Question

A sales manager collected the following data on annual sales for new customer accounts and the number of years of experience for a sample of salespersons.

Saleperson Year of experience Annual Sales ($1000)
1 1 80
2 3 97
3 4 92
4 4 102
5 6 103
6 8 111
7 10 119
8 10 123
9 11 117
10 13 136

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 the years of experience.
c. Use the estimated regression equation to predict annual sales for a salesperson with 9 years of experience.

Answer 1

A) Scatter diagram is attached

B) y = 80 + 4x

C) $116,000

Explanation:

A) I have attached the scatter diagram of Annual sales on the y-axis against years of experience on the X-axis

B) To develop an estimated regression equation, we need to find;

ΣX, ΣY, Σ(XY), ΣX²

Let X be the years of experience and let Y be the annual sales.

Thus, ΣX = 1+3+4+4+6+8+10+10+11+13 = 70

ΣY = 80+97+92+102+103+111+119+123+117+136 = 1080

ΣXY = (1x80) +(3x97)+(4x92)+(4x102)+(6x103)+(8x111)+(10x119)+(10x123)+(11x117)+(13x136) = 8128

ΣX² = 1²+3²+4²+4²+6²+8²+10²+10²+11²+13² = 632

In regression analysis ;

a = [{(ΣY)(ΣX²)} – {(ΣX)(ΣXY)}] / [{(n)(ΣX²)} - (ΣX)²]

And b= [{(n)(ΣXY)} – {(ΣX)(ΣY)}] / [{(n)(ΣX²)} - (ΣX)²]

Thus, plugging in the relevant values;

a = [{(1080)(632)} – {(70)(8128)}] / [{(10)(632)} - (70)²]

a=113600/1420 = 80

b = [{(10)(8128)} – {(70)(1080)}] / [{(10)(632)} - (70)²] = 4

So,a = 80 and b=4

Regression formula says that;

y = a + bx

Thus;

y = 80 + 4x

C) since x represents the years of experience, thus we can replace x with 9 in the above regression equation to obtain;

y = 80 + 4(9) = 116

Since y is in thousand dollars, thus;

y = 116 x 1000 = $116,000