While teaching a lesson on linear regression a student is co

While teaching a lesson on linear regression, a student is confused between r,r to the power of 2 and residual plot. How would you help the students differentiate between the three? Also, the student wonders if we can use r for non-linear regression

Solution

1. r- generally we use to find the relationship between the variables, without exsisting relationship between the variable we can\'t proceed forther analysis.

2. R-squared is a statistical measure of how close the data are to the fitted regression line. It is also known as the coefficient of determination, or the coefficient of multiple determination for multiple regression.

R-squared = Explained variation / Total variation

R-squared is always between 0 and 100%:

3. residual plot is a graph that shows the residuals on the vertical axis and the independent variable on the horizontal axis. If the points in a residual plot are randomly dispersed around the horizontal axis, a linear regression model is appropriate for the data; otherwise, a non-linear model is more appropriate.

4. r-is a very powerful analysis that can fit virtually any curve. However, it\'s not possible to calculate a valid R-for nonlinear regression. This topic gets complicated because,it gives an opproximate result not accurate.