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Statistics For Business Decision Making And Analysis 2nd Edition Robert Stine, Dean Foster - Solutions

1. Adjusted R2 is less than regular R2. 2. The statistic se falls when an explanatory variable is added to a regression model. 3. A slope in a simple regression is known as a partial slope because it ignores the effects of other explanatory variables. 4. A partial slope estimates differences
1. The partial slope corresponds to the direct effect in a path diagram. 2. The indirect effect of an explanatory variable is the difference between the marginal and partial slopes. 3. If we reject H0: β1 = β2 = 0 using the F-test, then we should conclude that both slopes are different from
An analyst became puzzled when analyzing the performance of franchises operated by a fast-food chain. The correlation between sales and the number of competitors within 3 miles was positive. When she regressed sales on the number of competitors and population density, however, she got a negative
In evaluating the performance of new hires, the human resources division found that candidates with higher scores on its qualifying exam performed better. In a multiple regression that also used the education of the new hire as an explanatory variable, the slope for test score was near zero.
The human resources department at a firm developed a multiple regression to predict the success of candidates for available positions. Drawing records of new hires from five years ago, analysts regressed current annual salary on age at the time of hire and score on a personality test given to new
A marketing research analysis considered how two customer characteristics affect their customers€™ stated desire for their product. Potential customers in a focus group were shown prototypes of a new convenience product and asked to indicate how much they would like to buy such a product.
The following correlation matrix shows the pairwise correlations among three variables: two explanatory variables X1 and X2 and the response denoted by Y. For example, corr(Y, X2) = 0.2359.(a) Why does it make sense to put 1s down the diagonal of this table? (b) Find the slope of the simple
The following correlation matrix shows the pairwise correlations among three variables. The variables are the €œexpert€ ratings assigned to wines by well-known connoisseurs (from 0 to 100), the year of the vintage (year in which the grapes were harvested), and the listed price on a Web site.
Identify the variable by matching the description below to the data shown in the following scatterplot matrix. The plot shows 80 observations.(a) The sequence 1, 2, 3, c , 80 (b) Has mean -200 (c) Most highly positively correlated pair of variables (d) Uncorrelated with Y (e) Identify any outliers
An airline developed a regression model to predict revenue from fights that connect “feeder” cities to its hub airport. The response in the model is the revenue generated by fights operating to the feeder cities (in thousands of dollars per month), and the two explanatory variables are the air
A national motel chain has a model for the operating margin of its franchises. The operating margin is defined to be the ratio of net profit to total revenue (as a percentage). The company plans to use this model to help it identify profitable sites to locate new hotels. The response in the model
This table gives further details of the multiple regression estimated in Exercise 31. Assume that the MRM satisfies the conditions for using this model for inference.(a) Fill in the t-statistics.(b) Estimate the p-values using the Empirical Rule. Only rough estimates are needed.(c) Does the
This table gives further details of the multiple regression estimated in Exercise 32. Assume that the MRM satisfies the conditions for using this model for inference.(a) Fill in the column of t-statistics.(b) Estimate the column of p-values using the Empirical Rule. Only rough estimates are
Refer to the context of the airline in Exercise 31 part (c). Assume that the estimated model meets the conditions for using the MRM for inference. (a) Does the estimated multiple regression equation explain statistically significant variation in revenue among these feeder cities? (b) If this model
Refer to the context of the motel chain in Exercise 32. Assume that the estimated model meets the conditions for using the MRM for inference. (a) Does the estimated multiple regression equation explain statistically significant variation in operating margins among these hotels? (b) If this model is
These data give the prices (in dollars) for gold link chains at the Web site of a discount jeweler. The data include the length of the chain (in inches) and its width (in millimeters). All of the chains are 14-carat gold in a similar link style. Use the price as the response.(a) Examine the
These data describe the sales over time at a franchise outlet of a major US oil company. Each row summarizes sales for one day. This particular station sells gas, and it also has a convenience store and a car wash. The response Sales gives the dollar sales of the convenience store. The explanatory
Before purchasing videoconferencing equipment, a company tested its current internal computer network. The tests measured how rapidly data moved through its network given the current demand on the network. Eighty files ranging in size from 20 to 100 megabytes (MB) were transmitted over the network
