1. Degrees of freedom. How is the number of degrees of freedom available for estimating σ2, the variance of ε, related to the number of independent variables in a regression model?
2. Accounting and Machiavellianism. Refer to the Behavioral Research in Accounting (January 2008) study of Machiavellian traits (e.g., manipulation, cunning, duplicity, deception, and bad faith) in accountants, Exercise 1.47 (p. 41). Recall that a Machiavellian (''Mach'') rating score was determined for each in a sample of accounting alumni of a large southwestern university. For one portion of the study, the researcher modeled an accountant's Mach score (y) as a function of age (x1), gender (x2), education (x3), and income (x4). Data on n = 198 accountants yielded the results shown in the table.
(a) Write the equation of the hypothesized model relating y to x1, x2, x3, and x4.
(b) Conduct a test of overall model utility. Use α = .05.
(c) Interpret the coefficient of determination, R2.
(d) Is there sufficient evidence (at α = .05) to say that income is a statistically useful predictor of Mach score?