1. (5+5+5+10+5+2 = 32 points) Use the "HospitalInfections" dataset. Preliminary data analyses have revealed that the variable Y = InfctRsk could be related to the variables X, = Stay, X= = Culture, Xs = Xray, X. = Beds, Xs = Census, and Xs = Nurses. a) Fit a multiple linear regression model that relates InfctRsk to the predictor variables X1-X Perform a hypothesis test at significance 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. b) Use a partial F-test to determine if the predictor variables Xs = Census and X. = Nurses can be deleted from the model while retaining the four remaining variables X1 = Stay, Xz = Culture, Xs = Xray, and X, = Beds. Again, state your null and alternative hypotheses in terms of regression coefficients, show your work in calculating the test statistic, state the decision rule and the conclusion. c) Confirm the value of the partial F-statistic from part (b) by calculating the F-statistic using the general linear F-test formula. State the full and reduced models and show your work in calculating the test statistic. d) Perform a hypothesis test to determine if X. = Beds can be dropped from a model with the four predictors, X1 = Stay, Xz = Culture, Xs = Xray, and X4 = Beds, by using: i. a t-statistic ii. an F-statistic (State your null and alternative hypotheses in terms of the regression coefficients, the test statistic values, the decision rules and the conclusions.) Is there any relationship between the two test statistics in (i) and (ii) above? e) Calculate the value of the coefficient of partial determination Ryan1,23 and explain in words what it measures. Write down the fitted regression equation based on your conclusion in part (d)