利用Excel进行统计分析Chapter14Introduction to Multiple Regression.pptVIP

Chap 14-* The Partial F-Test Statistic Consider the hypothesis test: H0: variable Xj does not significantly improve the model after all other variables are included H1: variable Xj significantly improves the model after all other variables are included Test using the F-test statistic: (with 1 and n-k-1 d.f.) Chap 14-* Testing Portions of Model: Example Test at the α = .05 level to determine whether the price variable significantly improves the model given that advertising is included Example: Frozen dessert pies Chap 14-* Testing Portions of Model: Example H0: X1 (price) does not improve the model with X2 (advertising) included H1: X1 does improve model α = .05, df = 1 and 12 F critical Value = 4.75 (For X1 and X2) (For X2 only) ANOVA ? df SS MS Regression 2 29460.02687 14730.01343 Residual 12 27033.30647 2252.775539 Total 14 56493.33333 ? ANOVA ? df SS Regression 1 17484.22249 Residual 13 39009.11085 Total 14 56493.33333 Chap 14-* Testing Portions of Model: Example Conclusion: Reject H0; adding X1 does improve model (For X1 and X2) (For X2 only) ANOVA ? df SS MS Regression 2 29460.02687 14730.01343 Residual 12 27033.30647 2252.775539 Total 14 56493.33333 ? ANOVA ? df SS Regression 1 17484.22249 Residual 13 39009.11085 Total 14 56493.33333 Chap 14-* Relationship Between Test Statistics The partial F test statistic developed in this section and the t test statistic are both used to determine the contribution of an independent variable to a multiple regression model. The hypothesis tests associated with these two statistics always result in the same decision (that is, the p-values are identical). Where a = degrees of freedom Chap 14-* Coefficient of Partial Determination for k Variable Model Measures the proportion of variation in the dependent variable that is explained by Xj while controlling for (holding constant) the other independent variables Chap 14-* Using Dummy Variables A dummy variable is a categorical independent