An epidemiologist was interested in examining the effects of three factors on an
ID: 3150923 • Letter: A
Question
An epidemiologist was interested in examining the effects of three factors on an obese person’s cholesterol levels. Let xi , i = 1, 2, 3, represent the effects of the three factors, respectively, and y be the total cholesterol. The following output was generated using statistical software.
Regression Analysis
S = 14.01 R-Sq = 95.1% R-Sq(adj) = 92.1
Analysis of Variance
a)Does the regression model appear to be useful? State the null and alternative hypotheses of interest, the critical and calculated test statistic, and justify your answer. (Use = 0.05.)
b. Construct a 2-sided 95% confidence interval for (male vs female). State the null and alternative hypotheses of interest, and interpret your confidence interval.
c. Use the values of SSR and Total SS in the results to calculate R2. Compare this value to the one given in the results.
d. Interpret the coefficient and test statistic for the ‘exercise’ factor in the model.
Explanation / Answer
An epidemiologist was interested in examining the effects of three factors on an obese person’s cholesterol levels. Let xi , i = 1, 2, 3, represent the effects of the three factors, respectively, and y be the total cholesterol. The following output was generated using statistical software.
Regression Analysis
predictor
Coef
Stdev
T
P
constant
225.19
65.70
3.43
0.019
male vs femal
12.725
3.570
3.56
0.016
vegetarian vs Non-vegetarian
-39.45
23.24
-1.70
0.150
Number od days with >= 60 min exercise
-33.48
12.29
-2.73
0.042
S = 14.01 R-Sq = 95.1% R-Sq(adj) = 92.1
Analysis of Variance
Source
DF
SS
MS
F
Regression
3
18,951.1
6,317.0
32.19
Residual Error
5
981.1
196.2
total
8
19,932.2
a)Does the regression model appear to be useful? State the null and alternative hypotheses of interest, the critical and calculated test statistic, and justify your answer. (Use = 0.05.)
Null hypothesis: The model is not useful.
Alternate hypothesis: The model is useful.
The critical value F(3,5) at 0.05 level =5.41
Calculated F=32.19 > 5.41, the null hypothesis is rejected.
We conclude that the model is useful.
b. Construct a 2-sided 95% confidence interval for (male vs female). State the null and alternative hypotheses of interest, and interpret your confidence interval.
t value at 0.05 level with 5 Df =2.57
Lower limit = 12.725-2.57*3.57 =3.5501
Lower limit = 12.725+2.57*3.57 =21.8999
95% CI for Regression coefficient =(3.55, 21.90).
We are 95% confident that Regression coefficient for Male vs female falls in the interval.
c. Use the values of SSR and Total SS in the results to calculate R2. Compare this value to the one given in the results.
R square = SSR/SST =18951.1/19932.2 =0.950778
Given value of R square =95.1% ( 0.951) which is same as we computed.
d. Interpret the coefficient and test statistic for the ‘exercise’ factor in the model.
Coefficient = -33.48
Calculated t=2.73, P=0.042 which is < 0.05 level.
The null hypothesis is rejected.
The variable exercise is significant.
Controlling other variables constant, those exercise Number of days with >= 60 min have cholesterol levels less 33.48 compared to exercise less than 60 minutes.
predictor
Coef
Stdev
T
P
constant
225.19
65.70
3.43
0.019
male vs femal
12.725
3.570
3.56
0.016
vegetarian vs Non-vegetarian
-39.45
23.24
-1.70
0.150
Number od days with >= 60 min exercise
-33.48
12.29
-2.73
0.042