Class Notes (835,342)
Tony Quon (67)
Lecture 21

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Tony Quon
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Degrees of freedom: Sum of Squares Mean Square = SSTotalhas n 1 d.f. Degrees of freedom Divide total deviation of y from y into two parts: SSR has 1 d.f. yi y = (yi ) + (yi i) n 2 n 2 n 2 SSE has n 2 d.f. (yi y) = (yi y) + (yi yi) i=1 i=1 i=1 Square both sides and sum over all observations: Sum of Squares Sum of Squares Sum of Squares n 2 n 2 = ANOVA: (i y) = yi y) (yi i Total Model Error i=1 i=1 n 2 n 2 SSTotal = SSR + SSE = (yi ) + (yi i) (cross products = 0) i=1 i=1 Source of Sum of Deg. of Mean Square F Var. Squares freedom Total Variation = Explained Var. + Unexplained Var. 1 MSR = SSR1 MSRMSE Error SSE n 2 MSE = SSE(n 2) Total SSTotal n 1 ANOVA Table: SSTotal = (y y) =(n1)s 2 i y i 1 2 xi i ( xi)( yi) 2 n Computational Formulas SSR = (yi y) = 1 2 i xi ( ) xi n SSE = SSTotalSSR 2 MSE = (yi yi) = s s = MSE n2 H :0 =0 1 H :0 = 0 Alternative Hypothesis Test: If we let r be the sample correlation coefcient and be the population correlation coefcient, then testing is equivalent to testing . Why? Test statistic:
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