Answer Happy

A firm that operates a large, direct-to-consumer sales force would like to build a system to monitor the progress of new agents. The response of interest is the profit to the firm (in dollars) of contracts sold by agents over their first year. The accompanying data summarize the early performance of 50 agents. Among the possible explanations of performance are the number of new accounts developed by the agent during the first 3 months of work and the commission earned on early sales activity. An analyst at the fir is using the equation (with natural logs) Log Proft - Bo + B₁ Log Accounts + B₂ Log Early Commission. For cases having value 0 for early commission, the analyst replaced 0 w $1. Complete parts (a) through (f) below. Click the icon to view the data table. (a) The choice of the analyst to fill in the 0 values of the early commission with 1 so as to be able to take the Log is a common choice. From the scatterplot of LogProfit on LogEarly Commission, you can see the effect of what the analyst did. What is the impact of these filled-in values on the marginal association? Choose the correct scatterplot below. A. O B. O C. O D. Q Q 10 10 Log Commission Log Commission 10 Lan Commission What is the impact of these filled-in values on the marginal association? These values are and the marginal association compared to the marginal association without these values. (b) Is there much collinearity between the explanatory variables? How does the presence of these filled-in values affect the collinearity? much collinearity. There is collinearity The VIF between the explanatory variables, LogAccounts and LogEarly Commission, is, which indicates that there than there would be without these filled-in values. (Round to three decimal places as needed.) (c) Using all of the cases, does collinearity exert a strong influence on the standard errors of the estimates in the analyst's multiple regression? Since the VIF is collinearity exert a strong influence on the standard errors of the estimates in the analyst's multiple regression. (d) Because multiple regression estimates the partial effect of an explanatory variable rather than its marginal effect, we cannot judge the effect of outliers on the partial slope from their position in the scatterplot of y on x. We can, however, see their effect by constructing a plot that shows the partial slope. To do this, we have to remove the effect of one of the explanatory variables from the other variables. Here's how to make a so-called partial regression leverage plot for these data. First, regress LogProfit on LogAccounts and save the residuals. Second, regress LogEarlyCommission on LogAccounts and save these residuals. These regressions remove the effects of the number Log Profit 12.4- 8+ -0.5 Q Q Log Profit 12.4+ -0.5 Log Profit 6.75 0.75 -0.5 Log Profit 12.4 -0.5 10 Log Commission
(d) Because multiple regression estimates the partial effect of an explanatory variable rather than its marginal effect, we cannot judge the effect of outliers on the partial slope from their position in the scatterplot of y on x. We can, however, see their effect by constructing a plot that shows the partial slope. To do this, we have to remove the effect of one of the explanatory variables from the other variables. Here's how to make a so-called partial regression leverage plot for these data. First, regress LogProfit on LogAccounts and save the residuals. Second, regress LogEarly Commission on LogAccounts and save these residuals. These regressions remove the effects of the number of accounts opened from the other two variables. Now, make a scatterplot of the residuals from the regression of LogProfit on LogAccounts on the residuals from the regression of LogEarly Commission on LogAccounts. Fit the simple regression for this scatterplot, and compare the slope in this fit to the partial slope for LogEarly Commission in the multiple regression. Are they different? Make the scatterplot of the residuals from the regression of Log Profit on Log Accounts on the residuals from the regression of Log Commission on Log Accounts. O A. O B. OC. D. Q Q Q Hali Commission on Accounts Con mission on Accounts Commission on Accounts Commission on Accounts Fit the simple regression for this scatterplot, that is, fit the regression of the residuals from the regression of Log Profit on LogAccounts on the residuals from the regression of LogEarly Commission on LogAccounts. State the regression equation below. Estimated LogProfit residuals = + LogEarly Commission (Round to three decimal places as needed.) Compare the slope in this simple regression to the partial slope for LogEarly Commission in the multiple regression. Are they different? The partial slope for LogEarly Commission in the multiple regression is. This slope is the slope in the simple regression from the regression of the residuals from the regression of LogProfit on LogAccounts on the residuals from the regression of LogEarly Commission on LogAccounts. (Round to three decimal places as needed.) Proft on Accounts Proft on Accounts 200 Profit on Accounts Profit on Accounts
(e) Are the filled-in cases leveraged in the partial regression leverage plot constructed in part (d)? What does this view of the data suggest would happen to the estimate for this partial slope if these cases were excluded? The filled-in cases The partial regression leverage plot constructed in part (d) suggests that the estimate for this partial slope would if these cases were excluded. (1) What do you think about filling in these cases with 1 so that we can take the log? Should something else be done with them? Filling in these cases with 1 to be a viable option. The fact that the slope in the regression equation from the regression of the residuals from the regression of Log Profit on Log Accounts on the residuals from the regression of Log Commission on Log Accounts is the partial slope for Log Commission in the multiple regression indicates that filling in the cases with 1 a collinearity issue.