# Slide12 - Bias and Variance of Slope and Intercept Slope ^ E 1 = 1 Intercept 2 ^)= V 1 S xx ^ E 0 = 0 2 ^)= 21 x V 0 n S xx 1 Variance Formulae

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1 Bias and Variance of Slope and Intercept ± Slope: ± Intercept: 1 1 ) ˆ ( E β = xx 2 1 S ) ˆ ( V σ = 0 0 ) ˆ ( E = + = xx 2 2 0 S x n 1 ) ˆ ( V 2 Variance Formulae ± Error sum of squares: ± Can show that ± Therefore is unbiased = = = = n 1 i 2 i i n 1 i 2 i E ) y ˆ y ( e SS 2 E ) 2 n ( ) SS ( E = 2 n SS ˆ E 2 =

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3 Variance Formulae ± Another formula for ± where E SS xy 1 T E S ˆ SS SS β = 2 n 1 i i T ) y y ( SS = 4 Estimated Standard Errors (definitions) ± Slope: ± Intercept: xx 2 1 S ˆ ) ˆ ( se σ =
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## This note was uploaded on 05/05/2008 for the course IE 121 taught by Professor Perevalov during the Spring '08 term at Lehigh University .

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Slide12 - Bias and Variance of Slope and Intercept Slope ^ E 1 = 1 Intercept 2 ^)= V 1 S xx ^ E 0 = 0 2 ^)= 21 x V 0 n S xx 1 Variance Formulae

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