Optimizing semiconductor material processing. Fluorocarbon plasmas are used in the production of semiconductor materials. In the Journal of Applied Physics

(Dec. 1, 2000), electrical engineers at Nagoya University

(Japan) studied the kinetics of fluorocarbon plasmas in order to optimize material processing. In one portion of the study, the surface production rate of fluorocarbon radicals emitted from the production process was measured at various points in time (in milliseconds) after the radio frequency power was turned off. The data are given in the table below. Consider a model relating surface production rate (y) to time (x).

Rate Time 1.00 0.1 0.80 0.3 0.40 0.5 0.20 0.7 0.05 0.9 0.00 1.1

-0.05 1.3

-0.02 1.5 0.00 1.7

-0.10 1.9

-0.15 2.1

-0.05 2.3

-0.13 2.5

-0.08 2.7 0.00 2.9

a. Graph the data in a scatterplot. What trend do you observe?

b. Fit a quadratic model to the data. Give the least squares prediction equation.

c. Is there sufficient evidence of upward curvature in the relationship between surface production rate and time after turnoff? Use a = .05.

Women in top management. The Journal of Organizational Culture, Communications and Conflict (July 2007) published a study on women in upper management positions at U.S. firms. 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). Determine which of the correlations reported in parts a–d results in a potential multicollinearity problem for the regression analysis.

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

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

c. The correlation relating number of males in managerial positions and number of males with a college degree: 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.