Question

Data from a small bookstore are shown in the accompanying table. The manager wants to predict Sales from Number of Sales People Working. Complete parts a through h below.

Number of sales people working	Sales​ (in $1000)
3	10
4	11
5	13
9	15
11	18
11	20
12	20
14	23
17	23
20	25
x overbar x=10.6	y overbar y=17.8
​SD(x)=5.56	​SD(y)=5.31

​a) Find the slope​ estimate, b1.

b1=???? ​(Round to two decimal places as​ needed.)

Answer 1

Solution:

The formula for slope is given as below:

Slope = b₁ = r*(S_y/S_x)

We are given S_y = 5.31

And S_x = 5.56

Now, we have to find the value for the correlation coefficient r. The formula for the correlation coefficient is given as below:

Correlation coefficient = r = [n∑xy - ∑x∑y]/sqrt[(n∑x^2 – (∑x)^2)*(n∑y^2 – (∑y)^2)]

The calculation table for the correlation coefficient is given as below:

.S no.	X	Y	XY	X^2	Y^2
1	3	10	30	9	100
2	4	11	44	16	121
3	5	13	65	25	169
4	9	15	135	81	225
5	11	18	198	121	324
6	11	20	220	121	400
7	12	20	240	144	400
8	14	23	322	196	529
9	17	23	391	289	529
10	20	25	500	400	625
Total	106	178	2145	1402	3422

Correlation coefficient = r = 0.971733 Correlation coefficient = r = [10*2145 – 106*178]/sqrt[(10*1402– 106*106)*(10*3422 – 178*178)]

Slope = b₁ = r*(S_y/S_x)

Slope = b₁ = 0.971733*(5.31/5.56) = 0.928039

Required answer: b₁ = 0.928039