Application of Binary Logistic Regression Model to Assess the Likelihood of Overweight

American Journal of Theoretical and Applied Statistics
2019; 8(1): 18-25
http://www.sciencepublishinggroup.com/j/ajtas
doi: 10.11648/j.ajtas.20190801.13
ISSN: 2326-8999 (Print); ISSN: 2326-9006 (Online)
Application of Binary Logistic Regression Model to Assess
the Likelihood of Overweight
Noora Shrestha
Department of Mathematics and Statistics, P. K. Multiple Campus, Tribhuvan University, Kathmandu, Nepal
Email address:
To cite this article:
Noora Shrestha. Application of Binary Logistic Regression Model to Assess the Likelihood of Overweight. American Journal of Theoretical
and Applied Statistics. Vol. 8, No. 1, 2019, pp. 18-25. doi: 10.11648/j.ajtas.20190801.13
Received: January 19, 2019; Accepted: February 20, 2019; Published: March 6, 2019
Abstract: This study attempts to assess the likelihood of overweight and associated factors among the young students by
analyzing their physical measurements and physical activity index. This paper has classified four hundred and fifteen subjects
and precisely estimated the likelihood of outcome overweight by combining body mass index and CUN-BAE calculated.
Multicollinearity is tested with multiple regression analysis. Box-Tidwell Test is used to check the linearity of the continuous
independent variables and their logit (log odds). The binary regression analysis was executed to determine the influences of
gender, physical activity index, and physical measurements on the likelihood that the subjects fall in overweight category. The
sensitivity and specificity described by the model are 55.9% and 96.9% respectively. The increase in the value of waist to
height ratio and neck circumference and drop in physical activity index are associated with the increased likelihood of subjects
falling to overweight group. The prevalence of overweight is higher (27.8%) in female than in male (14.7%) subjects. The odds
ratio for gender reveals that the likelihood of subjects falling to overweight category is 2.6 times higher in female compared to
male subjects.
Keywords: Overweight, Waist to Height Ratio, Neck Circumference, Binary Logistic Model, Odds Ratio
1. Introduction
Overweight and obesity has become a major public health
problem from the last two decades in the world. The
worldwide problem of overweight and obesity has affected
the individual, family, society, and the nation. The prevalence
of overweight people in 1990 was 8.1% men and 9.4%
women [1]. The prevalence of overweight and obesity in
Nepal has been mounting significantly for the past 26 years.
The proportion of overweight and obesity were 12% and
1.7% respectively in the age group 15 to 29 years for both
genders. The percentage of overweight and obesity in female
(12.3% & 2%) was higher than in male (11.8% &1.5%) on
the basis of Body Mass Index (BMI) [2]. Similar results of
overweight continued in Nepal demographic and health
survey, 2016. This survey observed 22% of female and 17%
of male were overweight (BMI ≥ 25 kg/m2
), at the age group
15-49 years [3].
The prevalence of overweight is different on the basis of
age, sex, and location division of the samples [4]. The
uppermost percentage is observed among women from the
richest families (45%) and from the Province 3, 35% of them
were reported to be overweight or obese. Among men, 28%
at age 30-39 years and 32% from wealthiest families are
more prone to be overweight or obese [5]. The prevalence of
overweight or obesity is also expected to differ by its method
of estimation. There are various ways to measure overweight
or obesity. The field methods are waist circumference, waist
to hip ratio, skinfold thickness, bioelectrical impedance, and
densitometry [6].
The most common method to identify overweight or
obesity is body mass index (BMI), which is cost effective,
easy to calculate, suitable for all age and gender, and very
popular in clinical practices. Nevertheless, BMI has limited
diagnostic performance; it fails to differentiate between body
fat and lean body mass. To overcome this drawback of BMI,
the body fat percentage (%) has to be estimated. The body fat
percentage is a ratio of fat mass to the total body weight
multiplied by 100; body fat includes essential body fat and
storage body fat [7]. There are multiple techniques to
measure body fat such as skin calipers, bioelectrical
impedance, hydrostatic weighing, three dimensional body

American Journal of Theoretical and Applied Statistics 2019; 8(1): 18-25 19
scan, and dual energy x-ray absorptiometry [8]. The previous
studies show that there is no specific cutoff point of obesity
or overweight for Asian young adult group as it differs with
various factors and this group has lower BMI but higher body
fat percentage [9].
