Question

A sociologist is interested in the relation between x = number of job changes and y = annual salary (in thousands of dollars) for people living in the Nashville area. A random sample of 10 people employed in Nashville provided the following information.

x (number of job changes)	6	5	4	6	1	5	9	10	10	3
y (Salary in $1000)	37	34	35	32	32	38	43	37	40	33

In this setting we have Σx = 59, Σy = 361, Σx² = 429, Σy² = 13,149, and Σxy = 2202.

If someone had x = 8 job changes, what does the least-squares line predict for y, the annual salary? (Round your answer to two decimal places.)
thousand dollars

Answer 1

Solution =

X	Y	XY	X^2	Y^2
6	37	222	36	1369
5	34	170	25	1156
4	35	140	16	1225
6	32	192	36	1024
1	32	32	1	1024
5	38	190	25	1444
9	43	387	81	1849
10	37	370	100	1369
10	40	400	100	1600
3	33	99	9	1089

n	10
sum(XY)	2202.00
sum(X)	59.00
sum(Y)	361.00
sum(X^2)	429.00
sum(Y^2)	13149.00
Numerator	721.00
Denominator	972.48
r	0.7414
r square	0.5497
Xbar(mean)	5.9000
Ybar(mean)	36.1000
SD(X)	1.7078
SD(Y)	2.2852
b	0.8912
a	30.8418

The least-squares line predict for y,

Given , x = 8

= a + bx

=  30.8418 + ( 0.8912 * 8 )

  = 37.97

Answer :   = 37.97