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Chapter 12: Q125E (page 803)

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.

Short Answer

Expert verified

  1. There is high level of multicollinearity between y and x1

  2. There is low level of multicollinearity between y and x2.

  3. There is moderate level of multicollinearity between x3 and x4.

  4. There is moderate level of multicollinearity between x3 and x5.

Step by step solution

01

Multicollinearity check

The r value between number of females in managerial positions (y) and number of females with a college degree (x1) is 0.983 which is very high degree of correlation.

Hence there is high level of multicollinearity between y and x1.

02

Multicollinearity check

The r value between number of females in managerial positions (y) and number of female high school graduates with no college degree (x2) is 0.074 which is very low degree of correlation.

Hence there is low level of multicollinearity between y and x2.

03

Multicollinearity check

The r value between number of males in managerial positions (x3) and number of males with a college degree (x4) is 0.722 which is moderate degree of correlation.

Hence there is moderate level of multicollinearity between x3 and x4.

04

Multicollinearity check

The r value between number of males in managerial positions (x3) and number of male high school graduates with no college degree (x5) is 0.528 which is moderate degree of correlation.

Hence there is moderate level of multicollinearity between x3 and x5.

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Most popular questions from this chapter

Personality traits and job performance. When attempting to predict job performance using personality traits, researchers typically assume that the relationship is linear. A study published in the Journal of Applied Psychology (Jan. 2011) investigated a curvilinear relationship between job task performance and a specific personality traitโ€”conscientiousness. Using data collected for 602 employees of a large public organization, task performance was measured on a 30-point scale (where higher scores indicate better performance) and conscientiousness was measured on a scale of -3 to +3 (where higher scores indicate a higher level of conscientiousness).

a. The coefficient of correlation relating task performance score to conscientiousness score was reported as r = 0.18. Explain why the researchers should not use this statistic to investigate the curvilinear relationship between task performance and conscientiousness.

b. Give the equation of a curvilinear (quadratic) model relating task performance score (y) to conscientiousness score (x).

c. The researchers theorized that task performance increases as level of conscientiousness increases, but at a decreasing rate. Draw a sketch of this relationship.

d. If the theory in part c is supported, what is the expected sign ofฮฒ2in the model, part b?

e. The researchers reportedฮฒ^2=0.32with an associated p-value of less than 0.05. Use this information to test the researchersโ€™ theory atฮฑ=0.05

Question: Orange juice demand study. A chilled orange juice warehousing operation in New York City was experiencing too many out-of-stock situations with its 96-ounce containers. To better understand current and future demand for this product, the company examined the last 40 days of sales, which are shown in the table below. One of the companyโ€™s objectives is to model demand, y, as a function of sale day, x (where x = 1, 2, 3, c, 40).

  1. Construct a scatterplot for these data.
  2. Does it appear that a second-order model might better explain the variation in demand than a first-order model? Explain.
  3. Fit a first-order model to these data.
  4. Fit a second-order model to these data.
  5. Compare the results in parts c and d and decide which model better explains variation in demand. Justify your choice.

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 oneโ€™s desire to undergo cosmetic surgery, Exercise 12.17 (p. 725). Recall that psychologists used multiple regression to model desire to have cosmetic surgery (y) as a function of gender(x1) , self-esteem(x2) , body satisfaction(x3) , and impression of reality TV (x4). The SPSS printout below shows a confidence interval for E(y) for each of the first five students in the study.

  1. Interpret the confidence interval for E(y) for student 1.
  2. Interpret the confidence interval for E(y) for student 4

Consider the model:

E(y)=ฮฒ0+ฮฒ1x1+ฮฒ2x2+ฮฒ3x22+ฮฒ4x3+ฮฒ5x1x22

where x2 is a quantitative model and

x1=(1receivedtreatment0didnotreceivetreatment)

The resulting least squares prediction equation is

localid="1649802968695" yโœ=2+x1-5x2+3x22-4x3+x1x22

a. Substitute the values for the dummy variables to determine the curves relating to the mean value E(y) in general form.

b. On the same graph, plot the curves obtained in part a for the independent variable between 0 and 3. Use the least squares prediction equation.
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