Introduction of Public Officials, Health Specialists, And Researchers

Public officials, health specialists, and researchers have long agreed on that increased exercise level is related negatively with weight or body fat. The relationships have confirmed by various empirical studies. The relationship between body mass index and physical activity has been derived from an assumption that energy intake of person with normal weight is nearly or exactly equal to his or her energy expenditure (Calvo). It means that person becomes obese or overweight if his or her energy intake is more than the energy expenditures and getting rid of extra calories helps to maintain the energy balance by performing physical activity. There are various statistical models that best describe the relationship between body fat and physical activity (Ferrera). A person with high body mass might be weak in physical activities. This paper attempts to analyse the relationship between BMI (Body Mass Index) and ACT (Physical Activity) using fixed effects model.

Methodology on Public officials, health specialists, and researchers

This paper is based on secondary data analysis using quantitative research technique. The data is provided by the instructor which contains data on two repeated measures: body mass index, BMI, measured at the start of each week; and the number of hours of undertaking physical activity in each week, ACT, as recorded by a wearable actigraphy device. These measures are taken on four separate weeks approximately four months apart, spanning a year of life amongst adolescents aged 14 to 16 years.

Repeated observations are stored by many datasets on the subject sample just like the given dataset on BMI (Body Mass Index) and physical activity (ACT). However, it is expected that mixed observations are encoded in separate rows from the subject i.e. BMI and ACT. The given data encode four repeated measurements of physical activities i.e. dependent variable (ACT1, ACT2, ACT3, and ACT4) from the subject observed at different BMI (BMI1, BMI2, BMI3, and BMI4). The data is prepared for Mixed in SPSS and the codes are presented in the appendix. There are three cases for each subject (Allison, Fixed Effects Regression Methods for Longitudinal Data Using SAS). A new variable is created named as Index1 having four new cases within the variable subject.

Fixed effects model is most suitable model for this data. In the given data, categorical variables are subject and effect of individual specific is correlated with physical activity. Since the entities of the group in given data are unique and focus of inference should be on these group, the fixed effects model seems to be best for this analysis. Fixed effects model is more robust in order to measure or analyse the within-group effects and between group differences are suspicious in the given data (Allison, Fixed Effects Regression Models).

Fixed Effects Models with the iid residual errors

The form of fitted model as:

In above equation, y represents vector of responses, X represents fixed effects design matrix, β represents fixed effects parameters’ vector, and ℇ represents vector of residual errors. In the given model, ℇ is assumed as distributed as  where R represents unknown covariance matrix.  is a common belief. With this assumption, mixed or GLM can be used to fit model. Using a growth study dataset’s subset, it is illustrated that how Mixed can be used to fit the fixed effects model. The command is given in appendix that fits the model of fixed effects to investigate the effects of BMI on ACT, that is growth rate measure. Before performing fixed effect test, following tests are performed on the data. The analysis and discussion is provided in the next section of paper.

Analysis and Discussion of Public officials, health specialists, and researchers

In the given data, ACT is equals to Y and BMI is equals to X.

Correlation Test of Public officials, health specialists, and researchers

Correlations
		ACT	BMI
ACT	Pearson Correlation	1	.056*
	Sig. (2-tailed)		.025
	N	1600	1600
BMI	Pearson Correlation	.056*	1
	Sig. (2-tailed)	.025
	N	1600	1600
*. Correlation is significant at the 0.05 level (2-tailed).

 

Interpretation: The table shows the correlation among ACT and BMI, Pearson correlation is performed; it can be seen in above table correlation between ACT and BMI is positive. The correlation of ACT on BMI and BMI on ACT is around 5%.

 

Case Processing Summary
	Cases
	Valid		Missing		Total
	N	Percent	N	Percent	N	Percent
ACT	1600	100.0%	0	0.0%	1600	100.0%
BMI	1600	100.0%	0	0.0%	1600	100.0%

 

Interpretation: The above table shows the processing summary of case that shows total 1600 observations are entered and there are no missing values.

 

Descriptives
			Statistic	Std. Error
ACT	Mean		7.9798	.04833
	95% Confidence Interval for Mean	Lower Bound	7.8850
		Upper Bound	8.0746
	5% Trimmed Mean		7.9878
	Median		8.0182
	Variance		3.737
	Std. Deviation		1.93313
	Minimum		2.38
	Maximum		13.33
	Range		10.95
	Interquartile Range		2.67
	Skewness		-.039	.061
	Kurtosis		-.297	.122
BMI	Mean		9.7531	.04679
	95% Confidence Interval for Mean	Lower Bound	9.6614
		Upper Bound	9.8449
	5% Trimmed Mean		9.7361
	Median		9.6294
	Variance		3.503
	Std. Deviation		1.87151
	Minimum		4.41
	Maximum		15.63
	Range		11.22
	Interquartile Range		2.63
	Skewness		.138	.061
	Kurtosis		-.294	.122

 

Interpretation: The above table represents the summary statistics of ACT and BMI. The mean value of ACT is lower than BMI i.e. 7.9798 and 9.7531 respectively while standard deviation of ACT is higher than BMI i.e. 1.93313 and 1.87151 respectively. Standard error of ACT is a little bit higher than BMI i.e. .04833 and .04679 respectively. Standard error of skewness and kurtosis is same for both ACT and BMI i.e. .061 and .122 respectively.

