0001001001000ˆˆˆˆˆ[|][|]E YXEXEEXXE YX3)(20 points) Start with the definition of goodness of fit,. Show mathematically how this is exactly equal to the square of the sample correlation coefficient, r. I never fail to be surprised by this result.
4)(20 points, 4 points for each piece.) Compare the following two regressions:i.01ˆˆiiiYXeii.01ˆˆˆ(4)iiiYXEquation i. is exactly the regression we’ve been working with thus far, so all the formulas we’ve derived thus far apply immediately. In equation ii all the values of the independent variable in the sample have been multiplied by 4. How does this change, if at all, the values of 1ˆ,0ˆ, SST, and r2? For the sake of clarity, please denote the OLS values for equation ii with a *, and compare them to the “regular” OLS estimates we derived in class.