Question

Discuss the statistics that must be evaluated when reviewing the regression analysis output. Provide examples of what the values represent and an explanation of why they are important.

Answer 1

P- value is one of the most important statistics which must be evaluated when reviewing the regression analysis output.

Regression analysis is a form of inferential statistics. The p-values help determine whether the relationships that we observe in our sample also exist in the larger population. The p-value for each independent variable tests the null hypothesis that the variable has no correlation with the dependent variable. If there is no correlation, there is no association between the changes in the independent variable and the shifts in the dependent variable. In other words, there is insufficient evidence to conclude that there is effect at the population level.

If the p-value for a variable is less than our significance level, our sample data provide enough evidence to reject the null hypothesis for the entire population. Our data favor the hypothesis that there is a non-zero correlation. Changes in the independent variable are associated with changes in the response at the population level. This variable is statistically significant and probably a worthwhile addition to our regression model.

On the other hand, a p-value that is greater than the significance level indicates that there is insufficient evidence in your sample to conclude that a non-zero correlation exists

example:

In the output below, we can see that the predictor variables of South and North are significant because both of their p-values are 0.000. However, the p-value for East (0.092) is greater than the common alpha level of 0.05, which indicates that it is not statistically significant.

coefficients

Term coef SE coef T P

constant 389.166 66.09 5.88 0.00

East 2.125 1.21 1.75 0.092

South 5.318   0.9629 5.52 0.00

North -24.132 1.868 -12.91 0.00

Typically, we use the coefficient p-values to determine which terms to keep in the regression model. In the model above, we should consider removing East.