To succeed in dealing with limitation of BMI for
categorization, this paper has combined the value of BMI and
body fat percentage to classify the subject in overweight or
no overweight group and further precisely estimate the
likelihood of overweight [10].
The several research studies have mentioned that
overweight and obesity are major reasons of co-morbidities,
diabetes, heart disease, cancer, and other health problems.
The related health care cost is also a significant factor. The
urban lifestyle, overreliance on technology, and less focus on
physical activities bring health related problems such as
overweight or obesity among the young students [10-11].
This raises the question about prevalence and contributing
factors about overweight using simple and cost effective
screening method in young students.
With the consideration of this fact, the present paper
attempts to assess the likelihood of overweight and its
associated factors among the young students by applying
binary logistic regression model.
2. Materials and Methods
The analysis and discussion of this paper were based on
the output of statistical analysis performed by using IBM
SPSS 23 for Windows. The study protocol was approved by
the ethical and research committee of the Dayananda Anglo
Vedic College, Bhanimandal, Nepal. This is a cross sectional
study conducted over a period of three months (June to
August) in 2018. The sample consisted of four hundred and
fifteen subjects (170 Male and 245 Female) that had been
obtained using convenience sampling method. The subjects
with the written consent, residing in the same urban area, not
having serious health issues, studying in bachelor’s level, and
an age from eighteen to twenty three years were inclusionary
criteria.
2.1. Measurements and Variables
For all the subjects, the physical measurements were
recorded by the researcher to negate any inter observer
variability. The explanatory variables height, weight, neck
circumference, waist circumference and hip circumference
were measured by the researcher on the basis of the report of
WHO expert consultation [8]. Body Mass Index (BMI) was
calculated dividing weight in kg by height in m2
. The
subjects were asked to fill a form that includes the activities
for intensity, duration, and frequency of physical activity. The
physical activity score was calculated by finding the product
of intensity, duration and frequency of activity. The physical
activity index (PAI) was categorized into high, very good,
fair and poor [8, 12].
The measurement of body fat percentage (BF%) using
sophisticated equipment was restricted for the subjects under
study. Thus, this study had calculated BF% using equation of
Clinica Universidad de Navarra- Body Adiposity Estimator
(CUN-BAE). The researchers claimed that CUN-BAE has
validated an easy to apply projecting equation, which may be
applied as a primary screening tool in clinical practice.
Body Fat % = − 44.988 + (0.503 × age) + (10.689 × sex) +
(3.172 × BMI) - (0.026 × BMI2
) + (0.181 × BMI × sex) -
(0.02 × BMI × age) - (0.005 × BMI2
× sex) + (0.00021 ×
BMI2
× age), where, BMI = body mass index, male = 0 and
female = 1 for sex and age in years [13-14].
This study considered a dichotomous outcome variable
overweight or no overweight. To improve the classification
of subjects and more specifically estimate the likelihood of
overweight, BMI, and BF% were combined. The female
subjects whose BMI ≥ 25 kg/m2
correspond to body fat >
32% were classified into overweight group and BMI < 25
kg/m2
correspond to body fat ≤ 32% were classified into no
overweight group. Considering BMI ≥ 25 kg/m2
correspond
to body fat > 23%, the male subjects were classified into
overweight group and BMI < 25 kg/m2
correspond to body
fat ≤ 23% were classified into no overweight group [10, 15,
16].
2.2. Statistical Analysis
Pearson's correlation coefficient was used to determine the
relationship between BMI and BF% with the continuous
explanatory variables. The association between the outcome
variable overweight/ no overweight and categorical
independent variables was examined using Pearson Chi
Square test. Phi and Cramer’s V tests were used to test the
strength of association between the variables. The prevalence
of overweight was calculated as dividing the number of
subjects who was classified in overweight (or no overweight)
by the number of subjects in whom it was measured, and
expressed as a percentage. To check the linearity of the
continuous independent variables and the logit (log odds)
transformation, Box- Tidwell Test was used. Multiple
regression model was applied to test the multicollinearity of
the variables [17-18].
