Refer to theSENICdata set in Appendixc.l.For predicting the average length of stay of patients in a hospital(Y),it has been decided to include age(XI)and infection risk(X2)as predictor variables. The question now is whether an additional predictor variable would be helpful in the model and, if so, which variable would be most helpful. Assume that a first-order multiple regression model is appropriate.

1. For each of the following variables, calculate the coefficient of partial determination given thatXIandX2areincludedinthemodel:routineculturingratio(X3),averagedailycensus(X4),number of nurses(Xs),and available facilities and services(X6).
2. Onthebasisoftheresultsinpart(a),whichofthefouradditionalpredictorvariablesisbest? Is the extra sum of squares associated with this variable larger than those for the other three variables?
3. Using the F* test statistic, test whether 9r not the variable determined to be best in part(b)ishelpfulintheregressionmosIelwhenXIandX2areincludedinthemodel;useex=.05.State the alternatives, decision rule, and conclusion. Would the F* test statistics for the other three potential predictor variables be as large as the one here? Discuss.

database: http://www.cnachtsheim-text.csom.umn.edu/Kutner/Appendix%20C%20Data%20Sets/APPENC01.txt