Regression and Correlation are two of the most often used and abused tools in re
ID: 3048060 • Letter: R
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