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:

Σx = 60; Σy = 359; Σx² = 442; Σy² = 13,013; Σxy = 2231

(a) Draw a scatter diagram for the data.

(b) Find x, y, b, and the equation of the least-squares line. Plot the line on the scatter diagram of part (a).

(c) Find the sample correlation coef­ficient r and the coeffi­cient of determination. What percentage of variation in y is explained by the least-squares model?

(d) Test the claim that the population correlation coef­ficient r is positive at the 5% level of signifi­cance.

(e) If someone had x = 2 job changes, what does the least-squares line predict for y, the annual salary?

(f) Verify that S_e ≈ 2.56.

(g) Find a 90% con­fidence interval for the annual salary of an individual with x = 2 job changes.

(h) Test the claim that the slope b of the population least-squares line is positive at the 5% level of signifi­cance.

(i) Find a 90% confi­dence interval for β and interpret its meaning.

Transcribed Image Text:

x (Number of job changes) 4 75615 9 0 0 3 y (Salary in S1000) 33 37 34 32 32 38 43 37 40 33