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Statistics for Business and Economics | 12th Edition | ISBN: 9780321826237 | Authors: James T. McClave, P. George Benson, Terry T Sincich
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Women in top management. Refer to the Journal

Chapter 12, Problem 123E

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QUESTION:

Problem 123E

Women in top management. Refer to the Journal ofOrganizational Culture, Communications and Conflict(July 2007) study on women in upper management positions at U.S. firms, Exercise 11.67 (p. 639). Monthly data(n = 252 months) were collected for several variables inan attempt to model the number of females in managerial positions (y). The independent variables included thenumber of females with a college degree (x1), the numberof 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 thenumber of male high school graduates with no collegedegree (x5). The correlations provided in Exercise 11.67are given in each part. Determine which of the correlations results in a potential multicollinearity problem forthe regression analysis.

a. The correlation relating number of females in managerial positions and number of females with a collegedegree: r = .983.

b. The correlation relating number of females in managerial positions and number of female high schoolgraduates with no college degree: r = .074.

c. The correlation relating number of males in managerial positions and number of males with a collegedegree: r = .722.

d. The correlation relating number of males in managerial positions and number of male high school graduates with no college degree: r = .528.

Questions & Answers

QUESTION:

Problem 123E

Women in top management. Refer to the Journal ofOrganizational Culture, Communications and Conflict(July 2007) study on women in upper management positions at U.S. firms, Exercise 11.67 (p. 639). Monthly data(n = 252 months) were collected for several variables inan attempt to model the number of females in managerial positions (y). The independent variables included thenumber of females with a college degree (x1), the numberof 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 thenumber of male high school graduates with no collegedegree (x5). The correlations provided in Exercise 11.67are given in each part. Determine which of the correlations results in a potential multicollinearity problem forthe regression analysis.

a. The correlation relating number of females in managerial positions and number of females with a collegedegree: r = .983.

b. The correlation relating number of females in managerial positions and number of female high schoolgraduates with no college degree: r = .074.

c. The correlation relating number of males in managerial positions and number of males with a collegedegree: r = .722.

d. The correlation relating number of males in managerial positions and number of male high school graduates with no college degree: r = .528.

ANSWER:

Step 1 of 4

For the given information 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 include

The number of females with a college degree ()

The number of female high school graduates with no college degree ()

The number of males in managerial positions ()

The number of males with a college degree ()

The number of male high school graduates with no college degree ()

Multicollinearity exists when two or more of the independent variables used in a

regression model contribute redundant information that is, the independent variables are

correlated with each other.

Using the correlation coefficient r to detect multicollinearity

Extreme multicollinearity:

Moderate multicollinearity:

Low multicollinearity:

a)  The correlation relating number of females in managerial positions and number of

     females with a college degree: r = 0.983.

     Here the value of correlation is 0.983; extreme multicollinearity exists between

     number of females in managerial positions and number of females with a college

     degree.

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