section9_handout_stat104_josh

section9_handout_stat104_josh - Stat 104 Section 9 Josh...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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....
View Full Document

{[ snackBarMessage ]}

Page1 / 3

section9_handout_stat104_josh - Stat 104 Section 9 Josh...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online