A manufacturer produces custom metal blanks that are used by its customers for computer- aided machining. The customer sends a design via computer, and the manufacturer comes up with an estimated cost per unit, which is then used to determine a price for the customer. The data for the analysis were
In order to help clients determine the price at which their house is likely to sell, a realtor gathered a sample of 150 purchase transactions in her area during a recent three-month period. For the response in the model, use the price of the home (in thousands of dollars). As explanatory variables,
This data table gives annual costs of 223 commercial leases. All of these leases provide office space in a Midwestern city in the United States. For the response, use the cost of the lease (in dollars per square foot). As explanatory variables, use the reciprocal of the number of square feet and
This data table contains accounting and financial data that describe 324 companies operating in the information sector. The variables include the expenses on research and development (R&D), total assets of the company, and the cost of goods sold (CGS). All columns are reported in millions of
The data table gives various characteristics of 318 types of cars sold in the United States during the 2011 model years. Use the combined mileage rating as the response and the horsepower of the engine (HP) and the weight of the car (given in thousands of pounds) as explanatory variables. (a)
An analyst at the United Nations is developing a model that describes GDP (gross domestic product per capita, a measure of the overall production in an economy per citizen) among developed countries. She is using national data for 29 countries from the 2005 report of the Organization for Economic
A firm that operates a large, direct-to-consumer sales force would like to build a system to monitor the progress of new agents. The goal is to identify “superstar agents” as rapidly as possible, offer them incentives, and keep them with the company. A key task for agents is to open new
These data describe promotional spending by a pharmaceutical company for a cholesterol-lowering drug. The data cover 39 consecutive weeks and isolate the area around Boston. The variables in this collection are shares. Marketing research often describes the level of promotion in terms of voice. In
This data table tracks monthly performance of stock in Apple Computer since 1990. The data include 264 monthly returns on Apple Computer, as well as returns on the entire stock market, Treasury Bills (short-term, 30-day loans to the government), and infation. (The column Market Return is the return
When car dealers lease a car, how do they decide what to charge? One answer, if you’ve got a lot of unpopular cars to move, is to charge whatever it takes to get the cars off the lot. A different answer considers the so-called residual value of the car at the end of the lease. The residual value
Promotion response is a key measure of the success of a firm’s advertising expenditures. It is essential that money spent to promote sales earns a good return. There’s little benefit in advertising if each dollar spent on commercials contributes only a $1 to the bottom line. As important as it
1. Test statistic unaffected by collinearity 2. Minimum value of VIF 3. Regression estimate without VIF 4. Effect of collinearity on se (b1) 5. Correlations among variables 6. Scatterplots among variables 7. Percentage of variation in residuals 8. Test whether adding X1 improves ft of model 9.
1. The use of correlated explanatory variables in a multiple regression implies collinearity in the model. 2. The presence of collinearity violates an assumption of the Multiple Regression Model (MRM). 3. If a multiple regression has a large F-statistic but a small t-statistic for each predictor
If the R2 of a multiple regression with two predictors is larger than 80%, then the regression explains a statistically significant fraction of the variance in y.
1. We can detect outliers by reviewing the summary of the associations in the scatterplot matrix. 2. A correlation matrix summarizes the same information in the data as is given in a scatterplot matrix. 3. In order to calculate the VIF for an explanatory variable, we need to use the values of the
The best remedy for a regression model that has collinear predictors is to remove one of those that are correlated.
Collinearity is sometimes described as a problem with the data, not the model. Rather than filling the scatterplot of X1 on X2, the data concentrate along a diagonal. For example, the following plot shows monthly percentage changes in the whole stock market and the S&P 500 (in excess of the
Regression models that describe macroeconomic properties in the United States often have to deal with large amounts of collinearity. For example, suppose we want to use as explanatory variables the disposable income and the amount of household credit debt. Because the economy in the United States
The version of the CAPM studied in this chapter specifies a simple regression model as 100 (St – rt) = α + 100 β (Mt – rt) + ε where Mt are the returns on the market, St are the returns on the stock, and rt are the returns on risk-free investments. (See About the Data.) Hence, 100(Mt – rt)
The following histograms summarize monthly re-turns on Sony, the whole stock market, and risk-free assets. Having seen this comparison, explain why it does not make much difference whether we subtract the risk-free rate from the variables in the CAPM regression.
