1.Describe the characteristics of the people included in the sample at the baseline examination.
2. Characterize the people who had casual serum glucose >200 mg/dL at the baseline examination and compare them to people who had ≤200 mg/dL casual serum glucose at the baseline examination in terms of age, body mass index (BMI), education and whether they were taking blood pressure medication at the time of the baseline examination.
3. 3.Are the results from the bivariate comparisons above (point 2) different if the actual casual serum glucose level at baseline examination is analysed, rather than the dichotomized glucose variable?
4.Considering only individuals with casual serum glucose level at baseline below 200 mg/dL, which of these variables (age, BMI, education and whether they were taking blood pressure medication) are significantly associated with casual serum glucose level at baseline in a multivariable analysis? Describe their relationship with casual serum glucose level, including which variables explain the most variation in casual serum glucose level. Report the ‘minimum model’ obtained. Explain any differences you observe between the results of the bivariate analysis in point 3 above and multivariable analysis.
Baseline Examination Data
At the baseline examination, data from 3950 people were collected in terms of sex, education level, age, Serum total cholesterol, Systolic blood pressure, Diastolic blood pressure, Current cigarette smoking, Number of cigarettes smoked each day, Body mass index, use of antihypertensive medication, Casual serum glucose. Out of 3950, 1725 are male and 2225 are female. 41.1 % people are education level 011 years where as 28.6% are diploma holder. 49.1 % people are currently smoker at baseline examination whereas 50.1% are not currently smoker. Only 3.1% people use anti hyper tension mediation. At baseline examination, mean serum total cholesterol is 237.41mmg/dL with standard deviation 44.779. Mean age of people at baseline examination is 49.95 years with standard deviation 8.644 years. Mean systolic blood pressure is 132.838 mmHg with standard deviation 22.3993. Mean systolic blood pressure is 83.047 mm/Hg with standard deviation 12.0522. People averagely smoke 8.87 cigarettes every day with standard deviation 11.844. At baseline examination people have average BMI 25.8523 Kg/m2 with standard deviation 4.07827. Mean casual serum glucose is observed as 82.18 mmg/dL with standard deviation 24.485.
2. We group the variable in two categories:
1: casual serum glucose >200 mg/dL at the baseline examination
2 : casual serum glucose 200 mg/dL at the baseline examination
Following table shows the descriptive statistics for the group 1 and 2 for age and BMI
Descriptive Statistic 
Age at baseline exam (years) 
Body Mass Index at baseline exam (kg/m^2) 

Group 1 
Group 2 
Group 1 
Group 2 

Mean 
55.71 
49.94 
28.3565 
25.8425 
Size 
31 
3556 
31 
3556 
Median 
56 
49 
28.5 
25.425 
Variance 
45.28 
74.613 
31.245 
16.388 
Std. Deviation 
6.729 
8.638 
5.58969 
4.04821 
Minimum 
43 
32 
17.17 
15.54 
Maximum 
67 
70 
43.67 
56.8 
Range 
24 
38 
26.5 
41.26 
Interquartile Range 
10 
14 
7.39 
4.99 
Skewness 
0.249 
0.199 
0.407 
0.961 
Kurtosis 
0.79 
1.014 
0.76 
2.507 
We have 31 people having casual serum glucose >200 mg/dL at the baseline examination and 3556 people having casual serum glucose 200 mg/dL at the baseline examination. Mean age of people having casual serum glucose >200 mg/dL at the baseline examination is 55.71 (6.729) years whereas mean age of people having casual serum glucose 200 mg/dL at the baseline examination is 49.94(8.638) years. BMI of group 1 is higher than group 2. One can observed the difference between other statistic from above table.
64.51 % people having casual serum glucose >200 mg/dL at the baseline examination has education 011 years whereas for other group this percentage is 42.28%. In Group 1 19.35% people are diploma holder whereas in Group 2 29.33% people are diploma holders. There is no one in Group 1 which has college degree or more whereas in Group 2 about 12% people have college degree or more.
9% People in group 1 taking mediation whereas only 3% people in Group 2 are taking medication for controlling the blood pressure.
3 No, the results from the bivariate comparisons above (point 2) different if the actual casual serum glucose level at baseline examination is analysed, rather than the dichotomized glucose variable.
Grouping of Variables and Descriptive Statistics
4. We considered the individuals with casual serum glucose level at baseline below 200 mg/dL. There are 3568 people having casual serum glucose level at baseline below 200 mg/dL. To test whether there is any significant relation between the casual serum glucose level at baseline and independent variables (age, BMI, education and whether they were taking blood pressure medication). We run the multiple regression analysis. In the independent variables Education and whether they were taking blood pressure medication are categorical variables, we need to create dummy variables for testing the above hypothesis, we create four dummy variables (3 for education and 1 for whether they were taking blood pressure medication. We take 111 years education and not taken any medication as a reference variable.
Following table shows the ANOVA of multiple regression analysis:
Source of Variation 
Sum of Squares 
df 
Mean Square 
F 
P Value 
Regression 
16607.05 
6 
2767.842 
12.84 
0 
Residual 
765023.7 
3549 
215.56 

