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	3	5	6	1	5	9	10	10	3
y (Salary in $1000)	35	36	37	32	32	38	43	37	40	33

Σx = 58; Σy = 363; Σx² = 422; Σy² = 13,289; Σxy = 2,173

(a) Find x bar, y-bar, b, and the equation of the least-squares line. (Round your answers for x and y to two decimal places. Round your least-squares estimates to three decimal places.)

(b) Draw a scatter diagram for the data. Plot the least-squares line on your scatter diagram.

(c) Find the sample correlation coefficient r and the coefficient of determination. (Round your answers to three decimal places.)

r =
r2 =

What percentage of variation in y is explained by the least-squares model? (Round your answer to one decimal place.)
%

(d) If someone had x = 9 job changes, what does the least-squares line predict for y, the annual salary? (Round your answer to two decimal places.)

Answer 1

Solution: We can use the excel regression data analysis tool to find the answer to the given questions. The excel output is given below:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.690092023
R Square	0.476227
Adjusted R Square	0.410755375
Standard Error	2.70912701
Observations	10
ANOVA
	df	SS	MS	F	Significance F
Regression	1	53.38504673	53.38504673	7.27379228	0.027200241
Residual	8	58.71495327	7.339369159
Total	9	112.1
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	31.71962617	1.902167291	16.67551867	1.69133E-07	27.33322053	36.1060318
x (number of job changes)	0.789719626	0.292814436	2.6969969	0.027200241	0.114488327	1.464950926

(a) Find x bar, y-bar, b, and the equation of the least-squares line. (Round your answers for x and y to two decimal places. Round your least-squares estimates to three decimal places.)

Answer:

The equation of the least-squares line is:

(b) Draw a scatter diagram for the data. Plot the least-squares line on your scatter diagram.

(c) Find the sample correlation coefficient r and the coefficient of determination. (Round your answers to three decimal places.)

r =	0.690
r2 =	0.476

What percentage of variation in y is explained by the least-squares model? (Round your answer to one decimal place.)
47.6%

(d) If someone had x = 9 job changes, what does the least-squares line predict for y, the annual salary? (Round your answer to two decimal places.)

Answer: