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Stat 4 Week 6 Simple Regression Formulas

# Stat 4 Week 6 Simple Regression Formulas - Degrees of...

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Simple Linear Regression: Building Blocks and Essential Formulas Building Blocks (all of the “Essential Formulas” below follow from the Building Blocks, which consist of the raw data and the core measures of central tendency and dispersion) 1. The raw data: the values for y and x, the number of values = n. 2. The core measures of central tendency: the means of y and x, n y y = and n x x = . 3. The core measures of dispersion: the deviation sums of squares and cross products. a) - = 2 ) ( y y SS yy b) - = 2 ) ( x x SS xx c) - - = ) )( ( y y x x SS xy Essential Formula Name, or Descriptor 1. xx xy SS SS b = 1 Point estimate of the slope. 2. x b y b 1 0 - = Point estimate of the y-intercept. 3. x b b y 1 0 ˆ + = The regression equation. 4. xy xx xy SS b SS SS SSR 1 2 ) ( = = Sum of squares for the regression (= explained variation). 5. SSE SSR SST = - ; yy SS SST = Sum of squares total – sum of squares due to regression = sum of squares residual (= unexplained variation). 6. Total df = n-1 Error df = n-2 Regression df = 1

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Unformatted text preview: Degrees of freedom. 7. 2-= n SSE s Standard error. 8. SST SSR r = 2 ; 2 r r + = r-squared, the proportion of the variability in y explained by x. 9. xx b SS x n s s 2 1 + = ; xx b SS s s = 1 Standard error of the estimate b , and standard error of the estimate 1 b . 10. b s b t = ; 1 1 b s b t = t for testing significance of the y-intercept; t for testing significance of the slope. 1 11. ) ( ) ( SSR df SSR R MS = ; ) ( ) ( SSE df SSE E MS = Mean square regression; mean square error. 12. ) ( ) ( E MS R MS F = Test of the model. 13. xx SS x x n 2 ) ( 1-+ Distance Value. 14. ceValue Dis s s y tan ˆ = ; ceValue Dis s s y y tan 1 ) ˆ ( + =-A measure of the distance between the value x of x and x . 15. y s t y ˆ 2 ˆ α ± ; ) ˆ ( 2 ˆ y y s t y-± Confidence Interval; Prediction Interval 2...
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Stat 4 Week 6 Simple Regression Formulas - Degrees of...

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