Total 
781630.7 
3555 
The Pvalue = 0 suggest that there is significant relation between the casual serum glucose level at baseline and independent variables (age, BMI, education and whether they were taking blood pressure medication). That is at least one of the coefficient is non zero. From following table we can see that which coefficient are significant or not.
Independent Variable 
Coefficient 
Std. Error 
t 
P Value 
(Constant) 
63.485 
2.197 
28.899 
0.000 
Age at baseline exam (years) 
0.192 
0.030 
6.471 
0.000 
Body Mass Index at baseline exam (kg/m^2) 
0.289 
0.062 
4.640 
0.000 
HighSchoolDiploma 
0.097 
0.612 
0.159 
0.873 
Some College and Vocation 
0.399 
0.729 
0.547 
0.584 
degree and more 
0.087 
0.822 
0.106 
0.916 
taken or not 
0.772 
1.423 
0.542 
0.588 
We can see that only age and BMI are significant whereas other variables education and whether they were taking blood pressure medication are found to be nonsignificant for predicting the casual serum glucose level at baseline. Both age and BMI have positive correlation with casual serum glucose level at baseline.
As the education and whether they were taking blood pressure medication are found to be nonsignificant for predicting the casual serum glucose level at baseline, we fit the model again using age and BMI variables only. Following is the equation of multiple regression analysis for predicting the casual serum glucose level at baseline using age and BMI as a predictor variables.
Casual serum glucose level at baseline = 63.35 + 0.192 × Age + 0.29 × BMI
Each incline in age results in 0.192 incline in casual serum glucose level whereas each unit of BMI incline results in 0.29 incline in casual serum glucose level.
From bivariate analysis, we observed that mean age and BMI for person having casual serum glucose >200 mg/dL at the baseline examination is more than the person having casual serum glucose 200 mg/dL at the baseline examination. And from the multivariate analysis we observed that each icline in age and BMI results in incline in the casual serum glucose level.
Multiple Regression Analysis
5. We carry the paired t test for the testing whether there is casual serum glucose level change significantly between the baseline examination and the followup examination. We observed t statistics is 1.854 and P value is 0.064 < 0.1 suggest that there is significant change in the casual serum glucose level change significantly between the baseline examination and the followup examination at 10% level of significance.
We now group the people having casual serum glucose >200 mg/dL and casual serum glucose 200 mg/dL. After that we used paired t test for both the groups.
We observed t statistics is 3.124 and P value is 0.008 < 0.1 suggest that there is significant change in the casual serum glucose level >200 mg/dL change significantly between the baseline examination and the followup examination at 10%.
We observed t statistics is 2.675 and P value is 0.008 < 0.1 suggest that there is significant change in the casual serum glucose level 200 mg/dL change significantly between the baseline examination and the followup examination at 10%.
From the test statistics we can observed that glucose level increases for people having casual serum glucose level >200 mg/dL at baseline examination and glucose level decreases for people having casual serum glucose level <= 200 mg/dL at baseline examination.
SPSS Output:
Sex 

Frequency 
Percent 
Valid Percent 
Cumulative Percent 

Valid 
Male 
1725 
43.7 
43.7 
43.7 
Female 
2225 
56.3 
56.3 
100.0 

Total 
3950 
100.0 
100.0 
Education level 

Frequency 
Percent 
Valid Percent 
Cumulative Percent 

Valid 
011 years 
1625 
41.1 
42.2 
42.2 
High school diploma 
1131 
28.6 
29.4 
71.6 

Some college, vocational school 
638 
16.2 
16.6 
88.2 

College degree or more 
456 
11.5 
11.8 
100.0 

Total 
3850 
97.5 
100.0 

Missing 
System 
100 
2.5 

Total 
3950 
100.0 
Current cigarette smoking at baseline exam 

Frequency 
Percent 
Valid Percent 
Cumulative Percent 

Valid 
Not current smoker 
2009 
50.9 
50.9 
50.9 
Current smoker 
1941 
49.1 
49.1 
100.0 

Total 
3950 
100.0 
100.0 
Use of antihypertensive medication at baseline exam 

Frequency 
Percent 
Valid Percent 
Cumulative Percent 

Valid 
Not currently used 
3771 
95.5 
96.8 
96.8 
Current use 
124 
3.1 
3.2 
100.0 

Total 
3895 
98.6 
100.0 

Missing 
System 
55 
1.4 

Total 
3950 
100.0 
casual serum at baseline exam 

Frequency 
Percent 
Valid Percent 
Cumulative Percent 

Valid 
1 
3568 
90.3 
99.1 
99.1 
2 
32 
.8 
.9 
100.0 

Total 
3600 
91.1 
100.0 

Missing 
System 
350 
8.9 

Total 
3950 
100.0 
Descriptive Statistics 

N 
Mean 
Std. Deviation 

Age at baseline exam (years) 
3950 
49.95 
8.644 
Systolic blood pressure at baseline exam (mmHg) 
3950 
132.838 
22.3993 
Diastolic blood pressure at baseline exam (mmHg) 
3950 
83.047 
12.0522 
Number of cigarettes smoked each day at baseline exam 
3920 
8.87 
11.824 
Body Mass Index at baseline exam (kg/m^2) 
3932 
25.8523 
4.07827 
Serum total cholesterol at baseline exam (mmg/dL) 
3904 
237.41 
44.779 
Casual serum glucose at baseline exam (mg/dL) 
3600 
82.18 
24.485 
Valid N (listwise) 
3552 
Case Processing Summary 

NewVar 
Cases 

Valid 
Missing 
Total 

N 
Percent 
N 
Percent 
N 
Percent 

Age at baseline exam (years) 
1 
31 
96.9% 
1 
3.1% 
32 
100.0% 
2 
3556 
99.7% 
12 
.3% 
3568 
100.0% 

Body Mass Index at baseline exam (kg/m^2) 
1 
31 
96.9% 
1 
3.1% 
32 
100.0% 
2 
3556 
99.7% 
12 
.3% 
3568 
100.0% 
Education level * NewVar Crosstabulation 

Count 

NewVar 
Total 

1 
2 

Education level 
011 years 
20 
1470 
1490 
High school diploma 
6 
1020 
1026 

Some college, vocational school 
5 
572 
577 

College degree or more 
0 
415 
415 

Total 
31 
3477 
3508 
Use of antihypertensive medication at baseline exam * NewVar Crosstabulation 

Count 

NewVar 
Total 

1 
2 

Use of antihypertensive medication at baseline exam 
Not currently used 
29 
3402 
3431 
Current use 
3 
113 
116 

Total 
32 
3515 
3547 
Case Processing Summary 

casual serum at baseline exam 
Cases 

Valid 
Missing 
Total 

N 
Percent 
N 
Percent 
N 
Percent 

Age at baseline exam (years) 
1 
3556 
99.7% 
12 
.3% 
3568 
100.0% 
2 
31 
96.9% 
1 
3.1% 
32 
100.0% 