In Example 24.1 the data show correlation between the income and age of the customer. This produces collinearity and makes the analysis tricky to interpret. The marketing research group could have removed this collinearity by collecting data in which these two variables were uncorrelated. For
To find out whether employees are interested in joining a union, a manufacturing company hired an employee relations firm to survey attitudes toward unionization. In addition to a rating of their agreement with the statement “I do not think we need a union at this company” (on a 1–7 Likert
Modern steel mills are very automated and need to monitor their substantial energy costs carefully to be competitive. In making cold-rolled steel (as used in bodies of cars), it is known that temperature during rolling and the amount of expensive additives (expensive metals like manganese
A builder is interested in which types of homes earn a higher price. For a given number of square feet, the builder gathered prices of homes that use the space differently. In addition to price, the homes vary in the number of rooms devoted to personal use (such as bathrooms or bedrooms) and rooms
These data give the prices (in dollars) for gold link chains at the Web site of a discount jeweler. The data include the length of the chain (in inches) and its width (in millimeters). All of the chains are 14-carat gold in a similar link style. Use the price as the response. For one explanatory
These data describe sales over time at a franchise outlet of a major US oil company. (The data fle has values for two stations. For this exercise, use only the 283 cases for site 1.) Each row summarizes sales for one day. This particular station sells gas, and it also has a convenience store and a
Before purchasing videoconferencing equipment, a company tested its current internal computer network. The tests measured how rapidly data moved through its network given the current demand on the network. Eighty files ranging in size from 20 to 100 megabytes (MB) were transmitted over the network
A manufacturer produces custom metal blanks that are used by its customers for computer-aided machining. The customer sends a design via computer, and the manufacturer comes up with an estimated cost per unit, which is then used to determine a price for the customer. The data for the analysis were
In order to help clients determine the price at which their house is likely to sell, a realtor gathered a sample of 150 purchase transactions in her area during a recent three-month period. The price of the home is measured in thousands of dollars. The number of square feet is also expressed in
This data table gives annual costs of 223 commercial leases. All of these leases provide office space in a Midwestern city in the United States. The cost of the lease is measured in dollars per square foot, per year. The number of square feet is as labeled, and Parking counts the number of parking
This data table contains accounting and financial data that describe 324 companies operating in the information sector in 2010. The largest of these provide telephone services. The variables include the expenses on research and development (R&D), total assets of the company, and the cost of goods
These data include the engine size or displacement (in liters) and horse-power (HP) of 318 vehicles sold in the United States in 2011. Fit a multiple regression with the log10 of the combined mileage rating as the response and the log10 of the horsepower of the engine (HP), the log10 of the weight
An analyst at the United Nations is developing a model that describes GDP (gross domestic product per capita, a measure of the overall production in an economy per citizen) among developed countries. For this analysis, she uses national data for 30 countries from the 2005 report of the Organization
A firm operates a large, direct-to-consumer sales force. The firm would like to build a system to monitor the progress of new agents. The goal is to identify “superstar agents” as rapidly as possible, offer them incentives, and keep them with the firm. A key task for agents is to open new
These data describe promotional spending by a pharmaceutical company for a cholesterol-lowering drug. The data cover 39 consecutive weeks and isolate the area around Boston. The variables in this collection are shares. Marketing research often describes the level of promotion in terms of voice. In
These data track monthly performance of stock in Apple Computer since 1990. The data include 264 monthly returns on Apple Computer, as well as returns on the entire stock market, the S&P 500 index, stock in IBM, and Treasury Bills (short-term, 30-day loans to the government). (The column Whole
Collinearity among the predictors is common in many applications, particularly those that track the growth of a new business over time. The problem is worse when the business has steadily grown or fallen. Because the growth of a business affects many attributes of the business (such as assets,
1. Intercept for high school graduate2. Intercept for college graduate3. Has units $thousand/year, high school graduate4. Has units $thousand/year, college graduate5. Difference in slopes6. Difference in intercepts7. Interaction8. Equal variances9. Average salary for high school graduate with 10
1. Confounding arises in a two-sample t-test when the groups differ in ways other than the labeling that distinguishes the groups. 2. An analysis of covariance is another name for the use of randomization to avoid confounding. 3. A dummy variable is a numerical encoding that as- signs the value +
1. Interactions introduce collinearity into a multiple regression and should be removed from the model if not statistically significant.2. If neither the interaction nor the dummy variable is statistically significant in an analysis of covariance, then there’s no lurking factor that confounds the
The following comparison box plots show the revenue generated by individual sales representatives who operate in divisions supervised by two different managers. What is the problem with using a two-sample t-test to judge the statistical significance of the apparent difference?
