# MATH 225 Week 7 Discussion: Correlation and Regression

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.

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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

## MATH 225 Week 7 Discussion: Correlation and Regression

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?

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