Body Mass Index at baseline exam (kg/m^2) 
1 
3556 
99.7% 
12 
.3% 
3568 
100.0% 
2 
31 
96.9% 
1 
3.1% 
32 
100.0% 
Descriptives 

casual serum at baseline exam 
Statistic 
Std. Error 

Age at baseline exam (years) 
1 
Mean 
49.94 
.145 

95% Confidence Interval for Mean 
Lower Bound 
49.66 

Upper Bound 
50.22 

5% Trimmed Mean 
49.82 

Median 
49.00 

Variance 
74.613 

Std. Deviation 
8.638 

Minimum 
32 

Maximum 
70 

Range 
38 

Interquartile Range 
14 

Skewness 
.199 
.041 

Kurtosis 
1.014 
.082 

2 
Mean 
55.71 
1.209 

95% Confidence Interval for Mean 
Lower Bound 
53.24 

Upper Bound 
58.18 

5% Trimmed Mean 
55.81 

Median 
56.00 

Variance 
45.280 

Std. Deviation 
6.729 

Minimum 
43 

Maximum 
67 

Range 
24 

Interquartile Range 
10 

Skewness 
.249 
.421 

Kurtosis 
.790 
.821 

Body Mass Index at baseline exam (kg/m^2) 
1 
Mean 
25.8425 
.06789 

95% Confidence Interval for Mean 
Lower Bound 
25.7094 

Upper Bound 
25.9756 

5% Trimmed Mean 
25.6369 

Median 
25.4250 

Variance 
16.388 

Std. Deviation 
4.04821 

Minimum 
15.54 

Maximum 
56.80 

Range 
41.26 

Interquartile Range 
4.99 

Skewness 
.961 
.041 

Kurtosis 
2.507 
.082 

2 
Mean 
28.3565 
1.00394 

95% Confidence Interval for Mean 
Lower Bound 
26.3061 

Upper Bound 
30.4068 

5% Trimmed Mean 
28.1757 

Median 
28.5000 

Variance 
31.245 

Std. Deviation 
5.58969 

Minimum 
17.17 

Maximum 
43.67 

Range 
26.50 

Interquartile Range 
7.39 

Skewness 
.407 
.421 

Kurtosis 
.760 
.821 
Use of antihypertensive medication at baseline exam * NewVar Crosstabulation 

Count 

NewVar 
Total 

1 
2 

Use of antihypertensive medication at baseline exam 
Not currently used 
29 
3402 
3431 
Current use 
3 
113 
116 

Total 
32 
3515 
3547 
Descriptives 

NewVar 
Statistic 
Std. Error 

Age at baseline exam (years) 
1 
Mean 
55.71 
1.209 

95% Confidence Interval for Mean 
Lower Bound 
53.24 

Upper Bound 
58.18 

5% Trimmed Mean 
55.81 

Median 
56.00 

Variance 
45.280 

Std. Deviation 
6.729 

Minimum 
43 

Maximum 
67 

Range 
24 

Interquartile Range 
10 

Skewness 
.249 
.421 

Kurtosis 
.790 
.821 

2 
Mean 
49.94 
.145 

95% Confidence Interval for Mean 
Lower Bound 
49.66 

Upper Bound 
50.22 

5% Trimmed Mean 
49.82 

Median 
49.00 

Variance 
74.613 

Std. Deviation 
8.638 

Minimum 
32 

Maximum 
70 

Range 
38 

Interquartile Range 
14 

Skewness 
.199 
.041 

Kurtosis 
1.014 
.082 

Body Mass Index at baseline exam (kg/m^2) 
1 
Mean 
28.3565 
1.00394 

95% Confidence Interval for Mean 
Lower Bound 
26.3061 

Upper Bound 
30.4068 

5% Trimmed Mean 
28.1757 

Median 
28.5000 

Variance 
31.245 

Std. Deviation 
5.58969 

Minimum 
17.17 

Maximum 
43.67 

Range 
26.50 

Interquartile Range 
7.39 

Skewness 
.407 
.421 

Kurtosis 
.760 
.821 

2 
Mean 
25.8425 
.06789 

95% Confidence Interval for Mean 
Lower Bound 
25.7094 

Upper Bound 
25.9756 

5% Trimmed Mean 
25.6369 

Median 
25.4250 

Variance 
16.388 

Std. Deviation 
4.04821 

Minimum 
15.54 

Maximum 
56.80 

Range 
41.26 

Interquartile Range 
4.99 

Skewness 
.961 
.041 

Kurtosis 
2.507 
.082 
DATASET COPY Q4.
DATASET ACTIVATE Q4.
FILTER OFF.
USE ALL.
SELECT IF (NewVar=2).
DATASET ACTIVATE DataSet1.
EXECUTE.
DATASET ACTIVATE Q4.
DATASET ACTIVATE DataSet1.
SAVE OUTFILE='C:UsersRaju ChavanDownloadsassignment stats.sav' /COMPRESSED.
DATASET ACTIVATE Q4.
SAVE OUTFILE='C:UsersRaju ChavanDesktopRR.xlsx' /COMPRESSED.
DATASET ACTIVATE DataSet1.
DATASET ACTIVATE DataSet1.
DATASET CLOSE Q4.
DATASET COPY Q4.
DATASET ACTIVATE Q4.
FILTER OFF.
USE ALL.
SELECT IF (NewVar=2).
DATASET ACTIVATE DataSet1.
EXECUTE.
DATASET ACTIVATE Q4.
RECODE educ (2=1) (ELSE=0) INTO Edu1.
VARIABLE LABELS Edu1 'HighSchoolDiploma'.
EXECUTE.
RECODE educ (3=1) (ELSE=0) INTO Vocation.
VARIABLE LABELS Vocation 'Some College and Vocation'.
EXECUTE.
RECODE SEX (4=1) (ELSE=0) INTO Degree.
VARIABLE LABELS Degree 'College Degree and more'.
EXECUTE.
RECODE BPMEDS.1 (1=1) (ELSE=0) INTO Meditation.
VARIABLE LABELS Meditation 'taken or not'.
EXECUTE.
Variables Entered/Removed^{b} 

Model 
Variables Entered 
Variables Removed 
Method 
1 
taken or not, HighSchoolDiploma, Body Mass Index at baseline exam (kg/m^2), degree and more, Age at baseline exam (years), Some College and Vocation^{a} 
. 
Enter 
a. All requested variables entered. 

b. Dependent Variable: Casual serum glucose at baseline exam (mg/dL) 
Model Summary 

Model 
R 
R Square 
Adjusted R Square 
Std. Error of the Estimate 
1 
.146^{a} 
.021 
.020 
14.682 
a. Predictors: (Constant), taken or not, HighSchoolDiploma, Body Mass Index at baseline exam (kg/m^2), degree and more, Age at baseline exam (years), Some College and Vocation 
ANOVA^{b} 

Model 
Sum of Squares 
df 
Mean Square 
F 
Sig. 

