Log Proft	Log Accounts	Log Early Commission
10.8547	2.8385	5.3091
9.5086	2.1892	7.4325
9.6436	2.6624	7.4615
9.3198	3.0866	7.4612
9.0978	1.6126	8.2905
9.5141	2.5893	4.0902
10.0764	2.1742	5.4368
10.3083	2.4057	8.6765
11.5507	3.8838	9.1892
9.6116	1.9245	5.0883
9.3231	1.1237	0.0000
9.1925	1.5879	5.7106
9.7883	3.3063	6.2452
8.7454	2.2066	5.7668
11.4001	2.9902	8.4394
9.8437	2.9827	4.4942
10.7204	2.8965	4.9352
10.6891	2.2644	5.7924
9.6944	3.5551	7.2612
9.9974	3.2769	3.6708
10.7602	3.2979	9.0545
10.4179	2.9411	8.6709
8.2731	1.7956	0.0000
8.5693	5.8361	7.0905
9.2876	4.2227	5.5878
10.2325	3.4454	8.3606
10.9891	3.5209	5.9488
11.0143	3.4386	9.7794
10.1554	3.3965	8.2062
10.3023	2.6391	7.2064
9.5093	2.3812	7.6228
9.9811	6.3643	8.7459
9.1925	2.8105	7.7668
10.3573	3.3844	6.3658
8.9648	2.4243	4.2211
10.3884	4.8702	7.3685
10.3776	2.7153	7.8675
9.7887	3.8736	8.3576
10.6309	3.1694	9.0176
10.8936	3.5635	9.1737
9.4249	3.1743	7.5981
10.2304	2.0778	1.6114
9.4311	2.3652	0.0000
8.8282	1.0737	4.7033
10.5179	3.3792	8.3327
10.1677	2.6666	7.5884
10.3918	3.6065	8.9742
9.7106	2.0361	4.8877
10.7126	3.2708	1.7799
8.4618	2.6496	4.141

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 firm is using the equation (with natural logs) Log Proft = Bo + B, Log Accounts +ByLog Early Commission. For cases having value 0 for early commission, the analyst replaced with $1. Complete parts (a) through (1) below. Click the icon to view the data table. . (a) The choice of the analyst to fill in the values of the early commission with 1 so as to be able to take the Log is a common choice. From the scatterplot of Log Profit 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. . . , OD 11.8 6.75 11.84 Q 11.84 8 8 8 CE 8-1 -0.5 10.5 Log Commission 0.75 -0.5 10.5 Log Commission 81 -0.5 10.5 Log Commission HIS 8 -0.5 10 5 Log Commission What is the impact of these filled-in values on the marginal association? These values are leveraged and strengthen 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? The VIF between the explanatory variables, LogAccounts and LogEarly Commission, is which indicates that there is not much collinearity. There is more collinearity 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 fairly close to 1, collinearity does not 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 Log Profit 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 LogEarlyCommission 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 . OC OD A Q . P. LE . .. IT TUTTI Commissionen Accounts -Je - Contnission 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 LogEarlyCommission on LogAccounts. State the regression equation below. Estimated LogProfit residuals - LogEarlyCommission (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 LogEarlyCommission in the multiple regression is This slope is the same as or extremely close to 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 LogEarlyCommission on LogAccounts (Round to three decimal places as needed.) 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 firm is using the equation (with natural logs) Log Proft = Bo + B, Log Accounts +ByLog Early Commission. For cases having value 0 for early commission, the analyst replaced with $1. Complete parts (a) through (1) below. Click the icon to view the data table. . (a) The choice of the analyst to fill in the values of the early commission with 1 so as to be able to take the Log is a common choice. From the scatterplot of Log Profit 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. . . , OD 11.8 6.75 11.84 Q 11.84 8 8 8 CE 8-1 -0.5 10.5 Log Commission 0.75 -0.5 10.5 Log Commission 81 -0.5 10.5 Log Commission HIS 8 -0.5 10 5 Log Commission What is the impact of these filled-in values on the marginal association? These values are leveraged and strengthen 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? The VIF between the explanatory variables, LogAccounts and LogEarly Commission, is which indicates that there is not much collinearity. There is more collinearity 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 fairly close to 1, collinearity does not 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 Log Profit 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 LogEarlyCommission 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 . OC OD A Q . P. LE . .. IT TUTTI Commissionen Accounts -Je - Contnission 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 LogEarlyCommission on LogAccounts. State the regression equation below. Estimated LogProfit residuals - LogEarlyCommission (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 LogEarlyCommission in the multiple regression is This slope is the same as or extremely close to 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 LogEarlyCommission on LogAccounts (Round to three decimal places as needed.)