4. Consider a data set on studying the relationship between death rate from cirrhosis (severe (b) Based on the following table, select a model using the backward elimination liver disease) and drinking in a population. Four explanatory variables of interest are (1) size of method. Take the significance level to stay SLS = 0.05. Some F quantiles are given below. urban population (1); (2) number of births to women between 25 and 40 (22); (3) consumption When describing your selection steps, give details for one test for step 1 and one test for step of wine per capita (13); (4) consumption of hard liquor per capita (24). In the data set with 2 in the backward elimination. That is, for the test you are reporting, give the hypotheses, the 46 observations (populations), the columns corresponding to T1, 12, 13, T4 are PopSize, Births, test statistic, its distribution and its observed value, and the corresponding constant F-to-stay Wine, and Liquor. The response variable Y is the death rate from cirrhosis, given by the for making decision in the selection step. column Death in the data set. (a) Comment on the following scatter plot matrix, and R output for the fit of a model. What do they tell you about the relationships between the variables? Are the findings from Table 2: The residual sum of squares, SS(Res), for all candidate models. the scatter plot matrix contradictory to the results from the model fit? Why or why not? Covariates in Model SS(Res) 24741 C1 10859 T2 9583 PopSize 7092 13235 T1, 12 8905 Births 5673 T1, C4 7053 Wine 12, 13 4632 12, T4 8603 2: Liquor C3, 24 6530 C1, [2, 3 4626 Death 1, 12, CA 7026 5048 C2, 3, X4 4629 I1, $2, T3, TA 4611 Call : Im (formula = Death ~ PopSize + Births + Wine + Liquor, data = dat) Residuals: Table 3: Some F distribution (upper) quantiles, Fo.05,d, ,dz Min 1Q Median 3Q Max -18.8723 -6.7803 0. 1507 7. 3252 16.4419 d1 Coefficients: d2 1 2 3 Estimate Std. Error t value Pr(>|t/) 41 4.079 3.226 2.833 2.600 (Intercept) -13.96310 11. 40035 -1. 225 0. 2276 42 4.073 3.220 2.827 2.594 PopSize 0. 09829 0. 24407 0. 403 0. 6893 43 4.067 3.214 2.822 2.589 Births 1 . 14838 0. 58300 1.970 0. 0556 44 4.062 3.209 2.816 2.584 Wine 1 . 85786 0. 40096 4. 634 3.61e-05 *** 45 4.057 3.204 2.812 2.579 Liquor 0. 04817 0. 13336 0. 361 0. 7198 46 4.052 3.200 2.807 2.574 Signif. codes: 0 '***' 0.001 '**' 0.01 '*> 0.05 ' . ' 0.1 ' ) 1 Residual standard error: 10.61 on 41 degrees of freedom Multiple R-squared: 0.8136, Adjusted R-squared: 0.7954 F-statistic: 44.75 on 4 and 41 DF, p-value: 1.951e-14