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STAT 301 (55)

Estimating the model, sum of squares, R2, extrapolation

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STAT 301
Brett Hunter

16 November Estimating the Model iid Our model is Y =iβ + 0 x +1ε1wher1 ε 1 N (0, σ ) We need to estimate β , 0 ,1and σ 2 Our estimated regression line is y 1 = b + b x 0 1 i b0is estimate for β0 b1is estimate for β1 Found by minimizing SSE 2 2 Seis the estimate for σ , where 2 SSE SSE 2 2 2 ∑ ei Seis the estimate for σ , where s =e n−2 = n−2 = df = MSE Mean squared error So √ MSE is the estimated standard deviation of the residuals, called the residual standard error. Note: We use n – 2 degrees of freedom so that MSE is an unbiased estimator of σ , as 2 we estimate 2 parameters (β , 0 ) 1eforehand. Sums of Squares In regression, we have a certain amount of variability in the y values. We want to understand what portion of this error can be accounted for by our model. 2 2 SSE = ∑ (yi−y i = ∑ ei Sum of squares error SSResid – residual sum of squares ̂y (¿¿i−y) 2 SSM = ∑ ¿ Sum of squares model SSR – sum of squares regression 2
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