17.14 What's wrong?

For each of the following, explain what is wrong and why.

17.15 What's wrong?

For each of the following, explain what is wrong and why.

17.16 Is a movie profitable?

In Example 17.6 (pages 17-7 to 17-8), we developed a model to predict whether a movie will be profitable based on log opening-weekend revenue. What are the predicted odds of a movie being profitable if the opening-weekend revenue is

17.17 Converting odds to probability.

Refer to the previous exercise. For each opening-weekend revenue, compute the estimated probability that the movie is profitable.

17.18 Finding the best model?

In Example 17.11 (pages 17-16 to 17-7), we looked at a multiple logistic regression for movie profitability based on three explanatory variables. Complete the analysis by looking at the three models with two explanatory variable models and the three models with single variables. Create a table that includes the parameter estimates and their -values as well as the statistic and degrees of freedom. Based on the results, which model do you think is the best? Explain your answer.

17.19 Tipping behavior in Canada.

The Consumer Report on Eating Share Trends (CREST) contains data that cover all provinces of Canada and that describe away-from-home food purchases by roughly 4000 households per quarter. Researchers recently restricted their attention to restaurants at which tips would normally be given.⁴ From a total of 73,822 observations, “high” and “low” tipping variables were created based on whether the observed tip rate was above 20% or below 10%, respectively. They then used logistic regression to identify explanatory variables associated with either “high” or “low” tips. Here is a table summarizing what they termed the stereotype-related variables for the high-tip analysis:

The starred odds ratios were significant at the 0.01 level. Write a short summary explaining these results in terms of the odds of leaving a high tip.

17.20 Sexual imagery in magazine ads.

In what ways do advertisers in magazines use sexual imagery to appeal to youth? One study classified each of 1509 full-page or larger ads as “not sexual” or “sexual,” according to the amount and style of the dress of the male or female model in the ad. The ads were also classified according to the target readership of the magazine.⁵ A logistic regression was used to describe the probability that the clothing in the ad was “not sexual” as a function of several explanatory variables. Here are some of the reported results:

Reader age is coded as 0 for young adult and 1 for mature adult. Therefore, the coefficient of 0.50 for this explanatory variable suggests that the probability that the model clothing is not sexual is higher when the target reader age is mature adult. In other words, the model clothing is more likely to be sexual when the target reader age is young adult. Model sex is coded as 0 for female and 1 for male. The explanatory variable men's magazines is 1 if the intended readership is men and 0 for women's magazines and magazines intended for both men and women (general interest). The variable women's magazines is coded similarly.

17.21 Interpret the results.

Refer to the previous exercise. The researchers also reported odds ratios with 95% confidence intervals for this logistic regression model. Here is a summary:

17.22 CEO overconfidence/dominance and corporate acquisitions.

The acquisition literature suggests that takeovers occur either due to conflicts between managers and shareholders or to create a new entity that exceeds the sum of its previously separate components. Other research has offered managerial hubris as a third option, but it has not been studied empirically. Recently, some researchers revisited acquisitions over a 10-year period in the Australian financial system.⁶ A measure of CEO overconfidence was based on the CEO's level of media exposure, and a measure of dominance was based on the CEO's remuneration relative to the firm's total assets. They then used logistic regression to see whether CEO overconfidence and dominance were positively related to the probability of at least one acquisition in a year. To help isolate the effects of CEO hubris, the model included explanatory variables of firm characteristics and other potentially important factors in the decision to acquire. The following table summarizes the results for the two key explanatory variables:

17.23 E-government use in Canada.

Electronic government (e-government) provides digital means, such as an email address or a website, for citizens to contact public officials. The vision behind e-government is to create a more citizen-focused government. One study used survey data to determine what factors are related to a citizen using an e-government website rather than visiting or calling a government office.⁷ The dependent variable refers to whether the citizen used the website or not. Explanatory variables include sex (1 = female, 0 =male), daily Internet use (1 = yes, 0=no), age (six ordered categories numbered 1 through 6), household income (seven ordered categories numbered 1 through 7), size of the community (six ordered categories numbered 1 through 6), and education (1 = at least some postsecondary education, 0 = other). The following table summarizes the results.

All but “Education” and “Income” were significant at the 0.05 level.

