Question

A sociologist is interested in the relation between x = number of job changes and y...

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 3 5 6 1 5 9 10 10 3
y (Salary in $1000) 38 34 31 32 32 38 43 37 40 33

In this setting we have ?x = 56, ?y = 358, ?x2 = 402, ?y2 = 12,960, and ?xy = 2079.

(a) Find x, y, 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 four decimal places.)

x =
y =
b =
? = +  x


(b) Draw a scatter diagram displaying the data. Graph the least-squares line on your scatter diagram. Be sure to plot the point (x, y).

Submission Data


(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) Test the claim that the population correlation coefficient ? is positive at the 5% level of significance. (Round your test statistic to three decimal places and your P-value to four decimal places.)

t =
P-value =


Conclusion

Reject the null hypothesis. There is sufficient evidence that ? > 0.Reject the null hypothesis. There is insufficient evidence that ? > 0.    Fail to reject the null hypothesis. There is sufficient evidence that ? > 0.Fail to reject the null hypothesis. There is insufficient evidence that ? > 0.


(e) 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

(f) Find Se. (Round your answer to two decimal places.)
Se =  

(g) Find a 95% confidence interval for the annual salary of an individual with x = 8 job changes. (Round your answers to two decimal places.)

lower limit     thousand dollars
upper limit     thousand dollars


(h) Test the claim that the slope ? of the population least-squares line is positive at the 5% level of significance. (Round your test statistic to three decimal places and your P-value to four decimal places.)

t =
P-value =

Homework Answers

Answer #1
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.658567891
R Square 0.433711668
Adjusted R Square 0.362925626
Standard Error 3.188240199
Observations 10
ANOVA
df SS MS F Significance F
Regression 1 62.28099548 62.28099548 6.127078986 0.03839229
Residual 8 81.31900452 10.16487557
Total 9 143.6
Coefficients Standard Error t Stat P-value Lower 95%
Intercept 31.09954751 2.149997363 14.46492356 5.10513E-07 26.1416447
x 0.839366516 0.339097744 2.475293717 0.03839229 0.057405715

a)

xbar =5.6

ybar = 35.8

b = 0.839366516 = 0.8394

y = 31.0995 + 0.8394 *x

b)

c)

r = 0.65856 = 0.6586

r^2 = 0.4337

hence

100* r^2 % = 43.37 % is explained

d)

t = 2.475

p-value= 0.03839/2 = 0.019195 = 0.0192

e)

y = 31.0995 + 0.8394 *x

= 31.0995 + 0.8394 *8 = 37.8147

f)

se = 3.18824 = 3.19

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