1. (5+5+5+10+5+2 = 32 points) Use the \"HospitalInfections\" dataset. Preliminary data analyses have revealed that the variable Y = lnfctRsk could be related to the variables X; = Stay, X2 = Culture, X3 = Xray, X4 = Beds, X5 = Census, and X6 = Nurses. a) b) d) Fit a multiple linear regression model that relates InfctRsk to the predictor variables Xl-X. Perform a hypothesis test at signicance level 0.05 to determine if at least one of the predictors in this model is useful in predicting Y. State your null and alternative hypotheses in terms of the regression coefficients (B's), the test statistic value with calculations shown, the decision rule and the conclusion. Use a partial F-test to determine if the predictor variables X5 = Census and X6 = Nurses can be deleted from the model while retaining the four remaining variables X1 = Stay, X2 = Culture, X3 = Xray, and X4 = Beds. Again, state your null and alternative hypotheses in terms of regression coefcients, show your work in calculating the test statistic, state the decision rule and the conclusion. Conrm the value of the partial F-statistic from part (b) by calculating the F-statistic using the general linear Ftest formula. State the full and reduced models and show your work in calculating the test statistic. Perform a hypothesis test to determine if X; = Beds can be dropped from a model with the four predictors, X1 = Stay, X2 = Culture, X3 = Xray, and X4 = Beds, by using: i. a tstatistic ii. an F-statistic (State your null and alternative hypotheses in terms of the regression coefcients, the test statistic values, the decision rules and the conclusions.) Is there any relationship between the two test statistics in (i) and (ii) above? Calculate the value of the coefcient of partial determination R2Y'4|1'2,3 and explain in words what it measures. Write down the tted regression equation based on your conclusion in part ((1)