17.24 Business Travel.

The Best Western Small Business Travel survey reported that 355 of 400 U.S. small business owners plan as many business trips this fall as last year.⁸

17.25 Stock options.

Different kinds of companies compensate their key employees in different ways. Established companies may pay higher salaries, while new companies may offer stock options that will be valuable if the company succeeds. Do high-tech companies tend to offer stock options more often than other companies? One study looked at a random sample of 200 companies. Of these, 91 were listed in the Directory of Public High Technology Corporations, and 109 were not listed. Treat these two groups as SRSs of high-tech and non-high-tech companies. Seventy-three of the high-tech companies and 75 of the non-high-tech companies offered incentive stock options to key employees.⁹

17.26 Log odds for high-tech and non-high-tech firms.

Refer to the previous exercise.

17.27 Do the inference.

Refer to the previous exercise. Software gives 0.3347 for the standard error of .

17.28 Suppose you had twice as many data.

Refer to Exercises 17.25 through 17.27. Repeat the calculations assuming that you have twice as many observations with the same proportions. In other words, assume that there are 182 high-tech firms and 218 non-high-tech firms. The numbers of firms offering stock options are 146 for the high-tech group and 150 for the non-high-tech group. The standard error of for this scenario is 0.2366. Summarize your results, paying particular attention to what remains the same and what is different from what you found in Exercises 17.25 through 17.27.

17.29 Poor service.

In the food service industry, some argue tipping encourages servers to provide discriminate service. If the server expects a good tip, he or she may provide better service. In one survey, 193 servers were surveyed and asked if they ever provided poor service because they did not expect a good tip. Ninety-six replied yes.¹⁰

17.30 Active retail companies versus failed companies.

Case 7.2 (page 389) compared the cash flow of 74 active retail firms with the cash flow for 27 firms that failed. Here we analyze the same data with a logistic regression. The outcome is whether or not the firm is active, and the explanatory variable is the cash flow. Here is the output from Minitab:

17.31 Analysis of a reduction in force.

To meet competition or cope with economic slowdowns, corporations sometimes undertake a “reduction in force” (RIF), in which substantial numbers of employees are terminated. Federal and various state laws require that employees be treated equally regardless of their age. In particular, employees over the age of 40 years are in a “protected” class, and many allegations of discrimination focus on comparing employees over 40 with their younger coworkers. Here are the data for a recent RIF:

17.32 Following brands through social media.

PricewaterhouseCoopers (PwC) surveyed 1000 online shoppers in the United States and China.¹¹ One question asked if the online shopper followed brands they purchased through social media. Here are the results:

17.33 Know your customers.

To devise effective marketing strategies, it is helpful to know the characteristics of your customers. A study compared demographic characteristics of people who use the Internet for travel arrangements and of people who do not.¹² Of 1132 Internet users, 643 had completed college. Among the 852 nonusers, 349 had completed college. Model the log odds of using the Internet to make travel arrangements with an indicator variable for having completed college as the explanatory variable. Summarize your findings.

17.34 Does income relate to use of the Internet?

The study mentioned in the previous exercise also asked about income. Among Internet users, 493 reported income of less than $50,000, and 378 reported income of $50,000 or more. (Not everyone answered the income question.) The corresponding numbers for nonusers were 477 and 200. Repeat the analysis using an indicator variable for income of $50,000 or more as the explanatory variable. What do you conclude?

17.35 Reduction in force using logistic regression.

In Exercise 17.31, hypothetical data are given for a reduction in force (RIF). If there is a statistically significant difference in the RIF proportions based on age group, the employer needs to justify the difference based on other (nondiscriminatory) variables.

17.36 Sexual imagery in ads.

Refer to Exercise 17.20 (page 17-18) concerning the use of sexual imagery in magazine ads. Here is the two-way table of counts for the 1509 ads.

Use the model dress, expressed as the odds that the dress is sexual, as the response variable and the magazine readership as the explanatory variable. Because there are three magazine readership categories, you will need two indicator variables for this multiple logistic regression analysis. Use the last category, general interest, for the “other” designation when creating these indicator variables.

17.37 Rerun the analysis with a different coding.

In the previous exercise, you used the last category, general interest, for the “other” designation when you constructed the indicator variables. Now use the women's magazine readership as the “other” category and reanalyze the data. Verify that the significance testing results for the effect of the two explanatory variables is the same as in the previous exercise.

17.38 Student athletes and gambling.

A survey of student athletes that asked questions about gambling behavior classified students according to the National Collegiate Athletic Association (NCAA) division.¹³ For male student athletes, the percent who reported wagering on collegiate sports are given here along with the numbers of respondents in each division:

17.39 Is there a trend?

Refer to the previous exercise. The coding of the indicator variables suggests a way to code models when you expect a pattern in the response that is based on some kind of ordering of the explanatory variable. In some settings this is called detecting a dose response.