1 
Regression 
16607.050 
6 
2767.842 
12.840 
.000^{a} 
Residual 
765023.664 
3549 
215.560 

Total 
781630.714 
3555 

a. Predictors: (Constant), taken or not, HighSchoolDiploma, Body Mass Index at baseline exam (kg/m^2), degree and more, Age at baseline exam (years), Some College and Vocation 

b. Dependent Variable: Casual serum glucose at baseline exam (mg/dL) 
Coefficients^{a} 

Model 
Unstandardized Coefficients 
Standardized Coefficients 
t 
Sig. 

B 
Std. Error 
Beta 

1 
(Constant) 
63.485 
2.197 
28.899 
.000 

Age at baseline exam (years) 
.192 
.030 
.112 
6.471 
.000 

Body Mass Index at baseline exam (kg/m^2) 
.289 
.062 
.079 
4.640 
.000 

HighSchoolDiploma 
.097 
.612 
.003 
.159 
.873 

Some College and Vocation 
.399 
.729 
.010 
.547 
.584 

degree and more 
.087 
.822 
.002 
.106 
.916 

taken or not 
.772 
1.423 
.009 
.542 
.588 

a. Dependent Variable: Casual serum glucose at baseline exam (mg/dL) 
ANOVA^{b} 

Model 
Sum of Squares 
df 
Mean Square 
F 
Sig. 

1 
Regression 
16477.435 
2 
8238.717 
38.257 
.000^{a} 
Residual 
765153.279 
3553 
215.354 

Total 
781630.714 
3555 

a. Predictors: (Constant), Body Mass Index at baseline exam (kg/m^2), Age at baseline exam (years) 

b. Dependent Variable: Casual serum glucose at baseline exam (mg/dL) 
Coefficients^{a} 

Model 
Unstandardized Coefficients 
Standardized Coefficients 
t 
Sig. 

B 
Std. Error 
Beta 

1 
(Constant) 
63.350 
2.009 
31.526 
.000 

Age at baseline exam (years) 
.192 
.029 
.112 
6.679 
.000 

Body Mass Index at baseline exam (kg/m^2) 
.290 
.061 
.079 
4.727 
.000 

a. Dependent Variable: Casual serum glucose at baseline exam (mg/dL) 
Paired Samples Statistics 

Mean 
N 
Std. Deviation 
Std. Error Mean 

Pair 1 
Casual serum glucose at baseline exam (mg/dL) 
81.04 
2824 
20.073 
.378 
Casual serum glucose at followup exam (mg/dL) 
81.83 
2824 
22.270 
.419 
Paired Samples Correlations 

N 
Correlation 
Sig. 

Pair 1 
Casual serum glucose at baseline exam (mg/dL) & Casual serum glucose at followup exam (mg/dL) 
2824 
.438 
.000 
Paired Samples Test 

Paired Differences 
t 
df 
Sig. (2tailed) 

Mean 
Std. Deviation 
Std. Error Mean 
95% Confidence Interval of the Difference 

Lower 
Upper 

Pair 1 
Casual serum glucose at baseline exam (mg/dL)  Casual serum glucose at followup exam (mg/dL) 
.785 
22.513 
.424 
1.616 
.045 
1.854 
2823 
.064 
Paired Samples Statistics 

Mean 
N 
Std. Deviation 
Std. Error Mean 

Pair 1 
Casual serum glucose at baseline exam (mg/dL) 
271.36 
14 
69.373 
18.541 
Casual serum glucose at followup exam (mg/dL) 
211.00 
14 
64.709 
17.294 
Paired Samples Correlations 

N 
Correlation 
Sig. 

Pair 1 
Casual serum glucose at baseline exam (mg/dL) & Casual serum glucose at followup exam (mg/dL) 
14 
.420 
.135 
Paired Samples Test 

Paired Differences 
t 
df 
Sig. (2tailed) 

Mean 
Std. Deviation 
Std. Error Mean 
95% Confidence Interval of the Difference 

Lower 
Upper 

Pair 1 
Casual serum glucose at baseline exam (mg/dL)  Casual serum glucose at followup exam (mg/dL) 
60.357 
72.298 
19.322 
18.613 
102.101 
3.124 
13 
.008 
Paired Samples Statistics 

Mean 
N 
Std. Deviation 
Std. Error Mean 

Pair 1 
Casual serum glucose at baseline exam (mg/dL) 
80.10 
2810 
14.186 
.268 
Casual serum glucose at followup exam (mg/dL) 
81.19 
2810 
19.887 
.375 
Paired Samples Correlations 

N 
Correlation 
Sig. 

