## Question

###### Hospital administrator wished to study the relation between patient satisfaction Y) and patient's age (X1, in years), severity of illness (X2 _ an index), and anxiety level (X3 an index): The administrator randomly selected 46 patients and collected the data presented below, where larger values of Y, X2_ and X3 are, respectively, associated with more satisfaction, increased severity of illness_ and more anxiety: (Exercise problem 6.15 in the textbook): Using the attached data (assignment2_

hospital administrator wished to study the relation between patient satisfaction Y) and patient's age (X1, in years), severity of illness (X2 _ an index), and anxiety level (X3 an index): The administrator randomly selected 46 patients and collected the data presented below, where larger values of Y, X2_ and X3 are, respectively, associated with more satisfaction, increased severity of illness_ and more anxiety: (Exercise problem 6.15 in the textbook): Using the attached data (assignment2_ 1.Rdata), answer the questions below_ You can load the .Rdata file using the 'load' function: load('assignment2 1.Rdata Create scatter plot matrix using plot() command: Can you detect any linear relationship? Fit multiple linear regression model using all the predictor variables (X1-X3)_ Create summary of the regression fit and interpret the results (using summary() function): Which coefficients are statistically significant? Which are not? (Use a = 0.10) Test the following null and alternative hypotheses: Ho: B1 Bz B3 0 vs Hi:at least one coefficient is not 0 What is the implication of the hypothesis test result? Fit the regression model again with only the significant variables. State the fitted model: Are the coefficients are all significant now? Can we say that the fitted model is useful for predict the patient satisfaction? Why? Find the confidence intervals for the coefficients in the model that you fitted in part d. Based on the model fitted in part d. find the prediction interval for new observation with X1-50 and X3-2.6_ Interpret the found interval. (Define 'new' dataset using the following command: xnew-data frame(X1-50,X3-2.6))