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## Regression analysis of HgbA1c and weight at baseline

1. A group of 10-year-old boys were first ascertained in a camp for diabetic boys.  They had their first weight measured at baseline and again when they returned to camp one year later.  Each time, a serum sample was obtained from which a determination of haemoglobin A1c (HgbA1c) was made.  HgbA1c (also called glycosylated haemoglobin) is routinely used to monitor compliance with taking insulin injections.  Usually, the poorer the compliance, the higher the HgbA1c level.  The hypothesis is that the level of HgbA1c is related to the weight.  The data are entered into an SPSS file called “assignment2_diabetes2018.sav”.  Download this file and use SPSS to answer the following questions:

a) Is HgbA1c a useful predictor for weight at baseline? Run a regression analysis with wgt1 as the dependent and HgbA1c_1 as the independent.  Does HgbA1c significantly predict weight?  Give the statistical evidence for your conclusion.  How well does HgbA1c explain the variability in weight in these data?  Give the statistical evidence for your conclusion.  Write a one-sentence summary of this analysis.

b) Repeat the above analysis for HgbA1c one year later.  Giving the statistical evidence, do your conclusions change?

c) Using transform -> compute, calculate 2 new variables:  wgtdiff = wgt2 – wgt1, which measures the change in weight from baseline to one year follow-up, and HgbA1cDiff = HgbA1c_2 – HgbA1c_1, which measures the change in HgbA1c from baseline to one year follow-up.  Use regression analysis to investigate whether or not the change in HgbA1c predicts the change in weight.  What is the statistical significance of the relationship?  How well does change in HgbA1c explain change in weight?  What is the direction of the relationship?

d) Using the results from all three of the analyses above, write a paragraph giving your conclusions, suitable for the conclusions/ discussions section of a paper. What further investigations would you suggest, based on these data?

2. Use the Framingham data set, with period = 1, to answer the following questions.

a. Does mean age (AGE) differ between those on antihypertensives (BPMEDS = 1) and those not on antihypertensives (BPMEDS = 0)?

b. Does mean systolic BP (SYSBP) differ between those on antihypertensives (BPMEDS = 1) and those not on antihypertensives (BPMEDS = 0)?

c. Does mean diastolic BP (DIABP) differ between those on antihypertensives (BPMEDS = 1) and those not on antihypertensives (BPMEDS = 0)?

For each analysis, summarize your findings in 1-2 sentences.

3. A nutrition expert is examining a weight-loss program to evaluate its effectiveness (i.e. whether participants lose weight on the program). Ten subjects are randomly selected for the investigation.  Each subject’s initial weight is recorded, they follow the program for 6 weeks, and they are weighed again.  The data are;

 subject Initial weight Final weight 1 180 165 2 142 138 3 126 128 4 138 136 5 175 170 6 205 197 7 116 115 8 142 128 9 157 144 10 136 130

Use SPSS to test if there is evidence of a significant weight loss.  Run the appropriate test at the 5% level of significance.  Write a 1-sentence summary of your analysis.

4. The following data reflect the ages of students at completion of year 7. Test if there is a significant difference in the mean age at completion of year 7 for rural, suburban and urban students using SPSS. Write a 1-2 sentence summary of your findings.

 rural 14 14 14 14 13 13 13 12 suburban 14 14 14 13 13 13 13 13 12 12 urban 16 16 15 15 15 14 14 14 13 12
 Model R R Square Adjusted R Square Std. Error of the Estimate 1 .204a .042 -.032 4.29418

## Regression analysis of HgbA1c and weight at baseline

a. Predictors: (Constant), HgbA1c_1

The value of R-Squared is 0.042; this implies that only 4.2% of the variation in weight is explained by HgbA1c.

 Model Sum of Squares df Mean Square F Sig. 1 Regression 10.429 1 10.429 .566 .465b Residual 239.720 13 18.440 Total 250.149 14

a. Dependent Variable: wgt1

b. Predictors: (Constant), HgbA1c_1

The coefficients table below shows that the p-value for the HgbA1c is 0.465; this value is higher than the 5% level of significance. The null hypothesis is not rejected suggesting that HgbA1c does not significantly predict weight.

