# slide14 - Prediction of new observations ^ ^ y Regression...

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1 Prediction of new observations ± Regression model: ± A 100(1- α ) percent interval on a future observation y 0 at the value x 0 is given by: + + + + + xx 2 0 2 2 n , 2 / 0 0 xx 2 0 2 2 n , 2 / 0 S ) x x ( n 1 1 ˆ t y ˆ y S ) x x ( n 1 1 ˆ t y ˆ σ α 0 1 0 0 x ˆ ˆ y ˆ β + = 2 Residual Analysis -20 -15 -10 -5 0 5 10 15 20 131 132 133 134 135 136 137 138 139 Sales Residual -20 -15 -10 -5 0 5 10 15 20 012345 Advertising

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3 Coefficient of determination (R 2 ) ± Definition ± R 2 is the amount of variability in the data explained by the regression model ± Misconceptions about R 2 1 R 0 SS SS 1 SS SS R 2 T E T R 2 = = 4 Lack-of-fit Test ± Hypotheses: ± H 0 : The simple linear regression model is correct ± H 1 : The simple linear regression model is not correct ± Error or residual sum of square ± SSPE: Sum of squares attributable to pure error ± SSLOF: Sum of squares attributable to the
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slide14 - Prediction of new observations ^ ^ y Regression...

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