Question

6. What is the difference between the correlation coefficient and ?2? Why should the correlation coefficient be -1 and 1?

7. What is the utility of marginal effects in regression models? How are they obtained?

8. What is heterocedasticity and homocedasticity? Explain how to detect and correct the first.

Answer 1

6. The difference between the correlation coefficient and R2 is that the correlation coefficient measures the strength of the linear relationship and R2 explains the variability in the dependent variable by all independent variables. The correlation coefficient should lie between -1 and +1 because negative sign shows that there exists a negative linear relationship and the positive sign shows that there exists a positive linear relationship.

7. Marginal effects are used to detect the changes in the dependent variable when a particular independent variable changes. These effects are obtained by calculating the derivative of the model with respect to the corresponding independent variable.

8. Heteroscedasticity means that the variance of residuals is different across all values of the independent variables and Homoscedasticity means that the variance of residuals is the same across all values of the independent variables. Residuals versus fit plots are used to detect Heteroscedasticity. There are three ways to correct it:

1. Redefining the independent variables

2. Weighted Regression

3. Transformation of the Dependent variable

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