Pair 1 
Casual serum glucose at baseline exam (mg/dL) & Casual serum glucose at followup exam (mg/dL) 
2810 
.231 
.000 
Paired Samples Test 

Paired Differences 
t 
df 
Sig. (2tailed) 

Mean 
Std. Deviation 
Std. Error Mean 
95% Confidence Interval of the Difference 

Lower 
Upper 

Pair 1 
Casual serum glucose at baseline exam (mg/dL)  Casual serum glucose at followup exam (mg/dL) 
1.090 
21.598 
.407 
1.889 
.291 
2.675 
2809 
.008 
References:
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Bickel, P. J., & Doksum, K. A. (2015). Mathematical statistics: basic ideas and selected topics, volume I (Vol. 117). CRC Press.
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Fox, J. (2015). Applied regression analysis and generalized linear models. Sage Publications.
Glantz, S. A., Slinker, B. K., & Neilands, T. B. (2016). Primer of applied regression & analysis of variance. McGrawHill Medical Publishing Division.
Paired Ttest for Glucose Level Change
LarsonHall, J. (2015). A guide to doing statistics in second language research using SPSS and R. Routledge.
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At the baseline examination, data from 3950 people were collected in terms of sex, education level, age, Serum total cholesterol, Systolic blood pressure, Diastolic blood pressure, Current cigarette smoking, Number of cigarettes smoked each day, Body mass index, use of antihypertensive medication, Casual serum glucose. Out of 3950, 1725 are male and 2225 are female. 41.1 % people are education level 011 years where as 28.6% are diploma holder. 49.1 % people are currently smoker at baseline examination whereas 50.1% are not currently smoker. Only 3.1% people use anti hyper tension mediation. At baseline examination, mean serum total cholesterol is 237.41mmg/dL with standard deviation 44.779. Mean age of people at baseline examination is 49.95 years with standard deviation 8.644 years. Mean systolic blood pressure is 132.838 mmHg with standard deviation 22.3993. Mean systolic blood pressure is 83.047 mm/Hg with standard deviation 12.0522. People averagely smoke 8.87 cigarettes every day with standard deviation 11.844. At baseline examination people have average BMI 25.8523 Kg/m2 with standard deviation 4.07827. Mean casual serum glucose is observed as 82.18 mmg/dL with standard deviation 24.485.
 Characterize the people who had casual serum glucose >200 mg/dL at the baseline examination and compare them to people who had ≤200 mg/dL casual serum glucose at the baseline examination in terms of age, body mass index (BMI), education and whether they were taking blood pressure medication at the time of the baseline examination.
We group the variable in two categories:
1: casual serum glucose >200 mg/dL at the baseline examination
2 : casual serum glucose 200 mg/dL at the baseline examination
Following table shows the descriptive statistics for the group 1 and 2 for age and BMI
Descriptive Statistic 
Age at baseline exam (years) 
Body Mass Index at baseline exam (kg/m^2) 

Group 1 
Group 2 
Group 1 
Group 2 

Mean 
55.71 
49.94 
28.3565 
25.8425 
Size 
31 
3556 
31 
3556 
Median 
56 
49 
28.5 
25.425 
Variance 
45.28 
74.613 
31.245 
16.388 
Std. Deviation 
6.729 
8.638 
5.58969 
4.04821 
Minimum 
43 
32 
17.17 
15.54 
Maximum 
67 
70 
43.67 
56.8 
Range 
24 
38 
26.5 
41.26 
Interquartile Range 
10 
14 
7.39 
4.99 
Skewness 
0.249 
0.199 
0.407 
0.961 
Kurtosis 
0.79 
1.014 
0.76 
2.507 
We have 31 people having casual serum glucose >200 mg/dL at the baseline examination and 3556 people having casual serum glucose 200 mg/dL at the baseline examination. Mean age of people having casual serum glucose >200 mg/dL at the baseline examination is 55.71 (6.729) years whereas mean age of people having casual serum glucose 200 mg/dL at the baseline examination is 49.94(8.638) years. BMI of group 1 is higher than group 2. One can observed the difference between other statistic from above table.
64.51 % people having casual serum glucose >200 mg/dL at the baseline examination has education 011 years whereas for other group this percentage is 42.28%. In Group 1 19.35% people are diploma holder whereas in Group 2 29.33% people are diploma holders. There is no one in Group 1 which has college degree or more whereas in Group 2 about 12% people have college degree or more.
9% People in group 1 taking mediation whereas only 3% people in Group 2 are taking medication for controlling the blood pressure.
 Are the results from the bivariate comparisons above (point 2) different if the actual casual serum glucose level at baseline examination is analysed, rather than the dichotomized glucose variable?
No, the results from the bivariate comparisons above (point 2) different if the actual casual serum glucose level at baseline examination is analysed, rather than the dichotomized glucose variable.
 Considering only individuals with casual serum glucose level at baseline below 200 mg/dL, which of these variables (age, BMI, education and whether they were taking blood pressure medication) are significantly associated with casual serum glucose level at baseline in a multivariable analysis? Describe their relationship with casual serum glucose level, including which variables explain the most variation in casual serum glucose level. Report the ‘minimum model’ obtained. Explain any differences you observe between the results of the bivariate analysis in point 3 above and multivariable analysis.
We considered the individuals with casual serum glucose level at baseline below 200 mg/dL. There are 3568 people having casual serum glucose level at baseline below 200 mg/dL. To test whether there is any significant relation between the casual serum glucose level at baseline and independent variables (age, BMI, education and whether they were taking blood pressure medication). We run the multiple regression analysis. In the independent variables Education and whether they were taking blood pressure medication are categorical variables, we need to create dummy variables for testing the above hypothesis, we create four dummy variables (3 for education and 1 for whether they were taking blood pressure medication. We take 111 years education and not taken any medication as a reference variable.
Following table shows the ANOVA of multiple regression analysis:
Source of Variation 
Sum of Squares 
df 
Mean Square 
F 
P Value 
Regression 
16607.05 
6 
2767.842 
12.84 
0 
Residual 
765023.7 
3549 
215.56 

