Mathematics Analysis and Interpretation

SECTION III: ANALYSIS AND INTERPRETATION

1) The variance inflation factor for each variable in a multiple regression analysis is listed below:

Given these VIFs what can you say about multicollinearity in a model that includes all three of these variables?

2) In conducting a multiple linear regression analysis, an R2 value of 0.46 is obtained. An extra variable is added and R2 improves to 0.52. The analyst conducting the regression analysis concludes that this is a meaningful increase in R2 and determines that the latter model is an appropriate model to be used. Is this decision justified? (3 points)

3) In exploring the relationship between two variables, the following scatter plot is obtained. The analyst conducting the research was hoping to do a linear regression to assess the degree to which the linear model explains the relationship between the two variables. Given the scatter plot below, should he continue with linear regression? If so, why? If not, what other options can be used to assess this relationship?

4) An online retailer wanted to see if purchasing patterns were different between male consumers and female consumers. Males were found to have spent a mean of $85 per month on online purchases, whereas females were found to have spent a mean of $78 per month. An independent samples t-test was conducted to assess the observed difference between the two groups of consumers. A two-tailed test was applied. The value of the t-Test Statistic for the observed differences was -4.7, where the p-value is less than 0.0002. What conclusion can be made about the observed difference?

5) The regression equation  = 3,698 + 2,538X gives an R2 value of 0.2645. This means that ________.

A) X and Y have a very high level of correlation

B) the percentage of variation in Y that is attributed to random factors is 26.45%

C) 26.45% of the variation in Y can be explained by X

D) a one-percent change in Y will lead to a 26.45% change in X