NRS 394 Correlation and Regression SOLVED

NRS 394 Correlation and Regression SOLVED

NRS 394 Correlation and Regression SOLVED

Congrats to all for surviving this course! Wasn’t this like trying to lean a new language in 8 weeks?

I found an excellent article in our library that compared different regression models for the best approach to predicting BMI: “Factors associated with overweight: are the conclusions influenced by choice of the regression method?” (Juvanhol et al., 2016).  The bottom line was the authors recommend using a combination of different approaches, as these furnish complementary information to the multifactorial predictors of obesity. The article was a little over my head as it discussed gamma regression, which I couldn’t find in our textbook, and quantiles, which also is not in our text but seems a lot like quartiles. But thanks to this course, I was able to understand more of this article than I would have before this course.

In this article, BMI distribution percentiles is on the x-axis of the following charts. The along the y-axis were the values of the estimated coefficients for age, physical inactivity, years of night-shift work, BMI at age 20, domestic overload (cleaning/cooking/laundry factored by number of residents at home) and self-rated health.  According to Juvanhol et al., (2016), these were the explanatory variables. This is still a little confusing to me, as Holmes et al. (2018) stated that a multivariate model or system is where more than one independent variable is used to predict an outcome, and there can only be one dependent variable, but unlimited independent variables. So why did the authors refer to age, etc., as explanatory variables, which would made them independent variables, but not put them on the x-axis?

Anyway, the independent variables are along the y-axis, and are shown in units of the values of the coefficients estimated. Coefficients provide an estimate of the impact of a unit change in the independent variable on the dependent variable (Holmes et al., 2018). The coefficient we use in a linear regression is the slope, or the rise over the run. However, this week we learned about another kind of coefficient, the coefficient of determination which is the explained variation over the total variation (Chamberlain University, 2021). I am not sure which coefficient the authors are referring to in the article.

The grey shaded areas around each line show the 95% confidence interval for the quantile estimates. It is interesting to note the narrowness of the spread of the confidence interval around the line in the “Age” graph and the “BMI at age 20” graphs in comparison to the other four graphs even though they are all at the 95% confidence level. We all know now that a narrow confidence interval is preferred over a wide one (Holmes et al., 2018).

To answer the final question, which statistic would show the value of that regression line in understanding BMI, I’d give more weight (pardon the pun) to the statistics of “Age” and “BMI at age 20” due to the narrowness of the confidence intervals, but also interesting is the way the “Years worked at night” regression line jumps at about the 80th quantile showing a suddenly stronger association in the upper quantiles. That would be an interesting area to investigate.

Elaine

Chamberlain University. (2021). MATH225. Week 8 Slide Deck [Online lesson]. Downers Grove, IL: Adtalem.

Holmes, A., Illowsky, B., & Dean, S.  (2018).  Introductory business statistics.  OpenStax.

Juvanhol, L.L., Lana, R.M., Cabrelli, R., Bastos, L.S., Nobre, A.A., Rotenberg, L., Griep, R.H. (2016). Factors associated with overweight: are the conclusions influenced by choice of the regression method? BMC Public Health 16, 642. http://doi.org/10.1186/s12889-016-3340-2 (Links to an external site.)

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