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420Hw04ans - STAT 420 Homework#4 Fall 2007 2.2 The dataset...

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STAT 420 Fall 2007 Homework #4 2.2 The dataset uswages is drawn as a sample from the Current Population Survey in 1988. Fit a model with weekly wages as the response and years of education and experience as predictors. Report and give a simple interpretation to the regression coefficient for years of education. Now fit the same model but with logged weekly wages. Give an interpretation to the regression coefficient for years of education. Which interpretation is more natural? > library(faraway) > data(uswages) > uswages[1:5,] # to see what the data set looks like wage educ exper race smsa ne mw so we pt 6085 771.60 18 18 0 1 1 0 0 0 0 23701 617.28 15 20 0 1 0 0 0 1 0 16208 957.83 16 9 0 1 0 0 1 0 0 2720 617.28 12 24 0 1 1 0 0 0 0 9723 902.18 14 12 0 1 0 1 0 0 0 > attach(uswages) > > fit1 = lm(wage ~ educ + exper) > summary(fit1) Call: lm(formula = wage ~ educ + exper) Residuals: Min 1Q Median 3Q Max -1018.23 -237.86 -50.87 149.88 7228.61 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -242.7994 50.6816 -4.791 1.78e-06 *** educ 51.1753 3.3419 15.313 < 2e-16 *** exper 9.7748 0.7506 13.023 < 2e-16 *** --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: 427.9 on 1997 degrees of freedom Multiple R-Squared: 0.1351, Adjusted R-squared: 0.1343 F-statistic: 156 on 2 and 1997 DF, p-value: < 2.2e-16
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The fitted regression function is wage = – 242.7994 + 51.1753 * educ + 9.7748 * exper. The regression coefficient for years of education is 51.1753. We would expect weekly wages to increase by 51.1753 on average for every 1-year increase of years of education with experience fixed.
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