plot for these data and describe what, if any, relationship appears to exist.b. Compute the regression equation based on these sample data and interpret
You are given the following sample data for variables y and x:y 140 120 80 100 130 90 110 120 130 130 100 x 5 3 2 4 5 4 4 5 6 5 4a. Develop a scatter plot for these data and describe what, if any, relationship exists.b. (1) Compute the correlation coefficient. (2) Test to determine whether the
A regional accreditation board for colleges and universities is interested in determining whether a relationship exists between student applicant verbal SAT scores and in-state tuition costs at the university. Data have been collected on a sample of colleges and universities and are in the file
Goldie’s Billiards, Inc., is a retailer of billiard supplies.It stands out among billiard suppliers because of the research it does to assure its products are top notch.One experiment was conducted to measure the speed a cue ball attains when it is struck by various weighted pool cues. The
Queries about whether the occurrence of high blood pressure increases significantly with age are rising.To study on the above issue, a health panel recorded 20 patients’ blood pressure measurements (mmHg)with their respective ages in the following table:Patient Age Blood Pressure (mmHg)1 47 150 2
Many banks issue MasterCard credit cards to their customers. A main factor in determining whether a credit card will be profitable to the bank is the average monthly balance the customer maintains on the card that is subject to finance charges. Bank analysts wish to determine whether there is a
A bank’s chief financial officer is interested in whether there is a relationship between account balances and the number of times a card is used each month. A random sample of 50 accounts was selected.The account balance and the number of charges during the past month were the two variables
The facilities management department at a university wants to analyze the expenditure (in $thousands) on the university facilities with the increasing number of students for the past 10 years. This is to ensure that all university facilities and lands support the academic, research and
For each of the following circumstances, perform the indicated hypothesis tests:a. HA: r 7 0, r = 0.53, and n = 30 with a = 0.01, using a test-statistic approachb. HA: r 0, r = -0.48, and n = 20 with a = 0.05, using a p-value approachc. HA: r 0, r = 0.39, and n = 45 with a = 0.02, using a
A random sample of the following two variables was obtained:x 29 48 28 22 28 42 33 26 48 44 y 16 46 34 26 49 11 41 13 47 16a. Calculate the correlation between these two variables.b. Conduct a test of hypothesis to determine if there exists a correlation between the two variables in the population.
An industry study was recently conducted in which the sample correlation between units sold and marketing expenses was 0.57. The sample size for the study was 15 companies. Based on the sample results, test to determine whether there is a significant positive correlation between these two
A survey conducted by a large brokerage company addressed the proportion of African Americans and White Americans who have money invested in the stock market. Suppose the file titled Stockrace contains data obtained in the surveys. The survey asked 500 African American and 500 White respondents if
A pharmaceutical company claims that if a blood pressure drug is taken properly, the amount of blood pressure decrease will be normally distributed with a mean equal to 10 points on the diastolic reading and a standard deviation equal to 4.0. One hundred patients were administered the drug, and
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