Total 
781630.7 
3555 
The Pvalue = 0 suggest that there is significant relation between the casual serum glucose level at baseline and independent variables (age, BMI, education and whether they were taking blood pressure medication). That is at least one of the coefficient is non zero. From following table we can see that which coefficient are significant or not.
Independent Variable 
Coefficient 
Std. Error 
t 
P Value 
(Constant) 
63.485 
2.197 
28.899 
0.000 
Age at baseline exam (years) 
0.192 
0.030 
6.471 
0.000 
Body Mass Index at baseline exam (kg/m^2) 
0.289 
0.062 
4.640 
0.000 
HighSchoolDiploma 
0.097 
0.612 
0.159 
0.873 
Some College and Vocation 
0.399 
0.729 
0.547 
0.584 
degree and more 
0.087 
0.822 
0.106 
0.916 
taken or not 
0.772 
1.423 
0.542 
0.588 
We can see that only age and BMI are significant whereas other variables education and whether they were taking blood pressure medication are found to be nonsignificant for predicting the casual serum glucose level at baseline. Both age and BMI have positive correlation with casual serum glucose level at baseline.
As the education and whether they were taking blood pressure medication are found to be nonsignificant for predicting the casual serum glucose level at baseline, we fit the model again using age and BMI variables only. Following is the equation of multiple regression analysis for predicting the casual serum glucose level at baseline using age and BMI as a predictor variables.
Casual serum glucose level at baseline = 63.35 + 0.192 × Age + 0.29 × BMI
Each incline in age results in 0.192 incline in casual serum glucose level whereas each unit of BMI incline results in 0.29 incline in casual serum glucose level.
From bivariate analysis, we observed that mean age and BMI for person having casual serum glucose >200 mg/dL at the baseline examination is more than the person having casual serum glucose 200 mg/dL at the baseline examination. And from the multivariate analysis we observed that each icline in age and BMI results in incline in the casual serum glucose level.
 Did the casual serum glucose level change significantly between the baseline examination and the followup examination? Is this result the same when casual serum glucose level is categorised according to the clinical threshold of >200 mg/dL versus ≤200 mg/dL?
We carry the paired t test for the testing whether there is casual serum glucose level change significantly between the baseline examination and the followup examination. We observed t statistics is 1.854 and P value is 0.064 < 0.1 suggest that there is significant change in the casual serum glucose level change significantly between the baseline examination and the followup examination at 10% level of significance.
We now group the people having casual serum glucose >200 mg/dL and casual serum glucose 200 mg/dL. After that we used paired t test for both the groups.
We observed t statistics is 3.124 and P value is 0.008 < 0.1 suggest that there is significant change in the casual serum glucose level >200 mg/dL change significantly between the baseline examination and the followup examination at 10%.
We observed t statistics is 2.675 and P value is 0.008 < 0.1 suggest that there is significant change in the casual serum glucose level 200 mg/dL change significantly between the baseline examination and the followup examination at 10%.
From the test statistics we can observed that glucose level increases for people having casual serum glucose level >200 mg/dL at baseline examination and glucose level decreases for people having casual serum glucose level <= 200 mg/dL at baseline examination.
SPSS Output:
Sex 

Frequency 
Percent 
Valid Percent 
Cumulative Percent 

Valid 
Male 
1725 
43.7 
43.7 
43.7 
Female 
2225 
56.3 
56.3 
100.0 

Total 
3950 
100.0 
100.0 
Education level 

Frequency 
Percent 
Valid Percent 
Cumulative Percent 

Valid 
011 years 
1625 
41.1 
42.2 
42.2 
High school diploma 
1131 
28.6 
29.4 
71.6 

Some college, vocational school 
638 
16.2 
16.6 
88.2 

College degree or more 
456 
11.5 
11.8 
100.0 

Total 
3850 
97.5 
100.0 

Missing 
System 
100 
2.5 

Total 
3950 
100.0 
Current cigarette smoking at baseline exam 

Frequency 
Percent 
Valid Percent 
Cumulative Percent 

Valid 
Not current smoker 
2009 
50.9 
50.9 
50.9 
Current smoker 
1941 
49.1 
49.1 
100.0 

Total 
3950 
100.0 
100.0 
Use of antihypertensive medication at baseline exam 

Frequency 
Percent 
Valid Percent 
Cumulative Percent 

Valid 
Not currently used 
3771 
95.5 
96.8 
96.8 
Current use 
124 
3.1 
3.2 
100.0 

Total 
3895 
98.6 
100.0 

Missing 
System 
55 
1.4 

Total 
3950 
100.0 
casual serum at baseline exam 

Frequency 
Percent 
Valid Percent 
Cumulative Percent 

Valid 
1 
3568 
90.3 
99.1 
99.1 
2 
32 
.8 
.9 
100.0 

Total 
3600 
91.1 
100.0 

Missing 
System 
350 
8.9 

Total 
3950 
100.0 
Descriptive Statistics 

N 
Mean 
Std. Deviation 

Age at baseline exam (years) 
3950 
49.95 
8.644 
Systolic blood pressure at baseline exam (mmHg) 
3950 
132.838 
22.3993 
Diastolic blood pressure at baseline exam (mmHg) 
3950 
83.047 
12.0522 
Number of cigarettes smoked each day at baseline exam 
3920 
8.87 
11.824 
Body Mass Index at baseline exam (kg/m^2) 
3932 
25.8523 
4.07827 
Serum total cholesterol at baseline exam (mmg/dL) 
3904 
237.41 
44.779 
Casual serum glucose at baseline exam (mg/dL) 
3600 
82.18 
24.485 
Valid N (listwise) 
3552 
Q2
Case Processing Summary 

NewVar 
Cases 

Valid 
Missing 
Total 

N 
Percent 
N 
Percent 
N 
Percent 

Age at baseline exam (years) 
1 
31 
96.9% 
1 
3.1% 
32 
100.0% 
2 
3556 
99.7% 
12 
.3% 
3568 
100.0% 

Body Mass Index at baseline exam (kg/m^2) 
1 
31 
96.9% 
1 
3.1% 
32 
100.0% 
2 
3556 
99.7% 
12 
.3% 
3568 
100.0% 
Education level * NewVar Crosstabulation 

Count 

NewVar 
Total 

1 
2 

Education level 
011 years 
20 
1470 
1490 
High school diploma 
6 
1020 
1026 

Some college, vocational school 
5 
572 
577 

College degree or more 
0 
415 
415 

Total 
31 
3477 
3508 
Use of antihypertensive medication at baseline exam * NewVar Crosstabulation 

Count 

NewVar 
Total 

1 
2 

Use of antihypertensive medication at baseline exam 
Not currently used 
29 
3402 
3431 
Current use 
3 
113 
116 

Total 
32 
3515 
3547 
Q3:
Case Processing Summary 

casual serum at baseline exam 
Cases 

Valid 
Missing 
Total 

N 
Percent 
N 
Percent 
N 
Percent 

Age at baseline exam (years) 
1 
3556 
99.7% 
12 
.3% 
3568 
100.0% 
2 
31 
96.9% 
1 
3.1% 
32 
100.0% 

