Question

# 3. A sales manager collected the following data on annual sales and years of experience. Salesperson...

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.

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

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