lecture+8_complete

# lecture+8_complete - y = b b 1 x u The Simple Regression...

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Unformatted text preview: y = b + b 1 x + u The Simple Regression Model (cont.) 2 OUTLINE 1. Transformation of variables (changing the units of measurement) 2. Functional forms 3. Regression through the origin 3 1. Changing the units of measurement: effect on the OLS estimates Changing the units of measurement of the dependent variable The SLR model is given by: y = b + b 1 x + u If we estimate the above population model by OLS i.e . run the regression of y on x , we get the following SRF: Suppose, instead, we run the regression of a new dependent variable ‘cy’ on the same independent variable x (where c is a constant), then we get the following SRF: x y 1 ˆ ˆ ˆ b b x c c y c ) ˆ ( ) ˆ ( ˆ 1 b b 4 1. Changing the units of measurement: effect on the OLS estimates Changing the units of measurement of the dependent variable Thus, when we run the regression of ‘cy’ on x, the OLS intercept estimate and the slope estimate are also multiplied by c. If, instead, we run the regression of ‘y/c’ on the same independent variable x (where c is a constant), then we get the following SRF: Thus, when we run the regression of ‘y/c’ on x, the OLS intercept estimate and the slope estimate both get divided by c. x c c c y ) ˆ ( ) ˆ ( ˆ 1 b b 5 1. Changing the units of measurement of the dependent variable: example Let y be annual salary in thousands of dollars for the population of CEOs. Let x be the average return on equity (roe) measured as a percentage. If we run the regression of salary on roe, we get the following SRF: ??¡?¢ = £???. ¤?¤ + ¤?. ?¥¤¢¦? n= 209, R 2 = 0.0132 Interpretation of intercept and slope estimate: If the return on equity is 0, then the predicted salary is the 963.191 thousands of dollars i.e. \$963,191 , holding all other factors constant . If the return on equity increases by 1 percentage point , then the salary is predicted to increase by 18.501 thousands of dollars i.e. \$18,501 , holding all other factors constant. 6 1. Changing the units of measurement of the dependent variable: example Now, suppose instead of measuring salary in thousands of dollars, we measure it in dollars. Let’s define a new dependent variable salardol, measured in dollars. So salardol=12,541, would be interpreted as \$12,541. salardol=(1000)salary What is the new SRF? ??¡?¢?£¡ = ¤??¥, ¦?¦ + ¦?, ?§¦¢£? n= 209, R 2 = 0.0132 Interpretation of intercept and slope estimate: If the return on equity is 0, then the predicted salary is \$963,191 , holding all other factors constant . If the return on equity increases by 1 percentage point , then the salary is predicted to increase by \$18,501 , holding all other factors constant....
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lecture+8_complete - y = b b 1 x u The Simple Regression...

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