Question

Answer the following questions:

1. In the multiple explanatory variable regression model, define the partial correlation coefficients, explain how they are interpreted, and how do the interpretations differ from the coefficients of the single explanatory variable regression model?
2. Explain the t-tests of the partial correlation coefficients. Have they changed?
3. Explain how the coefficient of determination has changed and why.
4. Explain how the null hypothesis has change for the F-test as compared to a single explanatory variable regression model.

Answer 1

a. In multiple explanatory variable regression model, partial correlation coefficients are the measure of strength and direction between two variables when the effect of the remaining variables are kept under control. It can be interpreted as the correlation between any two variables when the remaining variables are kept constant. In single explanatory variable regression, correlation considers only one variable whereas in multiple regression, partial correlation considers only one variable but under the constant influence of remaining variables.

b.

c. Coefficient of determination increases with addition of new variables. A model with a single variable may not be most adequate as more variables may be required. Usually larger value of coefficient of determination indicates better fit.

d. In multiple regression model, null hypothesis is that all the regression coefficients are not significant. Acceptance of null hypothesis just gives us an idea about the coefficients are not significant but does not exactly indicate which coefficient it is. In single variable model, null hypothesis is about only one regression coefficient indicating the coefficient is not significant.