 

Tests of Normality of Public officials, health specialists, and researchers
	Kolmogorov-Smirnova			Shapiro-Wilk
	Statistic	df	Sig.	Statistic	df	Sig.
ACT	.015	1600	.200*	.998	1600	.047
BMI	.027	1600	.008	.997	1600	.002
*. This is a lower bound of the true significance.
a. Lilliefors Significance Correction

 

Interpretation: In above table, normality test is performed in data to determine either ACT and BMI follow the normal distribution or not. The p-values in above table can be compared to the level of significance. According to Lilliefors Significance Correction, ACT does not follow normal distribution because the significance level is higher than 5% while BMI follows the normal distribution because the level of significance is less than 5%. On the other hand, according to Shapiro-Wilk, both ACT and BMI follows the normal distribution. Hence, it is concluded that the data in ACT and BMI follows the normal distribution.

Graphical Demonstration of Public officials, health specialists, and researchers

Following are the graphical representation of both variables i.e. BMI and ACT consisting on histogram, normality test, detrented normality, and observed values.

          

Tests of Between-Subjects Effects
Dependent Variable:   ACT
Source		Type III Sum of Squares	df	Mean Square	F	Sig.
Intercept	Hypothesis	1584.129	1	1584.129	856.910	.000
	Error	2299.860	1244.073	1.849a
BMI	Hypothesis	244.265	1	244.265	133.298	.000
	Error	2195.308	1198	1.832b
Index1	Hypothesis	1106.330	1	1106.330	603.734	.000
	Error	2195.308	1198	1.832b
Sex	Hypothesis	.000	0	.	.	.
	Error	.	.	.c
ID	Hypothesis	1336.491	398	.	.	.
	Error	.	.	.c
Sex * ID	Hypothesis	.000	0	.	.	.
	Error	.	.	.c
a. .011 MS(ID) + .989 MS(Error)
b.  MS(Error)
c. Cannot compute the appropriate error term using Satterthwaite's method.

In above table, Type III test is produced that shows BMI is significant at a 0.05 level which means that BMI is potentially an important variable of the physical activities. The significance value of intercept, BMI, and index1 is 0.000 that shows all of these significantly contributed to physical activity. The positive value of BMI shows its positive contribution towards physical activity.

Expected Mean Squaresa,b
Source	Variance Component
	Var(ID)	Var(Sex * ID)	Var(Error)	Quadratic Term
Intercept	.042	.042	1.000	Intercept, Sex
BMI	.000	.000	1.000	BMI
Index1	.000	.000	1.000	Index1
Sex	.000	.000	.000
ID	3.993	3.993	1.000
Sex * ID	.000	.000	.000
Error	.000	.000	1.000
a. For each source, the expected mean square equals the sum of the coefficients in the cells times the variance components, plus a quadratic term involving effects in the Quadratic Term cell.
b. Expected Mean Squares are based on the Type III Sums of Squares.

 Conclusion of Public officials, health specialists, and researchers

In a nutshell, the analysis of this paper is based on the relationship between BMI (Body Mass Index) and ACT (Physical Activity) using fixed effects model. The relationship between body mass index and physical activity has been derived from an assumption that energy intake of person with normal weight is nearly or exactly equal to his or her energy expenditure. This paper is based on secondary data analysis using quantitative research technique. In methodology section. The data is prepared for Mixed in SPSS and the codes are presented in the appendix. There are three cases for each subject. A new variable is created named as Index1 having four new cases within the variable subject. Fixed effects model is performed on the data because it is most suitable model for this data. In the given data, categorical variables are subject and effect of individual specific is correlated with physical activity. The analysis has shown that correlation between ACT and BMI is positive and data in ACT and BMI follows the normal distribution. Last but not least, the significance value of intercept, BMI, and index1 is 0.000 that shows all of these significantly contributed to physical activity. The positive value of BMI shows its positive contribution towards physical activity.

References on Public officials, health specialists, and researchers

Allison, Paul D. Fixed Effects Regression Methods for Longitudinal Data Using SAS. SAS Institute, 2005.

—. Fixed Effects Regression Models. SAGE Publications, 2009.

Calvo, Stephanie Ngirchoimei. A Descriptive Study of Physical Activity and Body Mass Index in Palauan Adolescents. University of Hawaii at Manoa, 2006.

Ferrera, Linda A. Body Mass Index: New Research. Nova Publishers, 2005.

 Appendix