Question

Afirm that operates a large, direct-to-consumer sales force would like to implement a system to monitor the progress of new agents. A key task for agents is to open new accounts; an account is a new customer to the business. To build such a system, the firm has been monitoring sales of new agents over the past 2 years. The response of interest is the profit to the firm (in dollars) of contracts sold by agents over their first year. Among the possible predictors of this performance is the number of new accounts developed by the agent during the first 3 months of work. Complete parts (a) through (f) below. Click the icon to view the description of the data and the data table. (a) Create a scatterplot for Profit from Sales on Number of Accounts. Does a line seem to be a good summary of the association between these variables? Construct the scatterplot. Choose the correct graph below. OA. ОВ. Proft (5000) Proft (5000) Profit($000) Profit (5000) 50 56 Accounts Accounts Accounts Accounts Does a line seem to be a good summary of the association between these variables? O A. The scatterplot shows weak association, but there is a curved pattern, so a line does not summarize any association. B. The scatterplot shows strong association and a line is a reasonable summary of the association. C. The scatterplot shows weak association. A line seems to be a reasonable summary of the association. OD. The scatterplot shows no obvious pattern, so there is no association and a line does not summarize any

Number_Of_Accounts Profit_From_Sales_($)

21 9232.93

18 18762.13

37 22865.68

15 11633.12

32 18140.04

41 32943.84

26 29576.92

18 19703.92

35 25807.72

41 31237.05

10 3253.59

6 15075.03

24 14574.02

12 12445.49

9 12723.51

9 14512.76

10 21364.92

28 28498.28

7 9050.42

28 8610.41

11 10294.72

11 9929.32

5 9895.91

12 3856.93

18 15990.73

48 30129.54

38 31284.61

13 21861.74

6 16140.46

24 12031.41

15 16484.17

7 19620.39

25 16535.41

32 35548.76

22 22145.01

26 28670.93

Answer 1

40000 35000 30000 Profit from Sales 10000 5000 HHHHHHHHHHHHHHHHHHHHHHHH 0 10 20 30 40 50 60 Number of Accounts Correct Answer: C. C. The scatter plot shows weak association. A line seems to be a reasonable summary of the association (b)

EXCEL (Mega Stat in Add-Ins) procedure: Step 1: Choose Mega Stat > Correlation/Regression > Regression Analysis Step 2: Select Input ranges, enter the variable Number of Accounts as the column of X, Independent variable(s) and enter the variable Profit from Sales as the column of Y, Dependent variable. Step 3: Check the appropriate options in Options. Step 4: Click OK EXCEL (Mega Stat in Add-Ins) output:

Regression Analysis 20.497 r 0.705 Std. Error 6140.239 n 36 k 1 Dep. Var. Profit from Sales ANOVA table Source SS Regression 1,268,247,613.0573 Residual 1,281,886,118,2472 Total 2,550,133.731.3045 df 1 34 MS 1,268,247,613.0573 37,702,532.8896 F 33.64 p-value 1.57E-06 Regression output variables Intercept Number of Accounts coefficients std. error 7.824.0457 2,082.8131 511.8462 88.2516 confidence interval t (dt=34) p-value 95% lower 95% upper std. coeff. 3.756 0006 3,591.2602 12,056.8312 0 .000 5.800 1.57E-06 332.4973 691. 1951 0.705 Estimated Profit from Sales ($) = 7824.05 + 511.35 Number of Accidents. B. The intercept estimates that with no accounts opened during the first three months, the firm would still have a $ 7824.05 profit from sales over the first year. B. The slope indicates that, on average for each account opened the profit from sales increases by $511.85. p2 = 0.4973 with no units.

Se=6140.24 with no units. B. The value of r2 means that the equation describes about 49.73% of the variation. The value of s, means that the standard deviation of the residuals is 6140.24 (d) y = 7824.05 +511.85x = 7824.05 +511.85(22) = 7824.05 +11260.70 = $19084.75 The profit increases by $19084.75.

EXCEL ( Mega Stat in Add-Ins) procedure: Step 1: Choose Mega Stat > Correlation Regression > Regression Analysis. Step 2: Select Input ranges, enter the variable Number of Accounts as the column of X, Independent variable(s) and enter the variable Profit from Sales as the column of Y, Dependent variable. Step 3: Check the appropriate options in Options Step 4: Click OK EXCEL (Mega Stat in Add-Ins) output: Regression Analysis 0.374 T 0.612 Std. Error 7100.192 n 17 k 1 Dep. Var. Profit from Sales MS ANOVA table Source SS Regression 452,316,872.4422 Residual 756,190,950.2870 Total 1,208,507 822.7292 p-value 0091 1 15 16 452,316,872.44228.97 50.412,730.0191 Regression output variables Intercept Number of Accounts coefficients std. error 2.246.7127 7.269.5303 681.1334 227.3950 confidence interval t (df=15) p-value 95% lower 95% upper std. coeff. 0.309 7615 -13,247.9242 17,741.3496 0.000 2.995 0091 196.4525 1.165.8144 0.612 Estimated Profit from Sales ($) = 2246.71 +681.13 Number of Accidents.