A binary logistic regression analysis has been applied to
predict the likelihood that a subject falls into any one of the
two groups of a dichotomous dependent variable (overweight
or no overweight) based on the independent variables that
were continuous, and categorical. The reasons for selecting
this model were i) it is particularly flexible and ii) gives
momentous interpretation in health studies [19-20].
Let us assume that a sample of n independent observations
of the pair (xi, yi), i = 1,2,….n. The probability distribution of
the outcome variable is Binomial i.e. yi ~ Bin (ni, π(xi))
where, yi denote the value of a dichotomous response
variable, and xi denotes the value of the independent variable
for the ith
subject.
Now,
y =
1, if the subject is overweight
0, Otherwise

20 Noora Shrestha: Application of Binary Logistic Regression Model to Assess the Likelihood of Overweight
Let us consider the conditional mean, as π(x), the expected
value of y given the value of x in logistic regression:
π x =
!"
#$ !" (1)
To fit the logistic regression model in equation (1) to a set
of data, the unknown parameters β0 and β1 have to be
estimated and for dichotomous data, 0 ≤ π(x) ≤1. The binary
regression model intends to predict the logit, which is the
natural log of the odds of subjects to be overweight or no
overweight with predictors such as gender, physical
measurement, and physical activity index. The term logit
transformation in this model is the transformation of π(x)
which is defined as:
logit π x = ln '
( )
#*( )
+ = β- + β#x (2)
Here, π(x) is the predicted probability of the event which
is coded with “1” overweight rather than “0” no overweight.
1- π(x) is the predicted probability of the other decision and x
is the independent variable. The logit value may be
continuous and range from -∞ to +∞. The expression for π(x)
in equation (1) provides the conditional probability P (Y=1|x)
and the term 1- π(x) gives the conditional probability P(Y=
0|x) for an arbitrary parameter β = β0 and β1, the vector
parameters. For those pairs (xi, yi), if yi = 1, the contribution
to the likelihood function is π(xi), and if yi = 0, it is 1- π(xi);
where π(xi) is the value of π(x) computed at xi [21]. It can be
expressed as:
/ 01
2341 − / 01 6#*23 (3)
For logistic regression, the observations are assumed to be
independent, so the likelihood function is obtained as
follows:
l β = ∏ π x 89:
;# 41 − π x 6#*89 (4)
For ease of mathematical calculations, log of equation (4),
log likelihood, can be written as:
L β = ln4l β 6 = ∑ {y ln4π x 6 +:
;# 1 − y ln41 −
π x 6} (5)
Differentiating equation (5) with respect to β0 and β1 for
maximizing likelihood function, L (β) and solving for β we
get the two likelihood equations as:
∑4y − π x 6 = 0 (6)
∑ x 4y − π x 6 = 0 (7)
For binary logistic regression the terms in equations (6)
and (7) are non linear in β0 and β1, and hence require iterative
methods for solution which is obtained by using an iterative
weighted least square technique. Then, the value of
maximum likelihood estimate @A will be obtained [22]. In the
present study, there is few major independent variables such
as gender, physical measurement, physical activity index for
which the expression of binary logistics regression model (i=
1,2,…, n subjects) is given by
ln '
( )9
#*( )9
+ = β- + β#x # + βBx B + ⋯ β:x : (8)
Here, xi1, xi2. ….xin are categorical or continuous
independent variables [23]. From equation (8), the equation
for the prediction of the probability can be derived and
solved the logit equation for π(xi) to obtain
π x =
e D $D!)9!$DE)9E$⋯DF)9F
1 + e D $D!)9!$DE)9E$⋯DF)9F
3. Results and Discussions
For the exposure of multicollinearity, the Pearson’s
correlation coefficients (r) between each pair of continuous
independent variables are observed in Table 1. It is assumed
that there is no multicollinearity because there is no high
degree of correlation among the independent variables.
Nevertheless, the correlation coefficient value between the
independent variables may be deliberated as the sufficient,
but not the necessary condition for the multicollinearity [24].
