Question

The general manager of a chain of furniture stores believes that experience is the most important factor in determining the level of success of a salesperson. To examine this belief she records last month’s sales (in $1,000s) and the years of experience of 10 randomly selected salespeople. These data are listed below.

Salesperson	Years of Experience	Sales ($1,000s)
1	0	7
2	2	9
3	10	20
4	3	15
5	8	18
6	5	14
7	12	20
8	7	17
9	20	30
10	15	25

(a) Given the following data, calculate β₁, β₀ and determine the regression line (hint #1:calculate β₁ first and use y̅ and x̅ in the linear formula to find β₀; hint #2: the slope coefficient measures the covariance of x and y accounted for by the variance of x)

n = 10             x̅ = 8.2           y̅ = 17.5       s_x² = 34.76      s_y² = 42.65      s_xy = 37.6

(b) Interpret the meaning of the β₁ or slope coefficient_.

(c) Based on the regression equation and the original raw data, with 10 years of

experience find the predicted level of sales and compare it to the actual level of sales.

Answer 1

scution :- given data 2:10 x =8-2 99.5 S's = 34.76 s'y = 42.65 Szy - 37.6 Required to find requession Equation: Regussion equation y = Bo + Bise where ßi= say St. 37.6 34.76 Bi= 1082 = Bot Bloc Boy - Bia : 17.5 -1-082x8-2 Bo : 8-628 Pegression Equalio y : 8-628 +1-08200 b) - in the above equation slope B1 = 1.082. slope au the units y variable | unit of the x variable + slope is the ratio o change of yl change in x. → This indicates that if years al espaience incuases by 1

The sales will get increased here given by 1.082 c) 8:10 we have f=8.628 +1-082x10 7=19.4487 for actual data , we get for I:10: y is equal 20 from above · regression we get 19-448 . there is Erroy is 0.552. → which is quite how this suggesting that our estimates ou good.