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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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Correlation and regression analysis are parametric, inferential statistics are often applied in the processes of data analysis. Correlation has helpful in the determination of the relationship that exist between two continuous variables in the dataset. For effective computation of the correlation coefficient, there is always the need for the data to be normally distributed. In other words, there is always the assumption of normality. Correlation can be computed between independent and dependent variable, both the variables need to be normally distributed (Kasuya, 2019). While correlation is only applied in the determination of the relationship that exist between one independent and one dependent variable, regression analysis can be applied in the determination of the relationship that exist between one dependent variable and one or more independent variables. In other words, regression analysis is important in the analysis of more variables in a given dataset.

When a regression analysis was to be completed on the body mass index (BMI), there are several independent variables that could be included in the processes of analysis. In other words, for the regression analysis on the body mass index, the independent variable can be activity level or frequency in undertaking physical activities. The activity level can be measured in terms of the amount of time taken while undertaking physical activities (Zhang et. Al., 2019). From the theoretical perspectives and from the previous research processes, it has been established that continuous physical exercise can lead to the reduction in weight. In other words, physical activities have direct impacts on body weight. For effective outcomes of the regression analysis, there is the need for the independent variables to have a normal distribution, also, they need to be continuous variables.

Another independent variable that may relate to the Body Mass Index is the amount of fatty food intake. In most cases, increased intake of fatty foods is one of the major contributors to increase in body mass index. Individuals who consume high amount of fatty foods often tend to experience increase in body weight. As a result, their body mass indices are likely to increase. While using amount of fatty foods intake as an independent variable, there is a need ensure that it is continuous and normally distributed. Finally, height may be considered as one of the independent variables in the regression analysis whereby BMI has been used as dependent variable. The determination of body mass index often involve the incorporation of the height of an individual. The body mass index is determined through dividing the weight of an individual with the square if the height. Therefore, height is an important determinant of the body mass index.

From the regression analysis, there is ANOVA outcomes that can be applied in the determination of whether the model is fit. From the ANOVA table, the significant values can always show if there is the relationship between the dependent and independent variables. The significant values can be tested against the alpha value at 0.05. Also, the mean square as well as the F-values obtained can be used to determine the values of body mass index. Also, the unstandardized coefficients can be applied in the determination of the correlation coefficient in the process of determining the relationship between the dependent and independent variables in the process of analysis.

 

References

Kasuya, E. (2019). On the use of r and r squared in correlation and regression (Vol. 34, No. 1, pp. 235-236). Hoboken, USA: John Wiley & Sons, Inc. https://doi/abs/10.1111/1440-1703.1011

Zhang, L., Shi, Z., Cheng, M. M., Liu, Y., Bian, J. W., Zhou, J. T., … & Zeng, Z. (2019). Nonlinear regression via deep negative correlation learning. IEEE transactions on pattern analysis and machine intelligence. Retrieved from: https://ieeexplore.ieee.org/abstract/document/8850209

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