Table 1 shows the coefficient of determination (R2
) value
calculated for the pairwise independent variables waist to hip
ratio (whr), neck circumference (nc), physical activity index
(PAI), and waist to height ratio (whtr). The R2
values of each
combination of independent variables may deliver the
noticeable indication for the presence of multicollinearity.
The value of R2
is low for the pairs that show there is less
chance of presence of multicollinearity but this cannot be
pondered as the best test for perceiving multicollinerity.
In case of female subjects, it has been observed that there
is positive and significant relationship between BMI and
independent variables namely neck circumference, waist to
hip ratio, waist to height ratio with p < 0.01. There is
significant negative correlation between BMI and physical
activity index. Similarly, BF% is significantly and positively
correlated with all these independent variables and negatively
correlated with physical activity index at the p < 0.01 level.
Regarding male subjects, there is significant and positive
correlation between BMI and variables neck circumference
and waist to height ratio but waist to hip ratio is not
significantly correlated with BMI. There is negative
correlation between physical activity index and BMI.
Similarly, BF% is positively and significantly correlated with
nc, whtr but negatively correlated with PAI at the 0.01 level.
There is no relationship between BF% and waist to hip ratio.
For both gender, there is high degree of positive and
significant correlation between projected output variables
BMI and BF% with p < 0.01.

Table 1. Result of Pearson’s Correlation.
Variables
BMI BF%
Female Male Female Male
r R2
r R2
r R2
r R2
whr 0.324 0.105 0.026+
0.00067 0.338 0.114 0.018+
0.00033
nc 0.457 0.209 0.168 0.028 0.375 0.141 0.166 0.028
whtr 0.658 0.433 0.488 0.238 0.641 0.411 0.483 0.233
PAI -0.32 0.106 -0.31 0.101 -0.28 0.079 -0.309 0.095
BMI 1 1 1 1 0.911 0.83 0.998 0.996
BF% 0.911 0.83 0.998 0.996 1 1 1 1
Correlation is significant at the 0.01 level (2-tailed)
whr- waist to hip ratio, nc- Neck Circumference, whtr- waist to height ratio, PAI- Physical activity index, BMI- Body mass index, BF%- Body fat percentage,
+ Correlation is not significant
Table 2 presents the dichotomous categorical variables that are obtained by classification of subjects on the basis of the
measurements [8]. The Chi Square test in table 2 demonstrates that there is statistically significant association between weight
status category of female and the categorical variables whr_cat, nc_cat, and whtr_cat with p = 0.0001. Phi and Cramer’s V tests
depict that the strength of association between the variables is very strong in female subjects (p = 0.0001).
Table 2. Result of Chi Square Test.
Categorical
Variables
Gender Category
Weight Status Category
Pearson Chi-
Square (p value)
Phi and Cramer’s
V(p value)
No Overweight Overweight
n, % n, %
Waist to hip ratio
(whr_cat)
Female
No Risk 168, 80.4% 41, 19.6%
0.000
Risk (≥ 0.85) 9, 25% 27, 75% 0.000
Male
No Risk 122, 88.4% 16, 11.6%
0.026
0.017
Risk (≥ 0.90) 23, 71.9% 9, 28.1%
Neck Circumference
(nc_cat)
Female
No Overweight 161, 85.6% 27, 14.4%
0.000
Overweight (≥ 34 cm) 16, 28.1% 41, 71.9% 0.000
Male
No Overweight 113, 86.3% 18, 13.7%
0.606
Overweight (≥ 37 cm) 32, 82.1% 7, 17.9% 0.515
Waist to height ratio
(whtr_cat)
Female
No Overweight 155, 88.1% 21, 11.9%
0.000
Overweight (≥ 0.49) 22, 31.9% 47, 68.1% 0.000
Male
No Overweight 136, 89.5% 16, 10.5%
0.000
0.000
Overweight (≥ 0.53) 9, 50% 9, 50%
Gender
Female 177, 72.2% 68, 27.8%
0.002 0.002
Male 145, 85.3% 25, 14.7%
In case of male subjects, Chi Square test and Phi &
Cramer’s V tests reveal that there is statistically significant
and very strong association between weight status category
and the categorical variables based on waist to hip ratio and
waist to height ratio with p = 0.0001. The strength of
association is very weak between weight status category and
neck circumference category in male subjects with p > 0.05.
