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 = .983.
2. The correlation relating number of females in managerial positions and number of female high school graduates with no college degree: r = .074.
3. The correlation relating number of males in managerial positions and number of males with a college degree: r = .722.
4. The correlation relating number of males in managerial positions and number of male high school graduates with no college degree: r = .528.

Short answer

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

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.

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.

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.

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.