Suppose we are interested in the relationship between the se

Suppose we are interested in the relationship between the seriousness rating of a crime y and the age of the accused x (in years) from a recent study of crime in the area. A sample of n = 10 crimes was sampled, and the following polynomial regression results of the data were reported.

y

Solution

d.f of error = 8, d.f of total = 9

R²_adj = 1 - MSE/ (SST/ d.f. of total) = 1 - (12.225/443.7889) = 1 - 0.02755 = 0.97245

R² = 1 - SSE/ (SST) = 1 - (97.8030/ 3994.1) = 0.9755

Adj R2 is less than R2 as Adj R2 explains the actual amount of variation explained by the model as by adding variables R2 always increases

To test the utility of quadratic equation we will R2 value as R2 = 0.9755 which means that 97.55% of the variation in the model is explained by the regressor variables.

The more the value of R2 less will be the MSE

The term x2 is important as this is a quadratic equation is giving R2 = 0.9755 which means that relationship between y and x is curvi linear .If x2 term is removed then the equation will become linear and in that case R2 will decrease and hence explain less variablilty in the model.