Part -1:
DataPro is a small but rapidly growing firm that provides electronic data-processing services to commercial firms, hospitals and other organizations. For each of the past 12 months, DataPro has tracked the number of contracts sold, the average contract price, advertising expenditures, and personal selling expenditures.
1. Find the correlation between number of contracts sold and average contract price. What does this correlation mean?
2. Estimate a regression model with number of contracts sold as the dependent variable and the average contract price as the only independent variable. Test for the significance of contract prices (note: use one tail test and significance level .05). Interpret the contract price coefficient. Interpret the R2 for the model.
3. Expand the regression model from (2) and add the advertising variable. Test for the significance of both contract price and advertising variables (note: use a one tail test for each and significance level .05). Interpret the coefficient of the advertising variable.
4. Expand the regression model from (3) to include personal selling expenditures. After testing for significance of personal selling, interpret the coefficient.
5. What happened to the R2 as you added independent variables to the model? Will this always happen? Explain.
6. What happened to the adjusted R2 as you added independent variables to the model? Will this always happen? Explain.
Part -2:
1. The correlation coefficient between number of contracts sold and average contract price is
A) -1.000
B) 0.000
C) -0.016
D) none of the above
2. In general, a negative correlation coefficient of -.005 would suggest there is a strong negative relationship between two variables.
A) True
B) False
Answer questions 3-5 after estimating a regression model with number of contracts sold as the dependent variable and the average contract price as the only independent variable.
3. The estimated coefficient for contract price is found to be
A) -0.0237
B) 0.4690
C) -0.0506
D) none of the above
4. Using a one-tailed test, contract prices are found to be statistically significant at the 0.05 level.
A) True
B) False
5. The R Square value of 0.000256 found in this scenario means that only 0.0256% of the variation in the dependent variable (number of contracts sold) is explained by the variation in the independent variable (average contract price).
A) True
B) False
For questions 6-8, expand the regression model and add the advertising variable. Test for the significance of both contract price and advertising variables.
6. Which of the following statements best reflects the interpretation of the advertising variable?
A) On average, when the advertising expense increases by .0937300, contracts sold increases by one, holding constant all other variables.
B) On average, for every one unit ($1) increase in advertising expense, contracts sold will increase by 0.09373 units (number of contracts sold), holding constant all other variables.
C) The advertising coefficient of 0.0937 indicates the increase in advertising expenditures as it relates to contract price for each movement in total contracts sold, holding constant all other variables.
D) none of the above
7. Which of the following represents the null hypothesis for the coefficient on contract price?
A) H0: contract price coefficient > 0
B) H0: contract price coefficient < 0
C) H0: contract price coefficient = 0
D) none of the above
8. According to the t-statistic and t-critical value, contract price is statistically insignificant.
A) True
B) False
Answer questions 9 and 10 after expanding the model to include personal selling expenditures.
9. The estimated coefficient for personal selling expenditures is found to be
A) 4.607 which implies that this variable is statistically insignificant.
B) 1.860 which implies that this variable is statistically insignificant.
C) 0.066 which implies that this variable is statistically insignificant.
D) none of the above
10. On average, for every one unit ($1) increase in personal selling expenditure, contracts sold will increase by 0.066 units (number of contracts sold), holding constant all other variable.
A) True
B) False
11. The R-square will sometimes increase as variables are added, but not always.
A) True
B) False
12. The adjusted R-Square only increases if the added variable(s) add significant explanatory power to your regression.
A) True
B) False
Attachment:- Data.xls