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=female; SMOKES-1=smokes regularly, 2=does not smoke regularly; The researchers collected the following data on a random sample of n = 91 individuals. The SAS output is in next page.

(a) Initially the researcher was wondering that there might have interactions between sex 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 interaction between sex and smoking status.

(d) Propose the formula to calculate the test statistic for (c); report your conclusion at = .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 (e)) useful? (please set up the hypotheses and report

your conclusion by SAS output at = .05).

23... 11 Observation pulse rate sex N900 NON activity data pulse_new; set pulse; Do i =1 TO N; If sex = 1 then z1=1; else zl=0; end; Do i =1 To N; If smokes = 1 then z2=1; else 22=0; end; z3=z1+z2; proc reg data=pulse new; Model pulsel=z1 22 23; proc reg data=pulse_new; Model pulsel=z1 22; Run; Parameter Estimates Analysis of Variance Variable DF Intercept 1 Parameter Standard Estimate Error t Value Pr > It 74.59259 2.00018 37.29 F Model 3 1522.71626 507.57209 4.70 0.0043 Error 88 9505.71852 108.01953 Corrected Total 91 11028 z3 Parameter Estimates Variable DF Intercept 1 Parameter Standard Estimate Error t Value Pr> It 75.94159 1.85862 40.86 <.0001 analysis of variance sum mean source df squares square f value pr>F Model 2 1205.56720 602.78360 5.46 0.0058 Error 89 9822.86758 110.36930 Corrected Total 91 11028 z2 23... 11 Observation pulse rate sex N900 NON activity data pulse_new; set pulse; Do i =1 TO N; If sex = 1 then z1=1; else zl=0; end; Do i =1 To N; If smokes = 1 then z2=1; else 22=0; end; z3=z1+z2; proc reg data=pulse new; Model pulsel=z1 22 23; proc reg data=pulse_new; Model pulsel=z1 22; Run; Parameter Estimates Analysis of Variance Variable DF Intercept 1 Parameter Standard Estimate Error t Value Pr > It 74.59259 2.00018 37.29 F Model 3 1522.71626 507.57209 4.70 0.0043 Error 88 9505.71852 108.01953 Corrected Total 91 11028 z3 Parameter Estimates Variable DF Intercept 1 Parameter Standard Estimate Error t Value Pr> It 75.94159 1.85862 40.86 <.0001 analysis of variance sum mean source df squares square f value pr>F Model 2 1205.56720 602.78360 5.46 0.0058 Error 89 9822.86758 110.36930 Corrected Total 91 11028 z2