Goodness of Fit Test

 

Goodness of Fit Test

After fitting a linear regression model, you must determine how well the model fits the data. Does it describe variations in the dependent variable well? There are several important goodness-of-fit statistics for regression analysis. In this piece, we'll look into standard error of the estimate and R-squared.

Standard Error of Estimate

The standard error of the estimate quantifies the response variable's dispersion around estimated values of response variable.

 Coefficient of Multiple Determination

The coefficient of multiple determination measures the proportion of variation in the dependent variable that can be explained by independent variables.

Adjusted Coefficient of Multiple Determination

The coefficient of multiple determinations is a non-decreasing function of the regressors in the model. The coefficient of multiple determinations grows in proportion to the number of regressors. Even if irrelevant regressors are included in the model, the coefficient of multiple determinations is increasing, giving an overly optimistic view of the reliance. This too hopeful picture is corrected by the modified coefficient of multiple determination

The degree of freedom determines the corrected coefficient of numerous determinations. The coefficient of multiple determinations is given by;

Practice Question 

Compute the standard error of the estimate, coefficient of determination and adjusted coefficient of determination for the data given below:

Solution:

The estimated regression model is given by

• Read More: Hypothesis Testing about Multiple Regression