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)
|
4
|
7
|
5
|
6
|
1
|
5
|
9
|
10
|
10
|
3
|
|
y (Salary in $1000)
|
33
|
37
|
34
|
32
|
32
|
38
|
43
|
37
|
40
|
33
|
(a) Draw a scatter diagram displaying the data.
(b) Find the equation of least -squares line and plot the line on the scatter diagram of part (a)
(c) Find the correlation coefficient r. Find the coefficient of determination r². What percentage of variation in y is explained by the variation in x and the least-squares model?
Σx = 60; Σy = 359; Σx² = 442; Σy² = 13,013; and Σxy = 2231
(d) If someone had x = 2 job changes, what does the least-squares line predict for y, the annual salary?