 Model Unstandardized Coefficients Standardized Coefficients t Sig. B Std. Error Beta 1 (Constant) 33.218 6.227 5.334 .000 HgbA1c_1 .553 .735 .204 .752 .465

a. Dependent Variable: wgt1

In summary, only a small proportion of variation (4.2%) in weight is explained by HgbA1c and also results showed that the independent variable (HgbA1c) does not significantly predict weight.

 Model R R Square Adjusted R Square Std. Error of the Estimate 1 .217a .047 -.026 5.76184

a. Predictors: (Constant), HgbA1c_2

 Model Sum of Squares df Mean Square F Sig. 1 Regression 21.405 1 21.405 .645 .436b Residual 431.585 13 33.199 Total 452.989 14

a. Dependent Variable: wgt2

b. Predictors: (Constant), HgbA1c_2

 Model Unstandardized Coefficients Standardized Coefficients t Sig. B Std. Error Beta 1 (Constant) 52.987 13.773 3.847 .002 HgbA1c_2 -1.370 1.706 -.217 -.803 .436

a. Dependent Variable: wgt2

One year later the results do not significantly change. Only 4.7% of the variation in weight is explained by HgbA1c. Again, the p-value for the HgbA1c is found to be 0.436; this value is higher than the 5% level of significance leading acceptance of the null hypothesis hence implying that HgbA1c does not significantly predict weight.

 Model R R Square Adjusted R Square Std. Error of the Estimate 1 .461a .213 .152 2.20266

a. Predictors: (Constant), HgbA1cDiff

The value of R-Squared is 0.213; this means that 21.3% of the variation in difference in weight is explained by difference in HgbA1c.

 Model Sum of Squares df Mean Square F Sig. 1 Regression 17.061 1 17.061 3.517 .083b Residual 63.072 13 4.852 Total 80.133 14

a. Dependent Variable: wgtdiff

b. Predictors: (Constant), HgbA1cDiff

 Model Unstandardized Coefficients Standardized Coefficients t Sig. B Std. Error Beta 1 (Constant) -3.874 .590 -6.569 .000 HgbA1cDiff .934 .498 .461 1.875 .083

a. Dependent Variable: wgtdiff

The p-value for the difference in HgbA1c is 0.083 (a value less than 10% level of significance), hence we can say that difference in HgbA1c significantly predicts difference weight at 10% level of significance.

d. The results obtained showed that HgbA1c does not significantly predict weight. This is true even after one year. However, when we obtain the difference in weight and the difference in HgbA1c for the two periods we saw some improvements. The difference in HgbA1c was able to significantly predict the difference in weight though at 10% level of significance. Further investigation should focus on controlling for time and seeing how the results behave.

 BPMeds N Mean Std. Deviation Std. Error Mean age Not on antihypertensive 603 53.9088 8.07358 .32878 On antihypertensive 41 57.6341 5.99481 .93623
 Levene's Test for Equality of Variances t-test for Equality of Means F Sig. t df Sig. (2-tailed) Mean Difference Std. Error Difference 95% Confidence Interval of the Difference Lower Upper age Equal variances assumed 7.330 .007 -2.900 642 .004 -3.7254 1.28470 -6.248 -1.203 Equal variances not assumed -3.754 50.423 .000 -3.7254 .99228 -5.718 -1.733

We performed an independent t-test was in order to compare the average age for those on antihypertensive (BPMEDS = 1) and those not on antihypertensive (BPMEDS = 0). Results showed that the average age for those on antihypertensive (M = 57.63, SD = 5.99, N = 41) was significantly different with the average age (M = 53.90, SD = 8.07, N = 603), t (642) = -2.900, p < .05, two-tailed. Those on antihypertensive were significantly older than those not on antihypertensive.

 BPMeds N Mean Std. Deviation Std. Error Mean sysBP Not on antihypertensive 603 141.6924 25.34485 1.03212 On antihypertensive 41 171.9512 30.08463 4.69843
 Levene's Test for Equality of Variances t-test for Equality of Means F Sig. t df Sig. (2-tailed) Mean Difference Std. Error Difference 95% Confidence Interval of the Difference Lower Upper sysBP Equal variances assumed 2.625 .106 -7.305 642 .000 -30.259 4.14235 -38.393 -22.125 Equal variances not assumed -6.290 43.947 .000 -30.259 4.81046 -39.954 -20.564

We performed an independent t-test was in order to compare the mean systolic BP for those on antihypertensive (BPMEDS = 1) and those not on antihypertensive (BPMEDS = 0). Results showed that the mean systolic BP for those on antihypertensive (M = 171.95, SD = 30.08, N = 41) was significantly different with the mean systolic BP (M = 141.69, SD = 25.34, N = 603), t (642) = -7.305, p < .05, two-tailed. Those on antihypertensive had higher mean systolic BP than those not on antihypertensive.

