By Jeffrey M. Woolridge
Introductory Econometrics: a contemporary procedure. 3rd version. From Indian
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56. 9 when rounded to the first decimal place. These figures do not exactly agree because we have rounded the average wage and education, as well as the intercept and slope estimates. If we did not initially round any of the values, we would get the answers to agree more closely, but to little useful effect. Writing each yi as its fitted value, plus its residual, provides another way to interpret an OLS regression. For each i, write yi ϭ yˆi ϩ uˆi. 32) From property (1), the average of the residuals is zero; equivalently, the sample average of the fitted values, yˆi, is the same as the sample average of the yi , or yˆ¯ ϭ y¯.
Let x be the average return on equity (roe) for the CEO’s firm for the previous three years. ) For example, if roe ϭ 10, then average return on equity is 10 percent. To study the relationship between this measure of firm performance and CEO compensation, we postulate the simple model salary ϭ ␤0 ϩ ␤1roe ϩ u. The slope parameter ␤1 measures the change in annual salary, in thousands of dollars, when return on equity increases by one percentage point. Because a higher roe is good for the company, we think ␤1 Ͼ 0.
Consequently, it is not surprising that the regression line does poorly at very low levels of education. 42 per hour (in 1976 dollars). 27) implies that one more year of education increases hourly wage by 54 cents an hour. 16 per hour. These are fairly large effects. 27), another year of education increases the wage by the same amount, regardless of the initial level of education. 4, we discuss some methods that allow for nonconstant marginal effects of our explanatory variables. 2 E X A M P L E 2 .