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Lecture 28 - Standard Error of the Estimate If the data...

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Standard Error of the Estimate If the data spread about the line is normal Standard deviation ” for the regression line 2 n S S r x y - = / Standard error of the estimate No error if n = 2 ( a 0 and a 1 )
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Spread of data around the mean Spread of data around the best-fit line Linear regression reduce the spread of data Normal distributions
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Standard Deviation for Regression Line S y/x S S : Spread around the mean 2 n S S 1 n S S r x / y t y - = - =
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Example: Linear Regression 5 . 119 ) 5 . 5 ( 7 ) 0 . 6 )( 6 ( ) 5 . 2 )( 5 ( ) 0 . 4 )( 4 ( ) 0 . 2 )( 3 ( ) 5 . 2 )( 2 ( ) 5 . 0 )( 1 ( y x S 140 7 6 5 4 3 2 1 x S 24/7 n / S y ; 0 . 24 5 . 5 0 . 6 5 . 3 0 . 4 0 . 2 5 . 2 5 . 0 y S 4 28/7 /n S x ; 28 7 6 5 4 3 2 1 x S i i xy 2 2 2 2 2 2 2 2 i xx y i y x i x = + + + + + + = = = + + + + + + = = = = = + + + + + + = = = = = = + + + + + + = = 9911 2 S 7143 22 S 5 119 S 140 S 0 24 S 28 S 1993 0 2908 4 5 38 49 5 5 7 7972 0 6122 6 0 36 36 0 6 6 5896 0 0051 0 5 17 25 5 3 5 3265 0 3265 0 0 16 16 0 4 4 3473 0 0408 2 0 6 9 0 2 3 5625 0 8622 0 0 5 4 5 2 2 1687 0 5765 8 5 0 1 5 0 1 x a a y y y y x x y x r t xy xx y x 2 i 1 0 i 2 i i i 2 i i i . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ) ( ) ( = = = = = = - - -
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Example: Linear Regression 839285714 0 a 071428573 0 a 5 119 24 a a 140 28 28 7 S S a a S S S n 1 0 1 0 xy y 1 0 xx x x . , .
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