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Chapter 12: Q140SE (page 807)

It is desired to relate E(y) to a quantitative variable x1and a qualitative variable at three levels.

  1. Write a first-order model.

  2. Write a model that will graph as three different second- order curves鈥攐ne for each level of the qualitative variable.

Short Answer

Expert verified

  1. A first-order model equation in one quantitative variable and one qualitative variable with 3 levels can be written asEy=尾0+尾1x1+尾2x2+尾3x3

  2. Graph

Step by step solution

01

First-order model

A first-order model equation in one quantitative variable and one qualitative variable with 3 levels can be written asE(y)=尾0+尾1x1+尾2x2+尾3x3

Where x1is the quantitative variable

And x2 and x3 represent level 1 and level 2 of the qualitative variable.

02

Graph

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Most popular questions from this chapter


Factors that impact an auditor鈥檚 judgment. A study was conducted to determine the effects of linguistic delivery style and client credibility on auditors鈥� judgments (Advances in Accounting and Behavioural Research, 2004). Two hundred auditors from Big 5 accounting firms were each asked to perform an analytical review of a fictitious client鈥檚 financial statement. The researchers gave the auditors different information on the client鈥檚 credibility and linguistic delivery style of the client鈥檚 explanation. Each auditor then provided an assessment of the likelihood that the client-provided explanation accounted for the fluctuation in the financial statement. The three variables of interest鈥攃redibility (x1), linguistic delivery style (x2) , and likelihood (y) 鈥攚ere all measured on a numerical scale. Regression analysis was used to fit the interaction model,y=尾0+尾1x1+尾2x2+尾3x1x2+蔚 . The results are summarized in the table at the bottom of page.

a) Interpret the phrase client credibility and linguistic delivery style interact in the words of the problem.

b) Give the null and alternative hypotheses for testing the overall adequacy of the model.

c) Conduct the test, part b, using the information in the table.

d) Give the null and alternative hypotheses for testing whether client credibility and linguistic delivery style interact.

e) Conduct the test, part d, using the information in the table.

f) The researchers estimated the slope of the likelihood鈥搇inguistic delivery style line at a low level of client credibility 1x1 = 222. Obtain this estimate and interpret it in the words of the problem.

g) The researchers also estimated the slope of the likelihood鈥搇inguistic delivery style line at a high level of client credibility 1x1 = 462. Obtain this estimate and interpret it in the words of the problem.

Production technologies, terroir, and quality of Bordeaux wine. In addition to state-of-the-art technologies, the production of quality wine is strongly influenced by the natural endowments of the grape-growing region鈥攃alled the 鈥渢erroir.鈥� The Economic Journal (May 2008) published an empirical study of the factors that yield a quality Bordeaux wine. A quantitative measure of wine quality (y) was modeled as a function of several qualitative independent variables, including grape-picking method (manual or automated), soil type (clay, gravel, or sand), and slope orientation (east, south, west, southeast, or southwest).

  1. Create the appropriate dummy variables for each of the qualitative independent variables.
  2. Write a model for wine quality (y) as a function of grape-picking method. Interpret the尾鈥檚 in the model.
  3. Write a model for wine quality (y) as a function of soil type. Interpret the尾鈥檚 in the model.
  4. Write a model for wine quality (y) as a function of slope orientation. Interpret the尾鈥檚 in the model.

Question: Reality TV and cosmetic surgery. Refer to the Body Image: An International Journal of Research (March 2010) study of the impact of reality TV shows on a college student鈥檚 decision to undergo cosmetic surgery, Exercise 12.43 (p. 739). The data saved in the file were used to fit the interaction model, E(Y)=尾0+尾1x1+尾2x4+尾3x1x4, where y = desire to have cosmetic surgery (25-point scale),x1= {1 if male, 0 if female}, and x4= impression of reality TV (7-point scale). From the SPSS printout (p. 739), the estimated equation is:y^=11.78-1.97x1+0.58x4-0.55x1x4

a. Give an estimate of the change in desire (y) for every 1-point increase in impression of reality TV show (x4) for female students.

b. Repeat part a for male students.

Buy-side vs. sell-side analysts鈥� earnings forecasts. Refer to the Financial Analysts Journal (July/August 2008) comparison of earnings forecasts of buy-side and sell-side analysts, Exercise 2.86 (p. 112). The Harvard Business School professors used regression to model the relative optimism (y) of the analysts鈥� 3-month horizon forecasts. One of the independent variables used to model forecast optimism was the dummy variable x = {1 if the analyst worked for a buy-side firm, 0 if the analyst worked for a sell-side firm}.

a) Write the equation of the model for E(y) as a function of type of firm.

b) Interpret the value of尾0in the model, part a.

c) The professors write that the value of尾1in the model, part a, 鈥渞epresents the mean difference in relative forecast optimism between buy-side and sell-side analysts.鈥� Do you agree?

d) The professors also argue that 鈥渋f buy-side analysts make less optimistic forecasts than their sell-side counterparts, the [estimated value of尾1] will be negative.鈥� Do you agree?

Question: Women in top management. Refer to the Journal of Organizational Culture, Communications and Conflict (July 2007) study on women in upper management positions at U.S. firms, Exercise 11.73 (p. 679). Monthly data (n = 252 months) were collected for several variables in an attempt to model the number of females in managerial positions (y). The independent variables included the number of females with a college degree (x1), the number of female high school graduates with no college degree (x2), the number of males in managerial positions (x3), the number of males with a college degree (x4), and the number of male high school graduates with no college degree (x5). The correlations provided in Exercise 11.67 are given in each part. Determine which of the correlations results in a potential multicollinearity problem for the regression analysis.

  1. The correlation relating number of females in managerial positions and number of females with a college degree: r =0.983.

  2. The correlation relating number of females in managerial positions and number of female high school graduates with no college degree: r =0.074.

  3. The correlation relating number of males in managerial positions and number of males with a college degree: r =0.722.

  4. The correlation relating number of males in managerial positions and number of male high school graduates with no college degree: r =0.528.
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