Regression and Correlation are two of the most often used and abused tools in re

Question

Regression and Correlation are two of the most often used and abused tools in research. People are quick to jump to conclusions that if a relationship exists between two variables, then one must cause (causation) the other. There are many reasons why two variables can be related without causality. Please respond to the following:

a.Comparing the amount of money people spend and the amount people save, your analysis revealed an R-squared=0.97. Should you use this for predictive purposes and why?

b.Comparing the number of cops on our streets and the number of reported crimes, your analysis revealed an R-squared=0.40. Should you use this for predictive purposes and why?

c.How could this apply in profession?

Explanation / Answer

c) Coefficient of determination (R-squared) explains how much of the variability of a factor can be caused or explained by its relationship to another factor.

Coefficient of determination is used in trend analysis. It is computed as a value between 0 (0 percent) and 1 (100 percent). The higher the value, the better the fit.

a) R-squared=0.97

this is close to 1 indicates that the model explains all the variability of the response data around its mean

We should use this for predictive purposes.

b)R-squared=0.40

this is close to 0 and far away from1 indicates that the model explains very few variability of the response data around its mean

We should not use this for predictive purposes to avoid errors

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