Transcription of Ch.6 Multiple Regression Multiple Regression …
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Ch.6 Multiple Regression Multiple Regression …
Chapter 06 Multiple Regression 4: Further Issues1 Econometrics1 Multiple Regression Analysisy = 0+ 1x1+ 2x2+ .. kxk+ u4. Further Multiple Regression : Further of Data Scaling on OLS on Functional on Goodness-of-Fit & Selection of & Residual Analysis* Effects of Data ScalingRedefining VariablesChanging the scale of the variable will lead to a corresponding change in the scale of the coefficients and standard errors, but no change in the significance or interpretation. seetable Redefining VariablesIf xjis multiplied by c, its coefficient is divided by yis multiplied by c, allOLS coefficients is multiplied by tnor Fstatistics are affected by changing the units of measurement of any the variables appears in logarithmic form, changing unit of measurement does not affect the slope of Data ScalingEconometrics5 DependentIndependentycy yx1 1(se1)c 1(c*se1) dx1 1/d(se1/d)x2 2(se2)c 2(c*se2) 2(se2)Intercept 0(se0)c 0(c*se0) 0(se0)R-squaredR2R2R2 SSRSSRc2*SSRSSRS tandard errors in parenthesesEconometrics6 Beta CoefficientsIdea is to replace yand each xvariable with a standardized version subtract mean and divide by standard reflects standard deviation of yfor a one standard deviation change in x.
Chapter 06 Multiple Regression 4: Further Issues 2 Econometrics 7 6.2 More on 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.
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