Suppose we have the regression model Show that the R² from the regression R² = r²y xy Hint: consider the following steps

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Suppose We Have The Regression Model Show That The R From The Regression R R Y Xy Hint Consider The Following Steps 1 (127.22 KiB) Viewed 10 times

Suppose we have the regression model Show that the R² from the regression R² = r²y xy Hint: consider the following steps • Note that R² = ESS = ● := Σ=1(X; − x)2V/Σ i That is, the R² from the regression is the same as the squared sample correlation between X and Y. ● Plug in Y₁ = Bo + B₁ Xij 2 Plug in Bo=Y - B₁X; ₁1(Y₁-Y)² Zi=1(Yi-Y)2; i=1 Yi Bo + B₁Xį + Uj = satisfies n Σ1 (Xį – X)(Y; – Ý) Σi-1(Yi - Y)² Plug in the formula that Â₁ = • Cancel out Y, collect terms, and take ₁ out of the summation sign; 2 (X-X(X) and simplify. (X₁-X)² i=1