Consider the patient satisfaction survey data (a) Estimate the mean satisfaction given that age = 24, severity = 38, Surg-Med = 0, and anxiety = 2.8. (b) Compute a 95% CI on this mean response. (c) Compute a 95% PI on a future observation at the same values of the regressors. (d) What do you notice about the relative size of these two intervals? Which is wider and why? Use Minitab to assist you in answering the following. (a) Estimate the regression coefficients. Write the multiple linear regression model. Comment on the relationship found between the set of independent variables and the dependent variable. (b) Compute the residuals. (c) Compute $SS_E$ and estimate the variance. (d) Compute the coefficient of determination, $R^2,$ and adjusted coefficient of multiple determination, $R_{\text { Adjusted }}^{2}.$ Comment on their values. (e) Construct the ANOVA table and test for significance of regression. Comment on your results. (f) Find the standard error of the individual coefficients. (g) Use a t-test to test for significance of the individual coefficients at $\alpha=0.05.$ Comment on your results. (h) Construct 95% CIs on the individual coefficients. Compare your results with those found in part (g) and comment. (i) Perform a model adequacy check, including computing studentized residuals and Cook's distance measure for each of the observations. Comment on your results. (j) Compute the variance inflation factors and comment on the presence of multicollinearity. Data from a patient satisfaction survey in a hospital are shown in the following table:

$\begin{matrix}
\text{Observation} & \text{Age} & \text{Severity } & \text{Surg-Med} & \text{Anxiety} & \text{Satisfaction}\\
\text{1} & \text{55} & \text{50} & \text{0} & \text{2.1} & \text{68}\\
\text{2} & \text{46} & \text{24} & \text{1} & \text{2.8} & \text{77}\\
\text{3} & \text{30} & \text{46} & \text{1} & \text{3.3} & \text{96}\\
\text{4} & \text{35} & \text{48} & \text{1} & \text{4.5} & \text{80}\\
\text{5} & \text{59} & \text{58} & \text{0} & \text{2.0} & \text{43}\\
\text{6} & \text{61} & \text{60} & \text{0} & \text{5.1} & \text{44}\\
\text{7} & \text{74} & \text{65} & \text{1} & \text{5.5} & \text{26}\\
\text{8} & \text{38} & \text{42} & \text{1} & \text{3.2} & \text{88}\\
\text{9} & \text{27} & \text{42} & \text{0} & \text{3.1} & \text{75}\\
\text{10} & \text{51} & \text{50} & \text{1} & \text{2.4} & \text{57}\\
\text{11} & \text{53} & \text{38} & \text{1} & \text{2.2} & \text{56}\\
\text{12} & \text{41} & \text{30} & \text{0} & \text{2.1} & \text{88}\\
\text{13} & \text{37} & \text{31} & \text{0} & \text{1.9} & \text{88}\\
\text{14} & \text{24} & \text{34} & \text{0} & \text{3.1} & \text{102}\\
\text{15} & \text{42} & \text{30} & \text{0} & \text{3.0} & \text{88}\\
\text{16} & \text{50} & \text{48} & \text{1} & \text{4.2} & \text{70}\\
\text{17} & \text{58} & \text{61} & \text{1} & \text{4.6} & \text{52}\\
\text{18} & \text{60} & \text{71} & \text{1} & \text{5.3} & \text{43}\\
\text{19} & \text{62} & \text{62} & \text{0} & \text{7.2} & \text{46}\\
\text{20} & \text{68} & \text{38} & \text{0} & \text{7.8} & \text{56}\\
\text{21} & \text{70} & \text{41} & \text{1} & \text{7.0} & \text{59}\\
\text{22} & \text{79} & \text{66} & \text{1} & \text{6.2} & \text{26}\\
\text{23} & \text{63} & \text{31} & \text{1} & \text{4.1} & \text{52}\\
\text{24} & \text{39} & \text{42} & \text{0} & \text{3.5} & \text{83}\\
\text{25} & \text{49} & \text{40} & \text{1} & \text{2.1} & \text{75}\\
\end{matrix}$

The regressor variables are the patient's age, an illness severity Index (larger values indicate greater severity), an indicator variable denoting whether the patient is a medical patient (0) or a surgical patient (1), and an anxiety index (larger values indicate greater anxiety)