formula_sheet-final-w09

formula_sheet-final-w09 - STAT 2607 Formulae Simple Linear...

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Unformatted text preview: STAT 2607: Formulae Simple Linear Regression ∑ n i =1 ( X i- ¯ X )( Y i- ¯ Y ) = ∑ n i =1 X i Y i- ∑ n i =1 X i ∑ n i =1 Y i n b = ¯ Y- b 1 ¯ X TSS = ∑ n i =1 ( Y i- ¯ Y ) 2 = ∑ n i =1 Y 2 i- ( ∑ n i =1 Y i ) 2 n b 1 = ∑ n i =1 X i Y i- ∑ n i =1 X i ∑ n i =1 Y i n ∑ n i =1 X 2 i- ( ∑ n i =1 X i ) 2 n SSR =  ∑ n i =1 X i Y i- ∑ n i =1 X i ∑ n i =1 Y i n  2 ∑ n i =1 X 2 i- ( ∑ n i =1 X i ) 2 n = b 2 1 • ∑ n i =1 X 2 i- ( ∑ n i =1 X i ) 2 n ‚ TSS = SSR + SSE A test statistics for H : β 1 = c t n- 2 = b 1- c q MSE ∑ n i =1 ( X i- ¯ X ) 2 100(1- α )% C.I. for β 1 : b 1 ± t n- 2 , α 2 s MSE ∑ n i =1 ( X i- ¯ X ) 2 100(1- α )% C.I. for E [ Y | X ] when X = X p : ˆ Y p ± t n- 2 , α 2 s MSE • 1 n + ( X p- ¯ X ) 2 ∑ n i =1 ( X i- ¯ X ) 2 ‚ 100(1- α )% C.I. for an individual Y p when X = X p : ˆ Y p ± t n- 2 , α 2 s MSE • 1 + 1 n + ( X p- ¯ X ) 2 ∑ n i =1 ( X i- ¯ X ) 2 ‚ Coefficient of correlation between...
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formula_sheet-final-w09 - STAT 2607 Formulae Simple Linear...

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