3. A physiological experiment was concluded to study the effect of various factors on a pulse rate. For the sake of simplicity, we consider the pulse rate as the response (y); two categorical variables are included as predictors: sex and smoking status. Sex: 1=male, 2=fernale; Smoking status: 1=smokes regularly, 2: does not smoke regularly; The researchers collected the following data on a random sample of n = 92 individuals. The SAS output is in next page Observation pulse rate sex smoking status 1 54 1 2 2 58 1 2 3 52 1 1 4 55 1 1 5 54 1 2 91 85 2 2 92 76 2 2 a Initial] the researcher was wonderin that there mi t have interactions between sex 3" g and smoking status. What does this mean? [b] Based on the SAS code and result, please write out the initial full theoretical model (include interactions]. {c} Please set up the hypotheses to test whether there have interactions between sex and smoking status. (d) Propose the formula to calculate the test statistic for (c): report your conclusion at o: = .05 based on SAS output. {e} Assume there is no interaction, please write out the theoretical model you will choose. (f) Overall is this model (model in [ED useful? [please set up the hypotheses and report your conclusion by SAS output at or = 35}. Output for question 3 data pulse_new; set pulse; Do i =1 To N ; If sex = 1 then z1=1; else z1=0; end; Do i =1 To N ; If smokes = 1 then z2=1; else z2=0; end; z3=z1*z2; proc reg data=pulse_new; Model pulsel=z1 z2 23; proc reg data=pulse_new; Model pulsel=z1 z2; Run; Parameter Estimates Parameter Standard Analysis of Variance Variable DF Estimate Error t Value Pr > It Sum of Mean Intercept 1 74.59259 2.00018 37 29 F 21 -4.59259 2.63062 -1.75 0.0843 Model 3 1522 71626 507.57209 4.70 0.0043 9.90741 4.18368 2.37 0.0201 Error 88 9505.71852 108.01953 23 -8.70741 5.08169 -1.71 0.0901 Corrected Total 91 11028 Parameter Estimates Analysis of Variance Parameter Standard Sum of Mean Variable DF Estimate Error t Value Pr > It) Source DF Squares Square F Value Pr > F Intercept 1 75.94159 1.85862 40.86 <.0001 model error corrected total>