Question

1. 
   Regression Analysis Example Sales Representative Copiers Sold Sales Calls 96 41 Brian Virost The sales manager of Copier Sales of America (see data set) collected information on: a) the number of sales calls made and b) the number of copiers sold for a random sample of 15 sales reps. Use the least squares regression model (LSM) to test the relationship between the two variables. In this example, the variable "sales calls" is the independent variable (X) and the variable "copiers sold" is the dependent variable (Y) 40 41 Carlos Ramirez Carol Saia 104 51 128 60 Greg Fish Jeff Hall 164 61 Mark Reynolds Meryl Rumsey Mike Kiel 76 29 39 72 80 50 Ray Snarsky 36 28 43 Rich Niles 84 Ron Broderick 180 70 80 Sal Spina Soni Jones Susan Welch 132 56 70 120 45 60 44 31 84 30 Tom Keller 1440 675 Total Number of Copiers Sold a b (Number of Sales Calls) 20 10 Based on the LSM analysis (see chart to the right), estimate the expected number of copiers that would be sold by a sales representative that makes 100 calls. 50 100 150 200 Sales Calls (X) gNa Copiers Sold (Y)
   Based on the data collected by the sales manager in the Copier case, it appears that she would have some difficulty predicting the sales based on only sales calls – especially at some levels of sales calls. For example, if one of her salespeople made between 70 and 80 calls, would she be able to predict a certain number of sales? Would it be easier to predict a range of sales? If yes, what would that range be?  Hint: Review the Chapter 13 PPT slides #18-27 for more information.

Answer 1

Sales Representative	Sales Calls	Copier Sold
1	96	41
2	40	41
3	104	51
4	128	60
5	164	61
6	76	29
7	72	39
8	80	50
9	36	28
10	84	43
11	180	70
12	132	56
13	120	45
14	44	31
15	84	30
Total	1440	675

Output:

Regression Statistics
Multiple R												0.865
R Square												0.748
Adjusted R Square												0.728
Standard Error												6.720
Observations												15.000
ANOVA
			df		SS			MS		F			Sig.
Regression			1.000		1738.890			1738.890		38.503			0.000
Residual			13.000		587.110			45.162
Total			14.000		2326.000
	Coeff	Standard Error		t Stat		P-value	Lower 95%		Upper 95%		Lower 95.0%			Upper 95.0%
Intercept	19.980	4.390		4.552		0.001	10.497		29.463		10.497			29.463
X Variable	0.261	0.042		6.205		0.000	0.170		0.351		0.170			0.351

Answer

Regression Equation: Y = a + bX

No. of Copier Sold = 19.980 + 0.261 (Sales Calls)

For 100 calls:

No. of Copier Sold = 19.980 + 0.261(100) = 19.980+26.1 = 46.08 = 46

For 70 Calls:

No. of Copier Sold = 19.980 + 0.261(70) = 38.25 = 38

For 80 Calls:

No. of Copier Sold = 19.980 + 0.261(80) = 40.86 = 41