Question

describe the difference between coefficient of multiple determination and adjusted coefficient of multiple determination and provide an example where adjusted R2 is necessary?

Answer 1

The coefficient of multiple determination is R^2 The multiple R^2 describe the variation explained by the independent variable about dependent variable. The R^2 increase as the independent variable increases irrespective of they are important for prediction

The Adjusted coefficient of multiple determination increase if the added variable.in model is really important for prediction of the depdndent ariable

Example

Suppose we have 3 independent variable and 3 model

1) 1st with only one independent variable

Let us assume

R^2= 72.1

Adjusted R^2= 71

2) model with previous and new variable

R^2= 85.9.

Adjust R^2= .84.9

3) model with 3 independent variable

R^2= 87.4

Adjusted R^2= 85.9

We can see that 3 model had low adjusted R^2 decrease as 3rd independent variable is not important that much for predicypre.

So we have to take decision on adjusted R^2

The model with high Adjusted R^2