39.* Right-to-work laws. Are state right-to-work laws related to the percent of public sector employees (Public) in unions and the percent of private sector employees (Private)

in unions? (Each predictor variable has a value between 0 and 100.) This data set looks at these percentages for the states in the United States in 1982. The dependent variable is whether the state had a right-to-work law or not (

Yes, No). The computer output for the logistic regression is given here. (Source: N. M. Meltz, “Interstate and Interprovincial Differences in Union Density,” Industrial Relations, 28:2 (Spring 1989), 142–158 by way of DASL.)

a) Write out the estimated regression equation.

b) What is the predicted log odds (logit) of the probability that a state has a right-to-work law if 20% of the public and 10% of the private sector employees are in unions?

c) What is the predicted probability of that state?

d) What is the probability log odds (logit) that a state has a right-to-work law if 40% of the public and 20% of the private sector employees are in unions?

e) What is the associated predicted probability?

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Logistic Regression Table Predictor Coeff SE(Coeff) Z P Intercept 6.19951 1.78724 3.47 0.001 publ -0.106155 0.0474897 -2.24 0.025 pvt -0.222957 0.0811253 -2.75 0.006