Question

A random sample of 11 employees produced the following data, where x is the consecutive hours worked, and y is current employee satisfaction (out of a maximum of 100 points). The data are presented below in the table of values.

x	y
4	86
5	76
7	92
8	71
10	63
11	70
12	58
14	57
16	49
18	45
19	46

What is the equation of the regression line?

ˆ=−3.864x+97.1

yˆ=−3.864x+87.3

yˆ=−2.864x+97.1

yˆ=−1.864x+87.3

Answer 1

X	Y	XY	X^2	Y^2
4	86	344	16	7396
5	76	380	25	5776
7	92	644	49	8464
8	71	568	64	5041
10	63	630	100	3969
11	70	770	121	4900
12	58	696	144	3364
14	57	798	196	3249
16	49	784	256	2401
18	45	810	324	2025
19	46	874	361	2116

From the above table and formula we get the value are as:

n	11
sum(XY)	7298.00
sum(X)	124.00
sum(Y)	713.00
sum(X^2)	1656.00
sum(Y^2)	48701.00

b	-2.864
a	97.1

ycap = a +bx

Ycap = 97.1 - 2.864x

yˆ=−2.864x+97.1