Question

4. The data set below shows the length of service (in years)and salaries in thousands of dollars) for 10 randomly selected employees. Length of service, 2 Salary, y 0.5 2 4 6 8 10 .75 39 41 41 40.5 42 41 40 1 6 8 38 41 42 (a) Construct a scatter plot for the data showing the regression line. (b) Find the equation of the regression line for the data. (c) Find the value of the correlation coefficient, r. Parts d to g. Use the regression equation to predict the value of y for the given value of x. If it is not meaningful to do that, explain why. (d) x = 3 (e) x = 4.5 (f) x = 8.5 (g) x = 15

Answer 1

X Y XY XX YY 39 19.5 0.25 1521 2 41 82 1681 4 41 164 16 1681 6 40.5 243 36 1640.25 8 42 336 64 1764 10 41 410 100 1681 0.75 40 30 0.5625 1600 1 38 38 1 1444 6 41 246 36 1681 8 42 336 64 1764 ΣΧ = 46.25.ΣΥ = 405.5 ΣΧΥ = 1904.5,ΣΧΧ = 321.8125,ΣΥΥ = 16457.25

a)

42.0 41.5 41.0- 40.5 40.0 39.5 39.0 - 38.5 38.0 - 3 6 8 10

b)

b)3 = + br ΣΥ * ΣXX -ΣΧ * ΣΧΥ ηΣ Χ2 – (ΣΧ)2 405.5 * 321.8125 - 46.25 * 1904.5 - 39,3043 " 10 * 321.8125 - 46.25 * 46.25 ηΣΧΥ - ΣΧ *ΣΥ = ηΣ x2 – (ΣΧ)2 10 και 1904.5 - 46.25 * 405.5 10 * 321.8125 - 46 25 ΔΕ 950.2693 Ο = 39.3043 + 0.2693r 6 2 10*

ηΣΧΥ - ΣΧ* ΣΥ ΣΧ2 – (ΣΧ)2) (nΣΥ2 – (ΣΥ)2) 10 και 1904.5 – 46.25 * 405.5 =R 0.7418 V(10 * 321.8125 - 46.252) (10 * 16457.25 – 405.52) γ =

d) x = 3

y = 39.3043 + 0.2693(3.0)

y = 40.1122

e)

x = 4.5

y = 39.3043 + 0.2693(4.5)

y = 40.5161

f)

x = 8.5

y = 39.3043 + 0.2693(8.5)

y = 41.5934

g)

x = 15

= 39.3043 + 0.2693(15.0)

= 43.3438