Correlation and Regression
Read/review the following resources for this activity:
Textbook: Chapter 13
Minimum of 1 scholarly source
In your reference for this assignment, be sure to include both your text/class materials AND your outside reading(s).
Initial Post Instructions
If a regression analysis was to be completed on body mass index (BMI), what could be an independent variable in that analysis? Why? If we could, what other independent variables should be included in the analysis? What statistic(s) would show the value of that regression in understanding BMI?
Alternatively, find an article that uses regression analysis to study a medical concern. In that study, what was the dependent variable and what were the independent variable(s)? Further, how would you use this study to highlight the difference between correlations and causation?
Correlation and Regression
Regression analysis provides information on the dependency relationship between two or more variables. For instance, in evaluating the body mass index (BMI), one should consider the factors influencing the value, such as the daily caloric intake. Caloric intake refers to the volume of calories one consumes on average per day. Current research suggests that the people who consume high-calory foods tend to gain weight (Buscemi et al., 2017). Hence, the daily caloric intake would serve as an excellent independent variable for a BMI regression analysis. One could also consider other variables, such as the average weekly exercise volume. One may express it in terms of hours spent exercising, the number of steps one takes, or any other objective metric. Again, exercise levels contribute to weight gain and loss (Grasdalsmoen et al., 2019), making it a worthwhile independent variable. Finally, one could also consider income levels, health literacy, and age.
The two statistics that would be vital in valuing the significance of the relationship are the p-value and the regression coefficient. The regression coefficient informs the statistician whether the relationship between the variables is positive or negative (Holmes et al., 2017). For example, one would expect that as caloric intake increases, so does the BMI, hence a positive coefficient. Conversely, the regression coefficient between exercise volume and BMI should be negative since people that generally spend more time exercising tend to have lower BMIs (Grasdalsmoen et al., 2019). One should also investigate the significance of the regression. The p-value facilitates this investigation where if it is less than the significance level, one can reject the null hypothesis, asserting a correlation between the variables. However, a p-value larger than the significance level indicates the lack of a significant correlation (Holmes et al., 2017).
Buscemi, J., Rybak, T. M., Berlin, K. S., Murphy, J. G., & Raynor, H. A. (2017). Impact of food craving and calorie intake on body mass index (BMI) changes during an 18-month behavioral weight loss trial. Journal of Behavioral Medicine, 40(4), 565–573. https://doi.org/10.1007/s10865-017-9824-4
Grasdalsmoen, M., Eriksen, H. R., Lønning, K. J., & Sivertsen, B. (2019). Physical exercise and body-mass index in young adults: a national survey of Norwegian university students. BMC Public Health, 19(1), 1354. https://doi.org/10.1186/s12889-019-7650-z
Holmes, A., Illowsky, B., & Dean, S. (2017). Introductory Business Statistics. OpenStax. https://openstax.org/details/books/introductory-business-statistics