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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 anti-hypertensive medication, Casual serum glucose. Out of 3950, 1725 are male and 2225 are female. 41.1 % people are education level 0-11 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 0-11 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 1-11 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 P-value = 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 non-significant 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 non-significant 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 follow-up 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 follow-up 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 follow-up 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 follow-up 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 0-11 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 anti-hypertensive 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 0-11 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 anti-hypertensive medication at baseline exam * NewVar Crosstabulation Count NewVar Total 1 2 Use of anti-hypertensive 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 anti-hypertensive medication at baseline exam * NewVar Crosstabulation Count NewVar Total 1 2 Use of anti-hypertensive 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.

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/Removedb 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 Vocationa . 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 .146a .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
 ANOVAb Model Sum of Squares df Mean Square F Sig. 1 Regression 16607.050 6 2767.842 12.840 .000a 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)
 Coefficientsa 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)
 ANOVAb Model Sum of Squares df Mean Square F Sig. 1 Regression 16477.435 2 8238.717 38.257 .000a 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)
 Coefficientsa 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 follow-up 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 follow-up exam (mg/dL) 2824 .438 .000
 Paired Samples Test Paired Differences t df Sig. (2-tailed) 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 follow-up 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 follow-up 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 follow-up exam (mg/dL) 14 .420 .135
 Paired Samples Test Paired Differences t df Sig. (2-tailed) 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 follow-up 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 follow-up 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 follow-up exam (mg/dL) 2810 .231 .000
 Paired Samples Test Paired Differences t df Sig. (2-tailed) 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 follow-up exam (mg/dL) -1.090 21.598 .407 -1.889 -.291 -2.675 2809 .008

References:

Abbott, M. L. (2016). Using Statistics in the Social and Health Sciences with SPSS and Excel. John Wiley & Sons.

Bickel, P. J., & Doksum, K. A. (2015). Mathematical statistics: basic ideas and selected topics, volume I (Vol. 117). CRC Press.

Chatterjee, S., & Hadi, A. S. (2015). Regression analysis by example. John Wiley & Sons.

Darlington, R. B., & Hayes, A. F. (2016). Regression analysis and linear models: Concepts, applications, and implementation. Guilford Publications.

Draper, N. R., & Smith, H. (2014). Applied regression analysis (Vol. 326). John Wiley & Sons.

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. McGraw-Hill Medical Publishing Division.

## Paired T-test for Glucose Level Change

Larson-Hall, J. (2015). A guide to doing statistics in second language research using SPSS and R. Routledge.

Pett, M. A. (2015). Nonparametric statistics for health care research: Statistics for small samples and unusual distributions. Sage Publications.

Pett, M. A. (2015). Nonparametric statistics for health care research: Statistics for small samples and unusual distributions. Sage Publications.

Rasch, D., & Schott, D. (2018). Basic Ideas of Mathematical Statistics. Mathematical Statistics, 1-38.

Schroeder, L. D., Sjoquist, D. L., & Stephan, P. E. (2016). Understanding regression analysis: An introductory guide (Vol. 57). Sage Publications.

Tabachnick, B. G., & Fidell, L. S. (2007). Using multivariate statistics. Allyn & Bacon/Pearson Education.

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 anti-hypertensive medication, Casual serum glucose. Out of 3950, 1725 are male and 2225 are female. 41.1 % people are education level 0-11 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.

1. 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 0-11 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.

1. 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.

1. 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 1-11 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 P-value = 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 non-significant 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 non-significant 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.

1. Did the casual serum glucose level change significantly between the baseline examination and the follow-up 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 follow-up 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 follow-up 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 follow-up 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 follow-up 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 0-11 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 anti-hypertensive 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 0-11 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 anti-hypertensive medication at baseline exam * NewVar Crosstabulation Count NewVar Total 1 2 Use of anti-hypertensive 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 anti-hypertensive medication at baseline exam * NewVar Crosstabulation Count NewVar Total 1 2 Use of anti-hypertensive 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.

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/Removedb 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 Vocationa . 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 .146a .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
 ANOVAb Model Sum of Squares df Mean Square F Sig. 1 Regression 16607.050 6 2767.842 12.840 .000a 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)
 Coefficientsa 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)
 ANOVAb Model Sum of Squares df Mean Square F Sig. 1 Regression 16477.435 2 8238.717 38.257 .000a 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)
 Coefficientsa 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 follow-up 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 follow-up exam (mg/dL) 2824 .438 .000
 Paired Samples Test Paired Differences t df Sig. (2-tailed) 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 follow-up 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 follow-up 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 follow-up exam (mg/dL) 14 .420 .135
 Paired Samples Test Paired Differences t df Sig. (2-tailed) 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 follow-up 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 follow-up 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 follow-up exam (mg/dL) 2810 .231 .000
 Paired Samples Test Paired Differences t df Sig. (2-tailed) 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 follow-up exam (mg/dL) -1.090 21.598 .407 -1.889 -.291 -2.675 2809 .008

References:

Abbott, M. L. (2016). Using Statistics in the Social and Health Sciences with SPSS and Excel. John Wiley & Sons.

Bickel, P. J., & Doksum, K. A. (2015). Mathematical statistics: basic ideas and selected topics, volume I (Vol. 117). CRC Press.

Chatterjee, S., & Hadi, A. S. (2015). Regression analysis by example. John Wiley & Sons.

Darlington, R. B., & Hayes, A. F. (2016). Regression analysis and linear models: Concepts, applications, and implementation. Guilford Publications.

Draper, N. R., & Smith, H. (2014). Applied regression analysis (Vol. 326). John Wiley & Sons.

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. McGraw-Hill Medical Publishing Division.

Larson-Hall, J. (2015). A guide to doing statistics in second language research using SPSS and R. Routledge.

Pett, M. A. (2015). Nonparametric statistics for health care research: Statistics for small samples and unusual distributions. Sage Publications.

Pett, M. A. (2015). Nonparametric statistics for health care research: Statistics for small samples and unusual distributions. Sage Publications.

Rasch, D., & Schott, D. (2018). Basic Ideas of Mathematical Statistics. Mathematical Statistics, 1-38.

Schroeder, L. D., Sjoquist, D. L., & Stephan, P. E. (2016). Understanding regression analysis: An introductory guide (Vol. 57). Sage Publications.

Tabachnick, B. G., & Fidell, L. S. (2007). Using multivariate statistics. Allyn & Bacon/Pearson Education.

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