Body Mass Index at baseline exam (kg/m^2) 
1 
3556 
99.7% 
12 
.3% 
3568 
100.0% 
2 
31 
96.9% 
1 
3.1% 
32 
100.0% 
Descriptives 

casual serum at baseline exam 
Statistic 
Std. Error 

Age at baseline exam (years) 
1 
Mean 
49.94 
.145 

95% Confidence Interval for Mean 
Lower Bound 
49.66 

Upper Bound 
50.22 

5% Trimmed Mean 
49.82 

Median 
49.00 

Variance 
74.613 

Std. Deviation 
8.638 

Minimum 
32 

Maximum 
70 

Range 
38 

Interquartile Range 
14 

Skewness 
.199 
.041 

Kurtosis 
1.014 
.082 

2 
Mean 
55.71 
1.209 

95% Confidence Interval for Mean 
Lower Bound 
53.24 

Upper Bound 
58.18 

5% Trimmed Mean 
55.81 

Median 
56.00 

Variance 
45.280 

Std. Deviation 
6.729 

Minimum 
43 

Maximum 
67 

Range 
24 

Interquartile Range 
10 

Skewness 
.249 
.421 

Kurtosis 
.790 
.821 

Body Mass Index at baseline exam (kg/m^2) 
1 
Mean 
25.8425 
.06789 

95% Confidence Interval for Mean 
Lower Bound 
25.7094 

Upper Bound 
25.9756 

5% Trimmed Mean 
25.6369 

Median 
25.4250 

Variance 
16.388 

Std. Deviation 
4.04821 

Minimum 
15.54 

Maximum 
56.80 

Range 
41.26 

Interquartile Range 
4.99 

Skewness 
.961 
.041 

Kurtosis 
2.507 
.082 

2 
Mean 
28.3565 
1.00394 

95% Confidence Interval for Mean 
Lower Bound 
26.3061 

Upper Bound 
30.4068 

5% Trimmed Mean 
28.1757 

Median 
28.5000 

Variance 
31.245 

Std. Deviation 
5.58969 

Minimum 
17.17 

Maximum 
43.67 

Range 
26.50 

Interquartile Range 
7.39 

Skewness 
.407 
.421 

Kurtosis 
.760 
.821 
Use of antihypertensive medication at baseline exam * NewVar Crosstabulation 

Count 

NewVar 
Total 

1 
2 

Use of antihypertensive medication at baseline exam 
Not currently used 
29 
3402 
3431 
Current use 
3 
113 
116 

Total 
32 
3515 
3547 
Descriptives 

NewVar 
Statistic 
Std. Error 

Age at baseline exam (years) 
1 
Mean 
55.71 
1.209 

95% Confidence Interval for Mean 
Lower Bound 
53.24 

Upper Bound 
58.18 

5% Trimmed Mean 
55.81 

Median 
56.00 

Variance 
45.280 

Std. Deviation 
6.729 

Minimum 
43 

Maximum 
67 

Range 
24 

Interquartile Range 
10 

Skewness 
.249 
.421 

Kurtosis 
.790 
.821 

2 
Mean 
49.94 
.145 

95% Confidence Interval for Mean 
Lower Bound 
49.66 

Upper Bound 
50.22 

5% Trimmed Mean 
49.82 

Median 
49.00 

Variance 
74.613 

Std. Deviation 
8.638 

Minimum 
32 

Maximum 
70 

Range 
38 

Interquartile Range 
14 

Skewness 
.199 
.041 

Kurtosis 
1.014 
.082 

Body Mass Index at baseline exam (kg/m^2) 
1 
Mean 
28.3565 
1.00394 

95% Confidence Interval for Mean 
Lower Bound 
26.3061 

Upper Bound 
30.4068 

5% Trimmed Mean 
28.1757 

Median 
28.5000 

Variance 
31.245 

Std. Deviation 
5.58969 

Minimum 
17.17 

Maximum 
43.67 

Range 
26.50 

Interquartile Range 
7.39 

Skewness 
.407 
.421 

Kurtosis 
.760 
.821 

2 
Mean 
25.8425 
.06789 

95% Confidence Interval for Mean 
Lower Bound 
25.7094 

Upper Bound 
25.9756 

5% Trimmed Mean 
25.6369 

Median 
25.4250 

Variance 
16.388 

Std. Deviation 
4.04821 

Minimum 
15.54 

Maximum 
56.80 

Range 
41.26 

Interquartile Range 
4.99 

Skewness 
.961 
.041 

Kurtosis 
2.507 
.082 
Q4:
DATASET COPY Q4.
DATASET ACTIVATE Q4.
FILTER OFF.
USE ALL.
SELECT IF (NewVar=2).
DATASET ACTIVATE DataSet1.
EXECUTE.
DATASET ACTIVATE Q4.
DATASET ACTIVATE DataSet1.
SAVE OUTFILE='C:UsersRaju ChavanDownloadsassignment stats.sav' /COMPRESSED.
DATASET ACTIVATE Q4.
SAVE OUTFILE='C:UsersRaju ChavanDesktopRR.xlsx' /COMPRESSED.
DATASET ACTIVATE DataSet1.
DATASET ACTIVATE DataSet1.
DATASET CLOSE Q4.
DATASET COPY Q4.
DATASET ACTIVATE Q4.
FILTER OFF.
USE ALL.
SELECT IF (NewVar=2).
DATASET ACTIVATE DataSet1.
EXECUTE.
DATASET ACTIVATE Q4.
RECODE educ (2=1) (ELSE=0) INTO Edu1.
VARIABLE LABELS Edu1 'HighSchoolDiploma'.
EXECUTE.
RECODE educ (3=1) (ELSE=0) INTO Vocation.
VARIABLE LABELS Vocation 'Some College and Vocation'.
EXECUTE.
RECODE SEX (4=1) (ELSE=0) INTO Degree.
VARIABLE LABELS Degree 'College Degree and more'.
EXECUTE.
RECODE BPMEDS.1 (1=1) (ELSE=0) INTO Meditation.
VARIABLE LABELS Meditation 'taken or not'.
EXECUTE.
Variables Entered/Removed^{b} 

