section9_handout_stat104_josh

section9_handout_stat104_josh - Stat 104 Section 9 Josh...

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Unformatted text preview: Stat 104 Section 9 Josh Zagorsky < [email protected] > ANOVA 1. Analysis of Variance Source Degrees of Freedom SS Mean Squares regression k SSR SSR k error n - k - 1 SSE SSE n- k- 1 total n -1 SST 2. R-squared = SSR SST = 1- SSE SST , but this always increases with more predictive variables, so many statisticians use adjusted R-squared, which penalizes additional variables. Adjusted R-squared = R 2 a = 1- 1 n- k- 1 SSE 1 n- 1 SST Intervals 1. Confidence Interval For the mean person with x = 5, the confidence interval = b + b 1 X ± 1 . 96 s e s 1 n + ( X- ¯ X ) 2 ( n- 1) s 2 x s e is taken from the Root MSE term in Stata output. To obtain a confidence interval for an x-value of 5 in Stata, type: adjust xvariable = 5, ci 2. Prediction Interval For any person with x = 5, the confidence interval = b + b 1 X ± 1 . 96 s e s 1 + 1 n + ( X- ¯ X ) 2 ( n- 1) s 2 x To obtain a predtiction interval for x = 5, type: adjust xvariable = 5, stdf ci The prediction interval is always wider than the confidence interval. At large n , it approaches b + b 1 X ± 1 . 96 s e Multiple Regression 1. Y = β + β 1 X 1 + β 2 X 2 + β 3 X 3 + ... + β k X k + ε 2. Omnibus F test : H : β 1 X 1 + β 2 X 2 + β 3 X 3 + ... + β k X k = 0. H a : any β i 6 = 0. f ∼ F k,n- k- 1 but just take the probability interpretation from Stata’s output line Prob > F 3. s e = r SSE n- k- 1 4. Backwards Stepwise Regression : put all the predictor variables in, then remove the least signifi- cant variable and re-run the regression. Repeat until all remaining predictor variables are significant.cant variable and re-run the regression....
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section9_handout_stat104_josh - Stat 104 Section 9 Josh...

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