A social scientist would like to analyze the relationship between educational at

Question

A social scientist would like to analyze the relationship between educational attainment and salary. He collects the following sample data, where Education refers to years of higher education and Salary is the individual's annual salary (in $1,000s): Education Salary 6 40 53 80 4270 50 110 38 a. Find the sample regression equation for the model. Salary 0 + |Education + . (Round intermediate calculations to at least 4 decimal places. Enter your answers in thousands rounded to 2 decimal places.) Education b. Interpret the coefficient for Education O As Education increases by 1 unit, an individual's annual salary is predicted to decrease by $9,380 O As Education increases by 1 unit, an individual's annual salary is predicted to decrease by $8,590 O As Education increases by 1 unit, an individual's annual salary is predicted to increase by $9,380 O As Education increases by 1 unit, an individual's annual salary is predicted to increase by $8,590 c. What is the predicted salary for an individual who completed 7 years of higher education? (Round intermediate coefficient values to 2 decimal places and final answer, in dollars, to the nearest whole number.) Salary

Explanation / Answer

a.

Line of Regression Y on X i.e Y = bo + b1 X

calculation procedure for regression

mean of X = X / n = 4

mean of Y = Y / n = 60.375

(Xi - Mean)^2 = 42

(Yi - Mean)^2 = 4355.87

(Xi-Mean)*(Yi-Mean) = 394

b1 = (Xi-Mean)*(Yi-Mean) / (Xi - Mean)^2

= 394 / 42

= 9.381

bo = Y / n - b1 * X / n

bo = 60.375 - 9.381*4 = 22.8512

value of regression equation is, Y = bo + b1 X

Y'=22.8512+9.381* X

b.

As Education increases by 1 unit, an individual’s annual salary is predicted to increase by $9.380

c.

Y'=22.8512+9.380* 7 = 88.5112

X Y (Xi - Mean)^2 (Yi - Mean)^2 (Xi-Mean)*(Yi-Mean) 3 40 1 415.1406 20.375 4 53 0 54.3906 0 6 80 4 385.1406 39.25 2 42 4 337.6406 36.75 5 70 1 92.6406 9.625 4 50 0 107.6406 0 8 110 16 2462.6406 198.5 0 38 16 500.6406 89.5

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