The strength of association between weight status category
and gender is statistically significant and very strong with p =
0.002.
Table 3 illustrates the output of multiple regression model,
which has been used to further test the multicollinearity
among the independent variables. In multiple regression,
multicollinearity can be identified by two collinearity
diagnostic factors; tolerance and variance inflation factor
(VIF). Regarding tolerance, all the independent variables
have more than 0.1 tolerance value in the output of
coefficients. The VIF values are also less than 10, which
indicate that there is no presence of multicollinearity in the
model. Similar results obtained when outcome variable is
changed in multiple regression model such as BF%.
Table 3. Result of Multiple Regression Analysis.
Coefficients a
Model 1
Unstandardized Coefficients Standardized Coefficients
t Sig.
Collinearity Statistics
B Std. Error Beta Tolerance VIF
(Constant) -.399 1.635 - .244 .807
nc .281 .046 .197 6.116 .000 .825 1.212
whtr 21.13 2.202 .325 9.599 .000 .749 1.335
PAI -.488 .137 - .109 -3.566 .000 .917 1.090
BF .218 .013 .546 16.800 .000 .810 1.234
a. Dependent Variable: BMI
Some assumptions have been made to fit the binary logistic regression model and for the validity of the outcome

result of the model.
(1) The categorical dependent variable has been measured
on dichotomous scale using “0” for no overweight and
“1” for overweight.
(2) The independent variables are continuous and
categorical and not necessarily linearly related with
dependent variable. This can be witnessed by multiple
regression table 3.
(3) There is independence of observations. The
independent variables are not highly correlated with
each other. This can be observed by Pearson’s
correlation in table 1.
(4) There is a linear association between the continuous
independent variables and their logit (log odds). This
can be noticed by result of Box- Tidwell test in table 4.
Table 4 demonstrates the output of Box–Tidwell Test,
which has been used to test the assumption of linearity of the
continuous variables. Before using binary logistic regression
model, it is assumed that the relationship between the
continuous independent variables and the logit (log odds) is
linear. This assumption is tested, by entering interactions
between the continuous independent variables and their logs
in the model. The interaction terms nc by nc_LN and PAI by
PAI_LN are not significant (p = 0.481 and p = 0.581). It
means there is linear association between the continuous
independent variables neck circumference and physical
activity index and the logit (log odds) with the outcome
variable weight status category. Finally, waist to height ratio,
neck circumference, physical activity index, and gender are
selected as the suitable explanatory variables with outcome
variable weight status category for the binary logistic
regression model. Furthermore, the outputs of the binary
logistic regression model are discussed.
Table 4. Result of Box – Tidwell Test.
B S.E. Wald df Sig. Exp(B)
Step 1a
Gender (1) 1.820 .375 23.554 1 .000 6.173
nc 5.447 7.120 .585 1 .444 232.092
nc by nc_LN -1.106 1.571 .496 1 .481 .331
PAI - .697 2.175 .103 1 .748 .498
PAI by PAI_LN - .234 .425 .304 1 .581 .791
Constant - 51.211 53.613 .912 1 .339 .000
a. Variables(s) entered on step 1: Gender, nc, nc *nc_LN, PAI, PAI*PAI_LN
Table 5 displays the output where 415 selected cases used in the analysis and no missing cases. There are two decision
options, majority 322/415 = 77.6% subjects are in no overweight group, coded as “0” whereas, 93/415 = 22.4% cases are
considered as overweight coded as “1”.
Table 5. Classification Tablea, b
.
Observed
Predicted
Percentage
Correct
Step 0
Weight Status Category No Overweight 322 0 100.0
Overweight 93 0 .0
Overall Percentage 77.6
Constant is included in the model.
