Question

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 activity level. SEX-1=male, 2=female; ACTIVITY-usual level of physical activity: 1=slight, 2=moderate, 3=a lot. The researchers collected the following data on a random sample of n = 91 individuals. The SAS output is in next page. Observation pulse rate sex activity 1 64 1 2 2 58 1 2 3 62 1 3 4 66 1 1 5 64 1 2 : 90 86 2 3 91 76 2 2 (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). 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 pulse1=z1 z2 z3; proc reg data=pulse_new; Model pulse1=z1 z2; Run; Parameter Estimates Variable DF Parameter Estimate Standard Error t Value Pr > |t| Intercept 1 74.59259 2.00018 37.29 <.0001 z1 1 -4.59259 2.63062 -1.75 0.0843 z2 1 9.90741 4.18368 2.37 0.0201 z3 1 -8.70741 5.08169 -1.71 0.0901 Analysis of Variance Source DF Sum of Squares Mean Square F Value Pr > F Model 3 1522.71626 507.57209 4.70 0.0043 Error 88 9505.71852 108.01953 Corrected Total 91 11028 Parameter Estimates Variable DF Parameter Estimate Standard Error t Value Pr > |t| Intercept 1 75.94159 1.85862 40.86 <.0001 z1 1 -6.92599 2.27506 -3.04 0.0031 z2 1 4.00555 2.40047 1.67 0.0987 Analysis of Variance Source DF Sum of Squares Mean 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

          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 activity level.
SEX-1=male, 2=female;
ACTIVITY-usual level of physical activity: 1=slight, 2=moderate, 3=a lot. The researchers collected the following data on a random sample of n = 91 individuals. The SAS output is in next page.

Observation pulse rate sex activity
1 64 1 2
2 58 1 2
3 62 1 3
4 66 1 1
5 64 1 2
:
90 86 2 3
91 76 2 2

(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).

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 pulse1=z1 z2 z3;

proc reg data=pulse_new;
Model pulse1=z1 z2;

Run;

Parameter Estimates
Variable DF Parameter Estimate Standard Error t Value Pr > |t|
Intercept 1 74.59259 2.00018 37.29 <.0001
z1 1 -4.59259 2.63062 -1.75 0.0843
z2 1 9.90741 4.18368 2.37 0.0201
z3 1 -8.70741 5.08169 -1.71 0.0901

Analysis of Variance
Source DF Sum of Squares Mean Square F Value Pr > F
Model 3 1522.71626 507.57209 4.70 0.0043
Error 88 9505.71852 108.01953
Corrected Total 91 11028

Parameter Estimates
Variable DF Parameter Estimate Standard Error t Value Pr > |t|
Intercept 1 75.94159 1.85862 40.86 <.0001
z1 1 -6.92599 2.27506 -3.04 0.0031
z2 1 4.00555 2.40047 1.67 0.0987

Analysis of Variance
Source DF Sum of Squares Mean 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

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 activity level.
SEX-1=male, 2=female;
ACTIVITY-usual level of physical activity: 1=slight, 2=moderate, 3=a lot. The researchers collected the following data on a random sample of n = 91 individuals. The SAS output is in next page.

Observation pulse rate sex activity
1 64 1 2
2 58 1 2
3 62 1 3
4 66 1 1
5 64 1 2
:
90 86 2 3
91 76 2 2

(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).

data pulsenew;
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=pulsenew;
Model pulse1=z1 z2 z3;

proc reg data=pulsenew;
Model pulse1=z1 z2;

Run;

Parameter Estimates
Variable DF Parameter Estimate Standard Error t Value Pr > |t|
Intercept 1 74.59259 2.00018 37.29 <.0001
z1 1 -4.59259 2.63062 -1.75 0.0843
z2 1 9.90741 4.18368 2.37 0.0201
z3 1 -8.70741 5.08169 -1.71 0.0901

Analysis of Variance
Source DF Sum of Squares Mean Square F Value Pr > F
Model 3 1522.71626 507.57209 4.70 0.0043
Error 88 9505.71852 108.01953
Corrected Total 91 11028

Parameter Estimates
Variable DF Parameter Estimate Standard Error t Value Pr > |t|
Intercept 1 75.94159 1.85862 40.86 <.0001
z1 1 -6.92599 2.27506 -3.04 0.0031
z2 1 4.00555 2.40047 1.67 0.0987

Analysis of Variance
Source DF Sum of Squares Mean 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

Added by Kayla B.

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