Question

• Discuss how the coefficient of determination and the coefficient of correlation are related. How are they used in regression analysis?
• A seasonal index may be less than one, equal to one, or greater than one. Explain what each of these values mean.

Answer 1

In any regression model, coefficient of determination R² tells about the proportion of variation explained by the model. The amount which remains unexplained is due to error involve in experiment.

The coefficient of determination, R², is similar to the correlation coefficient r. In case of simple linear regression model (the model involving only one predictor variable) we have:

The correlation coefficient tell how strong a linear relationship there is between two variables. R Squared is the square of the correlation coefficient, r (hence the term r squared)

That is, for simple linear regression, R² = r²

A seasonal index shows how the average value of a particular season compares with the average of all seasons

If the value is 1, that means this season is actually at the average

If the value is more than 1 implies higher values than expected for that season

If the value is less than 1 implies lower values than expected for that season