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) 7 4 5 6 1 5 9 10 10 3 y (Salary in $1000) 38 32 34 32 32 38 43 37 40 33 Σx = 60; Σy = 359; Σx2 = 442; Σy2 = 13,023; Σxy = 2,234 (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 three decimal places.) x = y = b = ŷ = + x (b) Draw a scatter diagram for the data. Plot the least-squares line on your scatter diagram. WebAssign Plot WebAssign Plot WebAssign Plot WebAssign Plot (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 = 5 job changes, what does the least-squares line predict for y, the annual salary? (Round your answer to two decimal places.) thousand dollars

Answer 1

x bar = 60 / 10 = 6 .00

y bar = 359 / 10 = 35.90

y = 30.046 + 0.976 x

( b )

scatter diagram

( c )

correlation coefficient ( r )

r = 0.761

coefficient of determination ( r²) = ( 0.761 )² = 0.5791 = 57.9%

57.9%  of variation in y is explained by the least-squares model

( d )

Given x = 5 then

y = 30.046 + 0.976 ( 5 )

y = 34.926

y = 34.93