Multiple regression analysis y-Bo+BixI+Bx2+.Bixk+u ◆4. Further Issues Economics 20- Prof anderson
Economics 20 - Prof. Anderson 1 Multiple Regression Analysis y = b0 + b1 x1 + b2 x2 + . . . bk xk + u 4. Further Issues
● Redefining v ariables e Changing the scale of the y variable will lead to a corresponding change in the scale of the coefficients and standard errors so no change in the significance or interpretation o Changing the scale of one x variable will lead to a change in the scale of that coefficient and standard error. so no change in the significance or interpretation Economics 20- Prof anderson
Economics 20 - Prof. Anderson 2 Redefining Variables Changing the scale of the y variable will lead to a corresponding change in the scale of the coefficients and standard errors, so no change in the significance or interpretation Changing the scale of one x variable will lead to a change in the scale of that coefficient and standard error, so no change in the significance or interpretation
Beta Coefficients Occasional you ll see reference to a standardized coefficient or beta coefficient which has a specific meaning A Idea is to replace y and each x variable with a standardized version -i.e. subtract mean and divide by standard deviation e Coefficient reflects standard deviation of y for a one standard deviation change in x Economics 20- Prof anderson
Economics 20 - Prof. Anderson 3 Beta Coefficients Occasional you’ll see reference to a “standardized coefficient” or “beta coefficient” which has a specific meaning Idea is to replace y and each x variable with a standardized version – i.e. subtract mean and divide by standard deviation Coefficient reflects standard deviation of y for a one standard deviation change in x
Functional form OLS can be used for relationships that are not strictly linear in x and y by using nonlinear functions of x and y-will still be linear in the parameters o Can take the natural log ofx, y or bot Can use quadratic forms of x Can use interactions of x variables Economics 20- Prof anderson 4
Economics 20 - Prof. Anderson 4 Functional Form OLS can be used for relationships that are not strictly linear in x and y by using nonlinear functions of x and y – will still be linear in the parameters Can take the natural log of x, y or both Can use quadratic forms of x Can use interactions of x variables
Interpretation of Log models o If the model is In()=Bo+BIn(x)+u o, is the elasticity of y with respect to x o If the model is In()=Bo+Bx+u e B, is approximately the percentage change in y given a l unit change in x o If the model is y=Bo+ BIn(x)+u B, is approximately the change in y for a 100 percent change in x Economics 20- Prof anderson 5
Economics 20 - Prof. Anderson 5 Interpretation of Log Models If the model is ln(y) = b0 + b1 ln(x) + u b1 is the elasticity of y with respect to x If the model is ln(y) = b0 + b1 x + u b1 is approximately the percentage change in y given a 1 unit change in x If the model is y = b0 + b1 ln(x) + u b1 is approximately the change in y for a 100 percent change in x