FinalFormulaetpmFinal_Fall_2012

1 chapter 7 confidence

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Unformatted text preview: r= sxy sx s y Simple linear regression model y = µ y| x + ε = β 0 + β1 x + ε Least squares point estimates !!!" !!" !! = = ! !!!! !! !! = ! − !! ! Sum of squared residuals ! !!!" !!" = !!!! − !!!! = !!! !!! − !! !!! !! − !! ! ! Standard error s= Total variation SSE n − 2 (!! − !)! = !!!! Unexplained variation (!! − !! )! = !!" Explained variation (!! − !)! Mean square error !! = !!" !−2 totalvariation F test for the simple linear regression model explainedvariation unexplainedvariation/(! − 2) (Estimated) Standard error of the estimator b1 ! !!!! 2 Simple correlation coefficient ! ! !! !! )/! ! ! !!!! = ! − 1 !! !!!! = (! − 1)!! ! ! !! !! )( !!!" = (! − 1)!!" −( !−1 !! , !! !"#!"#$%&!"#$%#&! !"#$%&$'() = !! = !! − ! !! − ! !−1 ! ! !! !! !! 1 (x − x ) Distance value = + 0 n SS xx (Estimated) Standard error of ! s y = s distance value ˆ Confidence interval for a mean value of y Ⱥ y ± tα / 2 s distance value Ⱥ ˆ Ⱥ Ⱥ Prediction interval for an individual value of y Ⱥ y ± tα / 2 s 1 + distance value Ⱥ ˆ Ⱥ Ⱥ Chapter 12 Multiple regression The multiple regression model y = µ y|x1 , x2 ,L , xk + ε = β0 + β1 x1 + β 2 x2 + ⋅⋅⋅ + β k xk + ε Standard error SSE s= n − ( k + 1) Mean square error SSE s2 = n − ( k + 1) Multiple coefficient of determination explained variation R2 = total variation Multiple correlation coefficient ! = !! An F test for the linear regression model explainedvariation/! unexplainedvariation/[! − ! + 1 ] Testing the significance of an independent variable bj t= sb j...
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