multiple regression noteshells 3

# multiple regression noteshells 3 - Multiple Regression Part...

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Multiple Regression I 1 Multiple Regression 2: Inference 1 Multiple Regression Part 2: Inference Sections 14.4 and (kind of) 14.5 Multiple Regression 2: Inference 2 Book's Example n = 34 stores in a chain Y = Monthly sales of the OmniPower bar X 1 = Price of the bar in cents. X 2 = In-store promotion expenditures (signs, displays, coupons, etc.) Used three prices and three promo levels

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Multiple Regression I 2 Multiple Regression 2: Inference 3 PhStat Output Two-variable regression Regression Statistics Multiple R 0.8705 R Square 0.7577 Adjusted R Square 0.7421 Standard Error 638.0653 Observations 34 ANOVA df SS MS F Significance F Regression 2 39472730.77 19736365.39 48.4771 0.0000 Residual 31 12620946.67 407127.31 Total 33 52093677.44 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 5837.5208 628.1502 9.2932 0.0000 4556.3999 7118.6416 Price -53.2173 6.8522 -7.7664 0.0000 -67.1925 -39.2421 Promotion 3.6131 0.6852 5.2728 0.0000 2.2155 5.0106 Multiple Regression 2: Inference 4 Tests on the β j Values H 0 : β j = 0 (X j does not help explain Y over and above the other Xs) H 1 : β j 0 (X j contains predictive information beyond that of the other Xs)
Multiple Regression I 3 Multiple Regression 2: Inference 5 OmniPower Example Y-hat = 5837.5 - 53.2173 Price + 3.6131 Promo (6.8522) (0.6852) With n=34, k=2, df = 31. Use t = 2.0395 Multiple Regression 2: Inference 6 Do the estimates make sense? Y-hat = 5837.5 - 53.2173 Price + 3.6131 Promo The coefficient estimates seem to. As price increases, ______________. As promotion expenditure increases, _____________. The correlations agree: Sales Price Promotion Sales 1 Price -0.7351 1 Promotion 0.5351 -0.0968 1

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Multiple Regression I 4 Multiple Regression 2: Inference 7 This isn’t always the case h Here, the correlation between X 1 and X 2 was only -.09, so the two Xs were more or less independent of each other. h With correlated Xs, the coefficient estimates can get mixed up, even to the point of having the wrong sign. h Significance may be affected. Multiple Regression 2: Inference 8 Our large data set We appear to have at least four strong predictors. Muscle
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multiple regression noteshells 3 - Multiple Regression Part...

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