The study focuses on application of regression in weight management. It assess the relationship between calorie intake and exercise among children. The motivation for the study is to find out whether behavioral changes can be effective in weight management. It is argued that calorie intake from food and exercise influence weight. We get calories from food which is used by our bodies. If the calories are more than what we need it is stored in the body which causes weight gain. Exercise expends the calories thus preventing weight gain in the process. Studies have shown that height is also a genetic determinant of weight. Sargent looked at the relationship between height and weight among college students. The study showed a positive relationship between weight and height . There was an increase in weight by one kilogram for every additional inch if height. Therefore, height was also included. In this study, we use survey data for a sample of 40 teens to build a model for weight. Weight is the dependent variable. The independent variables are height, exercise and calorie intake.
The Data
Secondary data was not readily available for the study. Therefore, a survey was done to collect the data that was required. The population of interest was all teenagers between 10 and 15 years. A sample of 40 teenagers from one school was selected. Data was collected from the teenagers using interviews. Their weight and height was first measured. The weight was measured using a weighing scale in kilograms. It was rounded up to the nearest kilogram. The height was measured using a tape measure in centimeters. It was rounded up to the nearest centimeter to avoid decimal points. After that, they were asked about how minutes do they exercise on average on a normal day. Additional questions were asked to assess the accuracy. They were also asked what they ate from the time they woke up until the time they slept on a normal day. A standard calorie chart for various foods was then used to estimate the calories that they consumed. The table below shows the dataset that was used.
A Model for Average Weight
As discussed, this study uses the following model to explain the average weight of teenagers:
E(y) = β0 + β1x1 + β2x2 + β3x3
The model assumes a linear relationship between the average weight and each of the independent variables.
The model fit for the data from the table resulting in the excel printout. The results can be interpreted as follows:
Global F = 57.02 (p-value = 9.3931E-14). At all significance level α > .0001, null hypothesis is rejected: H0:β1 = β2 = β3 = 0. We conclude sufficient evidence is available that shows that the model is statistically relevant for predicting the average weight, y.
R2 = .8116: After adjusting for sample size, the number of independent variables in the model explain approximately 81% of the sample variation in weight.
S = 3.26: Approximately 95 percent of the actual weight for the teenagers between 10 and 15 years will be within 2S = 6.62 kilograms of the values predicted by the model.
β1 = .189: Holding exercise (x2) and calorie intake per day (x3) constant, we estimate the weight of a teenager (y) to increase by 0.189 for every 1 centimeter increase in height(x1).
β2 =-0.035: Holding height (x1) and calorie intake per day (x3) constant, we estimate the weight of a teenager (y) to decrease by -0.035 for every 1 minute of exercise per day (x2).
Β3 =-0.019: Holding height (x1) and exercise per day (x3) constant, we estimate the weight of a teenager (y) to increase by 0.019 kilograms for every 1 calorie intake (x2).
The SPSS printouts are plots for the residual values against the predicted weight against the three independent variables. The plots appear to be normal hence no transformation for independent variables is needed.
Residual Plots for the model
Works Cited
Sargent , Dorothy. "Weight-Height Relationship of Young Men and Women." The American Journal of Clinical Nutrition (n.d.): 1-8. Print.
