Question

3. A sales manager collected the following data on annual sales and years of experience.
Salesperson Years of Experience Annual Sales ($000s)
1 1 132
2 3 160
3 4 145
4 5 168
5 6 168
6 8 180
7 10 188
8 11 218
9 11 193
10 13 229
a. Develop a scatter diagram for these data with years of experience as the independent variable.
b. Develop an estimated regression equation that can be used to predict annual sales given years of experience.
c. Provide an interpretation of the slope of the estimated regression equation.
d. Use the estimated regression equation to predict annual sales for a salesperson with nine years of experience.

Answer 1

Ans:

a)

b)

	experience(x)	Annual Sales,y	xy	x^2	y^2
1	1	132	132	1	17424
2	3	160	480	9	25600
3	4	145	580	16	21025
4	5	168	840	25	28224
5	6	168	1008	36	28224
6	8	180	1440	64	32400
7	10	188	1880	100	35344
8	11	218	2398	121	47524
9	11	193	2123	121	37249
10	13	229	2977	169	52441
Total	72	1781	13858	662	325455

slope,b=(10*13858-72*1781)/(10*662-72^2)=7.206

y-intercept,a=(1781-7.206*72)/10=126.22

Regression eqn:

y'=7.206x+126.22

c)

slope coefficient of 7,206,indicates that for each increment of experience(in years),there is 7.206 thousand of dollars increase in sales.

intercept of 126.22 means that when there is no experience i.e.x=0,annual sales=126.22 (in thousands)

d)

When x=9,

y'=7.206*9+126.22=191.074