# Cycle tour through multivariate statistics: Part 5 Multiple Regression

The research questions I wish to answer using multiple regression are:

- Which variables can be used to predict tourAwesomeness?
- Determine how much variance in tourAwesomeness can be accounted for by all the significant variables?
- Determine how much variance is tourAwesomeness can be accounted for by each significant variable after accounting for the other variables.

I ran a bivariate correlation between all variables. I checked to see which variables were significant and had a correlation above .3, (Pallant, 2010, p. 158). I found two variables: RideDays (-.425) and Blog (.304). I drew a Venn diagram to picture the analysis. I checked the sample size with two independent variables: the sample size is more than 50 + 8*2 = 50 + 16 = 66. I ran a standard multiple regression with dependent variable tourAwesomeness and independent variables Blog and RideDays, to determine a + b + c. I checked the collinearity statistics to ensure that tolerance > .10 and VIF < 10, see Table 8. I examined the Normal P-P plot of regression standardized residuals which showed a near linear line. I examined the scatterplot and did not see any clear or systematic pattern to the residuals. These test indicate that the model assumptions were met. I examined the model summary and noted that 25% of the variance in tourAwesomeness can be accounted for by RideDays and Blog, see Table 9. In the Venn diagram a + b + c = 25%. I ran a hierarchical regression with Blog in step 1 and RideDays in step 2. That is, I wanted to see how much variance in tourAwesomeness was accounted for by RideDays after controlling for Blog, or a in the Venn diagram. I examined the model summary for R^{2} change, see Table 9, and determined that 15.8% of tourAwesomeness is accounted for by RideDays after controlling for Blog, so a = 15.8%. I ran a hierarchical regression with RideDays in step 1 and Blog in step 2. That is, I wanted to see how much variance in tourAwesomeness was accounted for by Blog after controlling for RideDays, or c in the Venn diagram. I examined the model summary for R^{2} change, see Table 9, and determined that 7% of tourAwesomeness is accounted for by Blog after controlling for RideDays, so c = 7%. Finally, I calculated the value of b using the values of a + b + c = 25%, a = 15.8%, c = 7%; therefore, b = 2.2%.