A sociologist is interested in the relation between x = number of job changes an

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 = 62, y = 362, x2 = 462, y2 = 13,220, and xy = 2314.

(a) Draw a scatter diagram for the data.

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

Plot the line on the scatter diagram of part (a).

(c) Find the sample correlation coefficient r and the coefficient of determination r2. (Round your answers to three decimal places.)

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 = 2 job changes, what does the least-squares line predict for y, the annual salary? (Round your answer to two decimal places.)
thousand dollars

x (number of job changes) 5 7 6 6 1 5 9 10 10 3 y (Salary in $1000) 34 36 37 32 32 38 43 37 40 33 ADOBE" FLASH PLAYER

Explanation / Answer

from above data

xbar =6.20

ybar=36.20

b1=Sxy/SSx =0.897

b0=30.639

yhat=30.639+0.897x

bottom right curve is correct

r=0.735

r2 =0.540

54%

d)Yhat =0.897*2+30.639 =32.43

please revert for doubt

x y (X-Xbar)^2 (Y-Ybar)^2 (X-Xbar)(Y-Ybar) Yi' (Y-Yi')^2 5.00 34.000 1.44 4.84 68.64 35.12371 1.26272718 7.00 36.000 0.64 0.04 5.84 36.91753 0.84185354 6.00 37.000 0.04 0.64 -24.16 36.02062 0.95918801 6.00 32.000 0.04 17.64 126.84 36.02062 16.1653736 1.00 32.000 27.04 17.64 147.84 31.53608 0.21521947 5.00 38.000 1.44 3.24 -56.16 35.12371 8.27303645 9.00 43.000 7.84 46.24 -184.96 38.71134 18.3926028 10.00 37.000 14.44 0.64 -20.96 39.60825 6.80295462 10.00 40.000 14.44 14.44 -99.56 39.60825 0.15347008 3.00 33.000 10.24 10.24 106.24 33.3299 0.10883197 Total 62.00 362.00 77.60 115.60 69.60 53.1752577 mean 6.20 36.20 SSx Ssy Sxy

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