The cut value is .500
Table 6 presents, Block 0: beginning block output
variables in the equation, the intercept or constant only model
which is ln(odds) = -1.242. By exponentiation on both sides
of this expression, the predicted odds [Exp(B)] = Exp (-
1.242) = 0.289. It means the predicted odds of overweight
subjects are 0.289. Since 93 subjects are overweight and 322
subjects are no overweight, the observed odds are 93/322 =
0.289. In this output, the other variables are not in the
equation.
Table 6. Variables in the Equation.
B S.E. Wald Df Sig. Exp(B)
Step 0 Constant -1.242 0.118 111.3 1 .000 .289
Table 7 reports the result of an Omnibus test of model
coefficients and demonstrates a Chi- square value of 188.863
on 4 degrees of freedom (df), significant at 0.0001. In Block
1: Method = enter output, the variables gender, neck
circumference, waist to height ratio, and physical activity
index are added as predictors. It shows a test of null
hypothesis that adding the variables to the model has not
significantly increased the ability to predict the weight status
of the study subjects.
Table 7. Omnibus Tests of Model Coefficients.
Chi-square df Sig.
Step 1
Step 188.863 4 .000
Block 188.863 4 .000
Model 188.863 4 .000

The output table 8 Model Summary presents the variation
in the outcome variable weight status category explained by
the independent variables with Cox and Snell R2
and
Nagelkerke R2
(Pseudo R2
) values. The Cox & Snell R2
=
0.366 shows 36.6% variation in outcome variable weight
status category is explained by the predictors but the
remaining 63.4% is unexplained. These R2
values
demonstrate the explained variation in the outcome variable
weight status category, by set of variables, ranges from
36.6% (Cox and Snell R2
) to 55.8% (Nagelkerke R2
). It also
exhibits the -2 Log Likelihood statistic as 252.733. It
measures how poorly the model predicts the decision; the
smaller the statistic the better the model is. The block 0
model has the intercept 441.596. Adding variables to the
model, the statistic -2 Log Likelihood is reduced by 441.596
– 252.733 = 188.863, which is Chi- square statistic.
Table 8. Model Summary.
Step -2 Log likelihood Cox & Snell R2 Nagelkerke R2
1 252.733a
.366 .558
a. Estimation terminated at iteration number 6 because parameter estimates
changed by less than .001.
Table 9 presents the Hosmer-Lemeshow test, which tests
the null hypothesis that the predictions made by the model fit
absolutely with observed group memberships. A chi square
statistic (8.389, d.f. = 8) was computed comparing the
observed frequencies with those expected under the linear
model. It shows the non-significant Chi Square value and
indicates the model is good fit of data.
Table 9. Hosmer and Lemeshow Test.
Step Chi-square df Sig.
1 8.389 8 .396
Table 10 demonstrates the result of classification of
subjects. Unlike multiple regression, binary regression model
estimates the probability of a subject falling in an overweight
or no overweight group. The cut value in the classification
table is 0.5. The output classification table presents the
grouping of the subject as overweight, if the projected
probability of the event happening is ≥ 0.5. If the probability
of the event of occurring is < 0.5, the subject is classified as
no overweight. In the classification table, it can be observed
that the overall success rate of the model has increased from
77.6% in block 0 to 87.7% in block 1.
Table 10. Classification Tablea
.
Observed
Predicted
Percentage Correct
Step 1
No Overweight 312 10 96.9
Overweight 41 52 55.9
Overall Percentage 87.7
a. The cut value is .500
The classification table 10 shows the percentage accuracy
in classification is 87.7%. In addition, this value shows that
87.7% of cases are correctly classified as no overweight from
the added independent variables.
The sensitivity = P (correct prediction| event did occur)=
52/93 = 55.9% or true positive value is the percentage of
cases that had overweight and were acceptably anticipated by
the model.
The specificity = P (correct prediction | event did not
occur)= 312/322 = 96.9% or true negative value is the
percentage of cases that did not have overweight and were
appropriately projected as no overweight cases.
The false positive value = P (incorrect prediction| predicted
occurrence) = 10/62 = 16.1% is the percentage of suitably
expected cases with the detected feature of no overweight
compared to the total number of cases predicted as
overweight.
