6.1 (Data fie: UNI1) With the UN data, perform a test of NH : (6.6) against the alternative AH : (6.7), and summarize results. This is an overall F-test for a model with one factor and no additional regressors. 6.7 problems 151 6.2 (Data fie: UNI1) With the UN data, explain why there is no F-test comparing models (6.7) and (6.8). 6.3 (Data file: UN11) In the UN data. compute the F-test NH Model AH Model : (6 7) (6 9) and summarize results. 6.4 (Data fie: UN11) With the UN data, consider testing NH AH life ExpF ~ log(ppgdpl group: log(ppgdpl life ExpF - group I * og(ppgdpl * group: log(ppgp) The AH model is the most general model given at (6.10), but the NH is was not given previously. 6.4.1 Explain in a sentence or two the meaning of the NH model. 6.4.2 Perform the test and summarize results. 6.5 (Data fie: UN11) In the UN data, start with the parallel regression model (6.9). 6.5.1 Test for equality of intercepts for the oecd and other levels of the factor group. 6.5.2 Test for equality of the intercepts for group other and africa. 6.6 (Data fie: fuel2001) State the null and alternative hypotheses for the overall F-test for the fuel consumption date (Section 3.3). Perform the test and summarize results. 6.7 (Data fie: fuel2001) With the fuel consumption date, consider the following two models in Wilkinson-Rogers notation: fuel ~ Tax +Dlic+Income +log(Miles) (6.22) fuel - log(Miles)+Income +Dlic +Tax (6.23) These models are of course the same, as they only differ by the order in which the regressors are written. 6.7.1 Show that the Type I anove for (6.22) and (6.23) are different. Provide an interpretation of each of the tests. 6.7.2 Show that the Type II anova is the same for the two models. Which of the Type II tests are equivalent to Type | tests? 152 chapter 6 testing and analysis of variance 6.8 Show that the overall F-test for multiple regression with an intercept can be written as Fnp