An auditor collected a random sample of about 100 invoices sent out in the current fiscal year and compared the amounts of these invoices to those of a second random sample of invoices in the prior fiscal year. These box plots summarize the amounts (in dollars) of the two sets of invoices.Would you
When fitting the regression of Y on X for two groups, we can estimate the slope and intercept within each group either by fitting two simple regressions or by fitting one multiple regression. If simple regressions are so much easier to interpret, why combine them into one multiple regression?
Multiple regression requires an assumption that the combination of the two simple regressions does not require. What is it, and what condition of the multiple regression does it affect?
An industry analyst constructed a model describing the cost of building cars at plants operated by different manufacturers in North America. As a first step, the analyst regressed total production cost (in dollars) on the number of labor hours for a sample of vehicles. The data used came from two
Matsushita is well known for the efficiency of its automated factories. Facing pressure from developing Asian producers with lower labor costs, the company reconfigured robots in its factory in Saga, Japan. After the modification, it takes 40 minutes to configure the assembly line and start
A two-sample t-test has a lot in common with simple regression. This output summarizes the results of fitting a simple regression with only a dummy variable as the explanatory variable. The data are the same salary data used in the text, with salary regressed on Group.(a) Interpret the estimated
This output summarizes a simple regression fit to the data on marketing Courier Paks in Example 25.1.(a) Summarize the estimated equation of the simple regression model. (b) The t-statistic for the slope in this model is statistically significant. Assuming the conditions of the SRM hold, what does
The analysis of covariance emphasizes the use of regression to fix a problem with the two-sample t-test that has a confounding variable. You can also think of the use of a dummy variable as a way to fix a problem in the regression of Y on X. Take a look at this scatter-plot:(a) If we fit parallel
After a manufacturer closed an old assembly plant, it re-trained its production employees to use new machines in a more highly automated robotic facility. The automated facility allows the plant to fill small orders of customized parts rather than turn out identical copies. After a weeklong
The following output summarizes the fit of an analysis of covariance to the data in Exercise 35. The variable D denotes a dummy variable, with D = + for values colored green and 0 otherwise.(a) Does the fit of the model suggest parallel equations for the two groups?(b) How would the output change
The following output summarizes the fit of an analysis of covariance to the data in Exercise 36. The variable D denotes a dummy variable, with D = + for values colored green and 0 otherwise.(a) What is the interpretation of the coefficient of D in the fit of this multiple regression? Use the
Emerald Diamonds These data are a subset of the diamonds used in Chapter 19. This data table of 144 diamonds includes the price (in dollars), the weight (in carats), and the clarity grade of the diamonds. The diamonds have clarity grade either VS1 or VVS1. VVS1 diamonds are nearly flawless; VS1
Convenience Shopping (introduced in Chapter 19) These data expand the data table introduced in Chapter 19 by introducing data from a second location. For each of two service stations operated by a national petroleum refiner, we have the daily sales in the convenience store located at the service
Download (introduced in Chapter 19) Before purchasing videoconferencing equipment, a company ran tests of its current internal computer network. The goal of the tests was to measure how rapidly data moved through the network given the current demand on the network. Eighty files ranging in size from
Production Costs (introduced in Chapter 19) A manufacturer produces custom metal blanks that are used by its customers for computer-aided machining. The customer sends a design via computer (a 3-D blueprint), and the manufacturer comes up with an estimated price per unit, which is then used to
Seattle Home Prices This data table expands the data introduced in Chapter 19 on the prices of homes in the Seattle area. One realtor operating in Seattle listed all 28 homes for sale in the original data table. This table includes prices and sizes of 8 more homes listed by a different realtor in
Leases (introduced in Chapter 19) This data table includes the annual prices of 223 commercial leases. All of these leases provide office space in a Midwestern city in the United States. In previous exercises, we estimated the variable costs (costs that increase with the size of the lease) and
R&D Expenses (introduced in Chapter 19) This data file contains a variety of accounting and financial values that describe companies operating in the information and professional services sectors of the economy. One column gives the expenses on research and development (R&D), and another
Cars (introduced in Chapter 19) The cases that make up this dataset are types of cars. For each of 318 types of cars sold in the United States during the 2011 model year, we have the combined mileage and the horsepower of the engine (HP). In previous exercises, we found that a model for the
Wine These data give ratings and prices of 257 red and white wines that appeared in Wine Spectator in 2009. For this analysis, we are interested in how the rating given to a wine is associated with its price, and if this association depends on whether it’s a red or white wine.(a) Plot the natural
