Question

10

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) Y (Salary in $1000) 6. 5 10 10 3 36 34 35 32 32 38 43 37 40 33 In this setting we have Ex = 58, Ey = 360, Ex = 422, Ey = 13,076, and Exy = 2163. (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.) х (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). У У 44 44 42 42 40 40 38- 38 36- 36 34 34 32 32 30L 30 10 10 4 4

Answer 1

Y, S.No XY 36 36.0000 1296.0000 216.00 34 2 3 9.0000 1156.0000 102.00 3 35 25.0000 1225.0000 175.00 1024.0000 192.00 32 36.0000 1024.0000 32 1.0000 32.00 190.00 38 25.0000 1444.0000 387.00 43 81.0000 1849.0000 10 37 100.0000 1369.0000 370.00 10 40 100.0000 1600.0000 400.00 10 3 33 9.0000 1089.0000 99.00 ΣΧ total 58.0000 ΣΥ. 360.00 ΣΧΥ 13076.00 422.00 2163.00 10.0000 n= X-zXIn 5.8000 Y=zY/n 36.0000 s,=N[Ex*-{zH)*InM{n-1)) = s,-Nlzy?-lzyjin)Min-1)= Cov=sxy= (zXY-(1XZY)/n)/(n-1)%3 r=Cov(Sx'Sy)= 3.0840 3.5901 8.3333 0.753

a)

X̅=ΣX/n =	5.80
Y̅=ΣY/n =	36.00

b=0.8762

ŷ =	30.9182+0.8762x

c)

y 44 42 40 38 36 34 32 30 10 6. 2.

d)

r=Cov/(Sx*Sy)=

0.753

coefficient of determination r2 =

0.566

56.6%

e)

test statistic t =

r*(√(n-2)/(1-r2))=

3.233

0.005 < P-value < 0.010

Reject the null hypothesis. There is sufficient evidence that p > 0.

e)

predicted value =

39.68

f)

Se =√(SSE/(n-2))=

2.51

g)

std error of confidence interval =				s*√(1+1/n+(x0-x̅)2/Sxx)=			2.8653
for 90 % confidence and 8degree of freedom critical t=							1.860
lower limit =		34.35
uppr limit =		45.01

h)

test statistic t =

r*(√(n-2)/(1-r2))=

3.233

0.005 < P-value < 0.010

Reject the null hypothesis. There is sufficient evidence that B > 0.

i)

std error of slope sb1 =				s/√SSx=		0.2710
for 90 % confidence and -2degree of freedom critical t=						1.8600
90% confidence interval =b1 -/+ t*standard error=					(0.372,1.38)
lower limit =		0.372
uppr limit =		1.380