Examining the Effectiveness of a Weight-Loss Program

Biostatistics and Informatics
Student Name:
Instructor Name:
Course Number:
19th September 2018
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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.
Answer
Model Summary
Model R R Square Adjusted R
Square
Std. Error of the
Estimate
1 .204a .042 -.032 4.29418
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.
2

ANOVAa
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.
Coefficientsa
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.
b) Repeat the above analysis for HgbA1c one year later. Giving the statistical
evidence, do your conclusions change?
Answer
Model Summary
Model R R Square Adjusted R
Square
Std. Error of the
Estimate
1 .217a .047 -.026 5.76184
a. Predictors: (Constant), HgbA1c_2
3

ANOVAa
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
Coefficientsa
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.
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?
Answer
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