1. What is a correlation matrix, and what role  does it play in multiple regression?

2. One of the indicators that multicollinearity is present is when a variable that is known to be an important predictor ends up having a partial regression coefficient that is not significant. What are some of the other signals for the presence of  multicollinearity?

3. In linear regression models, for what types of uses or applications would multicollinearity tend to be a prob- lem? Are there any applications or uses for which multicollinearity would not be a problem?

4. A linear regression analysis was performed using x1 as a predictor variable. The p-value associated with the regression coefficient for x1 was 0.02, and the sign of the coefficient was negative. Another analysis was performed, this time using both x1 and x2  as predictor variables.  In the second analysis, the partial regression coefficient for x1 had a positive sign and the p-value associated with it was 0.39. Given these results, would multicollinearity appear to be present?

5. Four predictor variables are being considered for use in a linear regression model. Given the accompanying correlation matrix, does it appear that multicollinearity could be a problem?