Consider the patient satisfaction survey data. Using only first-order terms, build regression models using the following techniques: (a) All possible regressions. Find the Cp and S values. (b) Forward selection. (c) Backward elimination. (d) Comment on the models obtained. Which model would you prefer? 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)