Model 
Variables Entered 
Variables Removed 
Method 
1 
taken or not, HighSchoolDiploma, Body Mass Index at baseline exam (kg/m^2), degree and more, Age at baseline exam (years), Some College and Vocation^{a} 
. 
Enter 
a. All requested variables entered. 

b. Dependent Variable: Casual serum glucose at baseline exam (mg/dL) 
Model Summary 

Model 
R 
R Square 
Adjusted R Square 
Std. Error of the Estimate 
1 
.146^{a} 
.021 
.020 
14.682 
a. Predictors: (Constant), taken or not, HighSchoolDiploma, Body Mass Index at baseline exam (kg/m^2), degree and more, Age at baseline exam (years), Some College and Vocation 
ANOVA^{b} 

Model 
Sum of Squares 
df 
Mean Square 
F 
Sig. 

1 
Regression 
16607.050 
6 
2767.842 
12.840 
.000^{a} 
Residual 
765023.664 
3549 
215.560 

Total 
781630.714 
3555 

a. Predictors: (Constant), taken or not, HighSchoolDiploma, Body Mass Index at baseline exam (kg/m^2), degree and more, Age at baseline exam (years), Some College and Vocation 

b. Dependent Variable: Casual serum glucose at baseline exam (mg/dL) 
Coefficients^{a} 

Model 
Unstandardized Coefficients 
Standardized Coefficients 
t 
Sig. 

B 
Std. Error 
Beta 

1 
(Constant) 
63.485 
2.197 
28.899 
.000 

Age at baseline exam (years) 
.192 
.030 
.112 
6.471 
.000 

Body Mass Index at baseline exam (kg/m^2) 
.289 
.062 
.079 
4.640 
.000 

HighSchoolDiploma 
.097 
.612 
.003 
.159 
.873 

Some College and Vocation 
.399 
.729 
.010 
.547 
.584 

degree and more 
.087 
.822 
.002 
.106 
.916 

taken or not 
.772 
1.423 
.009 
.542 
.588 

a. Dependent Variable: Casual serum glucose at baseline exam (mg/dL) 
ANOVA^{b} 

Model 
Sum of Squares 
df 
Mean Square 
F 
Sig. 

1 
Regression 
16477.435 
2 
8238.717 
38.257 
.000^{a} 
Residual 
765153.279 
3553 
215.354 

Total 
781630.714 
3555 

a. Predictors: (Constant), Body Mass Index at baseline exam (kg/m^2), Age at baseline exam (years) 

b. Dependent Variable: Casual serum glucose at baseline exam (mg/dL) 
Coefficients^{a} 

Model 
Unstandardized Coefficients 
Standardized Coefficients 
t 
Sig. 

B 
Std. Error 
Beta 

1 
(Constant) 
63.350 
2.009 
31.526 
.000 

Age at baseline exam (years) 
.192 
.029 
.112 
6.679 
.000 

Body Mass Index at baseline exam (kg/m^2) 
.290 
.061 
.079 
4.727 
.000 

a. Dependent Variable: Casual serum glucose at baseline exam (mg/dL) 
Q5
Paired Samples Statistics 

Mean 
N 
Std. Deviation 
Std. Error Mean 

Pair 1 
Casual serum glucose at baseline exam (mg/dL) 
81.04 
2824 
20.073 
.378 
Casual serum glucose at followup exam (mg/dL) 
81.83 
2824 
22.270 
.419 
Paired Samples Correlations 

N 
Correlation 
Sig. 

Pair 1 
Casual serum glucose at baseline exam (mg/dL) & Casual serum glucose at followup exam (mg/dL) 
2824 
.438 
.000 
Paired Samples Test 

Paired Differences 
t 
df 
Sig. (2tailed) 

Mean 
Std. Deviation 
Std. Error Mean 
95% Confidence Interval of the Difference 

Lower 
Upper 

Pair 1 
Casual serum glucose at baseline exam (mg/dL)  Casual serum glucose at followup exam (mg/dL) 
.785 
22.513 
.424 
1.616 
.045 
1.854 
2823 
.064 
For Group 1:
Paired Samples Statistics 

Mean 
N 
Std. Deviation 
Std. Error Mean 

Pair 1 
Casual serum glucose at baseline exam (mg/dL) 
271.36 
14 
69.373 
18.541 
Casual serum glucose at followup exam (mg/dL) 
211.00 
14 
64.709 
17.294 
Paired Samples Correlations 

N 
Correlation 
Sig. 

Pair 1 
Casual serum glucose at baseline exam (mg/dL) & Casual serum glucose at followup exam (mg/dL) 
14 
.420 
.135 
Paired Samples Test 

Paired Differences 
t 
df 
Sig. (2tailed) 

Mean 
Std. Deviation 
Std. Error Mean 
95% Confidence Interval of the Difference 

Lower 
Upper 

Pair 1 
Casual serum glucose at baseline exam (mg/dL)  Casual serum glucose at followup exam (mg/dL) 
60.357 
72.298 
19.322 
18.613 
102.101 
3.124 
13 
.008 
For Group 2:
Paired Samples Statistics 

Mean 
N 
Std. Deviation 
Std. Error Mean 

Pair 1 
Casual serum glucose at baseline exam (mg/dL) 
80.10 
2810 
14.186 
.268 
Casual serum glucose at followup exam (mg/dL) 
81.19 
2810 
19.887 
.375 
Paired Samples Correlations 

N 
Correlation 
Sig. 

Pair 1 
Casual serum glucose at baseline exam (mg/dL) & Casual serum glucose at followup exam (mg/dL) 
2810 
.231 
.000 
Paired Samples Test 

Paired Differences 
t 
df 
Sig. (2tailed) 

Mean 
Std. Deviation 
Std. Error Mean 
95% Confidence Interval of the Difference 

Lower 
Upper 

Pair 1 
Casual serum glucose at baseline exam (mg/dL)  Casual serum glucose at followup exam (mg/dL) 
1.090 
21.598 
.407 
1.889 
.291 
2.675 
2809 
.008 
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