Hiring (introduced in Chapter 19) A firm that operates a large, direct-to-consumer sales force would like to be able to put in place a system to monitor the progress of new agents. A key task for agents is to open new accounts; an account is a new customer to the business. The goal is to identify
Promotion (introduced in Chapter 19) These data describe spending by a pharmaceutical company to promote a cholesterol-lowering drug. The data cover 39 consecutive weeks and isolate the metropolitan areas near Boston, Massachusetts, and Portland, Oregon. A subset of these data was introduced in
The music on an Apple iPod can be stored digitally in several formats. A popular format for Apple is known as AIFF, short for Audio Interchange File Format. Another format is known as AAC, short for Advanced Audio Coding. Files on an iPod can be in either of these formats or both. The 596 songs in
Many airlines offer credit cards that reward customers who use the card with frequent-flyer miles. The more the customer uses the card, the more miles earned. Do these cards work? Do customers who get such a card fly more on that airline? To find out, an airline compared the number of miles flown
A national real-estate developer builds luxury homes in three types of locations: urban cities (“city”), suburbs (“suburb”), and rural locations that were previously farmlands (“rural”). The response variable in this analysis is the change in the selling price per square foot from the
1. Observed response2. Number of cases in j th group3. Fitted value4. Residual5. Mean of data in omitted category6. Difference of two sample means7. Difference of two population means8. Null hypothesis of F-test9. F-statistic10. R2 in disguise(a)
1. A balanced experiment does not benefit from the use of randomization to assign the treatments to the subjects. 2. The one-way analysis of variance requires balanced data, with an equal number of observations in each group. 3. A two-sample t-test that pools the variances is equivalent to a simple
1. The F-test in an ANOVA tests the null hypothesis that all of the groups have equal variance. 2. The average of the residuals within a category used in an ANOVA is zero. 3. The within mean square in an ANOVA is another name for s2e, the sample variance of the residuals in the corresponding
Does the p-value of the two-sample t-test that does not assume equal variances match the p-value of the slope on a regression of Y on a dummy variable?
A company operates in the United States, Europe, South America, and the Pacific Rim. Management is comparing the costs incurred in its health benefits program by employees across these four regions. It ft an ANOVA regression of the amount spent for samples of 25 workers in each of the four regions.
The analysis in Exercise 25 uses South America as the omitted category. What would change and what would be the same had the analysis used the United States as the omitted reference category?
Consider the data shown in the following plot. Each group has 12 cases. Do the means appear statistically significant? Estimate the p-value: Is it about 0.5, about 0.05, or less than 0.0001?
Consider the data shown in the following plot. Each group has 12 cases. Do the means appear statistically significant? Estimate the p-value: Is it about 0.5, about 0.05, or less than 0.0001?
It can be shown that for any data y1, y2, c , yn the smallest value foris obtained by setting M = y̅. Explain why this implies that the fitted values in ANOVA are the sample averages of the groups.
A Web site monitors the number of unique customer visits, producing a total for each day. The following table summarizes the totals by day of the week, averaged over the last 12 weeks. (For example, during this 12-week period, the site averaged 2,350 visitors on Mondays.)A regression model
Rather than create five dummy variables to represent a categorical variable C with five labels, an analyst defined the variable X by converting the categories to the numbers 1, 2, 3, 4, and 5. Does the regression of Y on X produce the same results as a regression of Y on four dummy variables that
A line of men’s shirts was offered in a chain of retail stores at three prices: $32, $35, and $40. Weekly sales were monitored, producing totals at 30 stores in the chain (10 at each price). Which produces a higher R2: a linear regression of sales on price or an analysis of variance of sales
Suppose an ANOVA meets the conditions of the MRM and the F-test rejects the overall null hypothesis that four groups have equal means. Group 1 has the largest sample mean and Group 4 has the smallest. Does the confidence interval for μ1 - μ4 contain 0?
Suppose an ANOVA meets the conditions of the MRM and the F-test rejects the overall null hypothesis that five groups have equal means. If the Bonferroni confidence interval (adjusted for pairwise comparisons) for μ1 - μ2 does not include zero, does the Tukey confidence interval for μ1 - μ2
A research chemist uses the following laboratory procedure. He considers the yield of 12 processes that produce synthetic yarn. He then conducts the two-sample t-test with a = 0.05 between the process with the lowest yield and the process with the highest yield. What are his chances for a Type
A modeler has constructed a multiple regression with k = 10 explanatory variables to predict costs to her firm of providing health care to its employees. To decide which of the 10 explanatory variables is statistically significant, she rejects H0: βj = 0 if the p-value for the t-statistic of a

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