An economist was interested in modeling the relation among annual income, level of education, and work experience. The level of education is the number of years of education beyond eighth grade, so 1 represents completing 1 year of high school, 8 means completing 4 years of college, and so on. Work experience is the number of years employed in the current profession. From a random sample of 12 individuals, he obtained the following data:

(a) Construct a correlation matrix between work experience, level of education, and annual income. Is there any reason to be concerned with multicollinearity based on the correlation matrix?
(b) Find the least-squares regression equation yÌ… = b0 + b1x1 + b2x2, where x1 is work experience, x2 is level of education, and y is the response variable, annual income.
(c) Draw residual plots and a boxplot of the residuals to assess the adequacy of the model.
(d) Interpret the regression coefficients for the least-squares regression equation.
(e) Determine and interpret R2 and the adjusted R2.
(f) Test H0: b1 = b2 = 0 versus H1: at least one of the bi ≠ 0 at the a = 0.05 level of significance.
(g) Test the hypotheses H0: b1 = 0 versus H1: b1 ≠ 0 and H0: b2 = 0 versus H1: b2 ≠ 0 at the a = 0.05 level of significance.
(h) Predict the mean income of all individuals whose experience is 12 years and level of education is 4.
(i) Predict the income of a single individual whose experience is 12 years and level of education is 4.
(j) Construct 95% confidence and prediction intervals for income when experience is 12 years and level of education is 4.

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Work Experience (years) Level of Annual Income ($ thousands) Education 21 6. 34.7 14 3 17.9 4 8. 22.7 63.1 16 8. 12 4 33.0 20 4 41.4 25 1 20.7 14.6 3 97.3 24 12 72.1 28 49.1 11 15 4 52.0