This study seeks to assess the relationship between weight and height among children. Sargent evaluated the relationship between weight and height using data from 160,000 college students. The study revealed that there is a positive relationship between height and weight. However, the regression coefficient different with age a group. Weight was relatively stable for men between 21 and 29 years, while for women it is between 17 and 29 years. A regression analysis of the sub-set revealed that weight increases by approximately one kilogram for every increase in height. This study assesses the relationship using survey data that was collected in 1993 for the Growth Survey. The survey comprises of children below the commonly defined adult age; 18 years.
Data Description
The population of interest is children below the age of 18 years. A sample of 200 was used. The data contained two main variables: height and weight. The height was in inches. The shortest was 63.43 and the tallest was 73.90. The mean was 67.95 while the first and third quartiles were 66.52 and 69.20 respectively. The histogram below shows the distribution of age. It assumes an almost normal distribution with most data concentrated at the centre with few data points at the extremes. There are no obvious outliers
The weight was measured in pounds. The lightest was 97.9 pounds and the heaviest was 159 pounds. The mean was 127.2 while the first and third quartiles were 119.9 and 159 respectively. The histogram below shows the distribution of weight.
The scatterplot below gives a visual representation of the distribution of weight according to height. The weight appears to be increasing with height hence portraying a positive relationship.
Results
Regression analysis was used to analyze the relationship between weight and height. Weight is the dependent variable and height is the independent variable.
Weight = β0 + β1 Height
Regression Output
Call:
lm(formula = Weight ~ Height)
Residuals:
Min 1Q Median 3Q Max
-29.3119 -5.2735 -0.5228 6.4324 22.1303
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -106.0277 24.7348 -4.287 2.83e-05 ***
Height 3.4327 0.3639 9.434 < 2e-16 ***
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Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 9.96 on 198 degrees of freedom
Multiple R-squared: 0.3101, Adjusted R-squared: 0.3066
F-statistic: 89 on 1 and 198 DF, p-value: < 2.2e-16
A change in height by one inch results in an increase in weight by 3.43 pounds. The co-efficient is statistically significant at one percent. The model has an adjusted R-square of 0.3066. The model explains 30.66 percent of changes in weight. The entire model is statistically significant at one percent (P<.01).
The confidence intervals based on 5% significance as presented below
Confidence Intervals
2.5 % 97.5 %
(Intercept) -154.805165 -57.250248
Height 2.715122 4.150231
The graph below provides a visual presentation of the distribution of the data points and the regression line.
Residual vs Fitted and Normal Q-Q plots were used to test the linear regression assumptions.
The Residual vs Fitted plot tests whether the assumption that the variance is homoscedastic/constant hold. The residual variance does not show any unique pattern with changes in x as shown by the red line.
The normal Q-Q plot tests whether the assumption that the distributions of errors is normal holds. Most of the data points are along the dashed line. Therefore, they are normally distributed. The linear regression assumptions hold
Conclusion
The study evaluated the relationship between weight and height. The study concludes that there is a positive relationship between height and weight. Height explains the weight of children.
Works Cited
Sargent , Dorothy. "Weight-Height Relationship of Young Men and Women." The American Journal of Clinical Nutrition (n.d.): 1-8. Print.