The false negative value = P (incorrect prediction|
predicted non-occurrence) = 41/353 = 11.6% is the
percentage of accurately forecasted cases without the
detected feature of overweight compared to the total number
of cases forecasted as no overweight. False negative rate tells
the subjects predicted as no overweight but actually, they do
have overweight.
Table 11 illustrates the influence of each predictor variable
to the logistic model and statistical significance (p < 0.05) of
Wald Chi Square test, which is obtained by squaring the ratio
of coefficient to its standard error.
Table 11. Parameter Estimates Table.
B S.E. Wald df Sig. Exp(B)
95% C.I.for EXP(B)
Lower Upper
Step 1a
Gender (1) .958 .394 5.906 1 .015 2.606 1.204 5.641
nc .287 .083 11.865 1 .001 1.333 1.132 1.569
whtr_cat(1) -2.495 .380 43.050 1 .000 .082 .039 .174
PAI -2.177 .323 45.556 1 .000 .113 .060 .213
Constant - 4.132 3.085 1.793 1 .181 .016
a. Variable(s) entered on step 1: Gender, nc, whtr_cat, PAI.

Wald Statistics tests the unique contribution of each
independent variable, in the context of the other variables
with significance values. The categorical variables gender (1)
(p = 0.015), whtr_cat (p = 0.0001) and the continuous
variables nc (p = 0.001) and PAI (p = 0.0001) have added
significant contribution to the model.
Hence, the binary logistic regression function is given by
ln(odds) = − 4.132 + 0.958 (gender ) + 0.287 (nc) – 2.495
(whtr_cat) − 2.177 (PAI).
The odds prediction equation is
Odds = e (− 4.132 + 0.958 (gender) + 0.287 (nc) – 2.495 (whtr_cat) − 2.177(PAI).
This function can be used to predict the odds that a subject
of a given gender, nc, whtr_cat and PAI will be overweight.
Effect of neck circumference is smaller, with a one-unit
increase on the neck circumference being associated with the
odds of subjects falling in the overweight group increasing
by a multiplicative factor of 1.333. Inverted odds ratios for
the whtr_cat variable indicated that the odds of falling in
overweight group were 12.19 times higher for the subjects
classified in overweight group of waist to height ratio.
Inverting the odds ratio 0.113 for physical activity index
shows that for one unit increase in the PAI value there was
8.85 of the odds that the subject would not fall in the
category of overweight. Female subjects are 2.6 times more
likely to be overweight than males. The odds of falling in
overweight group, is 0.384 times lower in male as opposed to
female subjects. By converting odds to probabilities, for
female, odds / (1+ odds) = 2.6/3.6 = 0.722. It means the
model predicts that 72.2% of female will be in the category
of no overweight and 27.8% of them will be overweight. In
overweight group, 14.7% of male subjects are classified and
85.3% are grouped into no overweight.
4. Conclusion
The present study has used meaningful statistical tools to
identify the association of significant variables with the
overweight of the subjects. The binary logistic regression
analysis was performed to determine the effects of gender,
neck circumference, waist to height ratio, and physical
activity index on the likelihood that subjects have
overweight. The model was statistically significant based
on Chi square =188.863, p < 0.0001 with d.f. 4. The model
explained 55.8% (Nagelkerke R2
) of the variance in the
overweight and correctly classified 87.7% of cases. The
odds ratio for gender indicates that when holding all other
variables constant, female subjects were 2.6 times more
likely to demonstrate overweight than males. The subjects
classified to no overweight group based on waist to height
ratio were associated with a reduction in the likelihood of
falling to overweight group. The increment in the value of
neck circumference was associated with an increased
likelihood of falling to overweight category of subjects, but
increasing physical activity index was related with a
reduction in the likelihood of falling to overweight group.
Hence, the prevalence of overweight for both subjects is
22.4%. The prevalence of overweight is higher in female
(27.8%) than in male (14.7%) subjects, which is consistent
with the result of previous studies [2, 3]. It is very
important for each individual to focus on the food intake
pattern, physical activity, lifestyle, and also their physical
measurements. The awareness about the importance of
physical activities and measurement of neck circumference
and waist to height ratio to live a healthy life should be
communicated among the young students. Further research
can be carried out by taking into account significant risk
factors associated with the overweight of a person.
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