Regression analysis of HgbA1c and weight at baseline
1. A group of 10yearold 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 onesentence 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 followup, and HgbA1cDiff = HgbA1c_2 – HgbA1c_1, which measures the change in HgbA1c from baseline to one year followup. 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 12 sentences.
3. A nutrition expert is examining a weightloss 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 1sentence 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 12 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 
.204^{a} 
.042 
.032 
4.29418 
Regression analysis of HgbA1c and weight at baseline
a. Predictors: (Constant), HgbA1c_1
The value of RSquared 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 
.465^{b} 
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 pvalue 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 
.217^{a} 
.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 
.436^{b} 
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 pvalue 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 
.461^{a} 
.213 
.152 
2.20266 
a. Predictors: (Constant), HgbA1cDiff
The value of RSquared 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 
.083^{b} 
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 pvalue 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 
ttest for Equality of Means 

F 
Sig. 
t 
df 
Sig. (2tailed) 
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 ttest 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, twotailed. 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 
ttest for Equality of Means 

F 
Sig. 
t 
df 
Sig. (2tailed) 
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 ttest 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, twotailed. 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 
ttest for Equality of Means 

F 
Sig. 
t 
df 
Sig. (2tailed) 
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 ttest 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, twotailed. 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. (2tailed) 

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 pairedsamples ttest was conducted to compare initial weight and final weight of individuals after a weightloss 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 weightloss program really does have an effect weight of individuals. Specifically, our results suggest that before the weightloss 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 (IJ) 
Std. Error 
Sig. 
95% Confidence Interval 

Lower Bound 
Upper Bound 

Rural 
SubUrban 
.27500 
.45670 
1.000 
.8969 
1.4469 
Urban 
1.02500 
.45670 
.102 
2.1969 
.1469 

SubUrban 
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 
SubUrban 
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. Posthoc test using Bonferroni showed that significance difference exists in the mean age at completion of year 7 for the urban and SubUrban regions.
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