Multiple Regression. Patient satisfaction. A hospital administrator wished to study the relation be- tween patient satisfaction (7) and patient's age (X,, ini year), severity of illness (X2, m index), and anxiety level (Ky, an index). She randomly selected 23 pa- tients and collected the data presented below, where larger values of Y', X2, and X, are, respectively, associated with more satisfaction, Increased severity of illness. and more anxiety. 12 1 2 3 4 S 6 7 8 9 10 II 50 36 41 25 45 45 SL 46 45 44 43 54 50 48 50 53 2.3 2.2 1.8 1.8 2.9 2.2 2.4 2.9 2.1 24 2.4 2.3 57 65 70 36 46 54 26 89 48 20 21 15 14 17 44 43 35 34 33 33 29 58 50 51 54 23 2.2 23 2.2 20 1.9 21 2.3 29 52 YA 47 57 49 a) Obtain the regression equation using Excel b) Test whether there is a regression relation (for each independent variable): use a .10 level of significance. State the alternatives, decision rule, and conclusion. What does your test imply about Pa, Pz, Ps? c) (Bonus-2 points) Suppose you found out fa has no regression relationship (not necessarily true in this case), what do you do with that information?SUMMARY OUTPUT Regression Statistics Multiple F 0.826376 R Square 0.682897 Adjusted | 0.632828 Standard ( 10.12727 Observati 23 ANOVA df MS F gnificance F Regressio 3 4196.548 1398.849 13.63912 5.57E-05 Residual 19 1948.67 102.5616 Total 22 6145.217 Coefficientandard Err t Stat P-value Lower 95%Upper 95%ower 95.09pper 95.0% Intercept 157.7016 19.06137 8.273361 1.01E-07 117.8057 197.5975 117.8057 197.5975 Years -1.3555 0.310085 -4.37139 0.000328 -2.00452 -0.70649 -2.00452 -0.70649 Severity -0.37028 0.325692 -1.1369 0.269715 -1.05196 0.311402 -1.05196 0.311402 Anxiety -10.6041 9.423097 -1.12533 0.274466 -30.3268 9.118716 -30.3268 9.118716 y = 157.7016-1.3555x,-5.079587X2 -10.6041x3