 BPMeds N Mean Std. Deviation Std. Error Mean diaBP Not on antihypertensive 603 86.2736 13.72689 .55900 On antihypertensive 41 97.3902 14.43542 2.25443
 Levene's Test for Equality of Variances t-test for Equality of Means F Sig. t df Sig. (2-tailed) Mean Difference Std. Error Difference 95% Confidence Interval of the Difference Lower Upper diaBP Equal variances assumed .003 .955 -5.001 642 .000 -11.117 2.22276 -15.481 -6.752 Equal variances not assumed -4.786 45.058 .000 -11.117 2.32270 -15.795 -6.439

We performed an independent t-test was in order to compare the mean diastolic BP for those on antihypertensive (BPMEDS = 1) and those not on antihypertensive (BPMEDS = 0). Results showed that the mean diastolic BP for those on antihypertensive (M = 97.39, SD = 14.44, N = 41) was significantly different with the mean diastolic BP (M = 86.27, SD = 13.73, N = 603), t (642) = -5.001, p < .05, two-tailed. Those on antihypertensive had higher mean diastolic BP than those not on antihypertensive.

 Mean N Std. Deviation Std. Error Mean Pair 1 Initial Weight 151.7000 10 27.42687 8.67314 Final Weight 145.1000 10 24.86162 7.86193
 N Correlation Sig. Pair 1 Initial Weight & Final Weight 10 .980 .000
 Paired Differences t df Sig. (2-tailed) Mean Std. Deviation Std. Error Mean 95% Confidence Interval of the Difference Lower Upper Pair 1 Initial Weight - Final Weight 6.60000 5.81569 1.83908 2.43971 10.76029 3.589 9 .006

A paired-samples t-test was conducted to compare initial weight and final weight of individuals after a weight-loss program. There was a significant difference in the initial weight (M = 151.70, SD = 27.43) and final weight (M = 145.10, SD = 24.86) conditions; t(9) = 3.589, p = 0.006. These results suggest that the weight-loss program really does have an effect weight of individuals. Specifically, our results suggest that before the weight-loss program, the individual’s weight more as compared after the weight loss program.

 Age Levene Statistic df1 df2 Sig. 2.064 2 25 .148
 Age Sum of Squares df Mean Square F Sig. Between Groups 9.254 2 4.627 4.991 .015 Within Groups 23.175 25 .927 Total 32.429 27
 Dependent Variable:   Age Bonferroni (I) Region (J) Region Mean Difference (I-J) Std. Error Sig. 95% Confidence Interval Lower Bound Upper Bound Rural Sub-Urban .27500 .45670 1.000 -.8969 1.4469 Urban -1.02500 .45670 .102 -2.1969 .1469 Sub-Urban Rural -.27500 .45670 1.000 -1.4469 .8969 Urban -1.30000* .43058 .017 -2.4049 -.1951 Urban Rural 1.02500 .45670 .102 -.1469 2.1969 Sub-Urban 1.30000* .43058 .017 .1951 2.4049

The mean difference is significant at the 0.05 level.

First, we checked for the homogeneity of variances where we observed the variances to be homogenous (p = 0.148). For the ANOVA test, results showed that there is significant difference in the mean age at completion of year 7 for at least one region. Post-hoc test using Bonferroni showed that significance difference exists in the mean age at completion of year 7 for the urban and Sub-Urban regions.

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[Accessed 26 May 2024].

My Assignment Help. 'SPSS Analysis: Relationship Between HgbA1c And Weight In Diabetic Boys - Essay.' (My Assignment Help, 2020) <https://myassignmenthelp.com/free-samples/clnr403-biostatistics-and-informatics/modal-summary.html> accessed 26 May 2024.

My Assignment Help. SPSS Analysis: Relationship Between HgbA1c And Weight In Diabetic Boys - Essay. [Internet]. My Assignment Help. 2020 [cited 26 May 2024]. Available from: https://myassignmenthelp.com/free-samples/clnr403-biostatistics-and-informatics/modal-summary.html.

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