Question

1)      A personal director is interested in studying the relationship (if any) between age and salary. Sixteen employees are randomly selected and their age and salary are recorded.

AGE AND SALARY
AGE	SALARY (in Thousands of $)
25	$22
55	$45
27	$43
30	$30
22	$24
33	$53
19	$18
45	$38
49	$39
37	$45
62	$60
40	$35
35	$34
29	$30
58	$73
52	$42

a)      Plot the data points on a scatterplot.

b)      Determine the correlation coefficient   

c)       Describe the relationship indicated by the correlation coefficient and the scatterplot.

d)      If there is a linear relationship, find the equation of the line of regression

e)      Graph the line of regression on the same axes where you constructed the scatterplot in (a) above

f)       Use either your line of regression or the equation of the line of regression to predict salaries for Age = 50 and Age = 70.

Answer 1

a.

b.

X Values
∑ = 618
Mean = 38.625
∑(X - Mx)2 = SSx = 2715.75

Y Values
∑ = 631
Mean = 39.438
∑(Y - My)2 = SSy = 3045.938

X and Y Combined
N = 16
∑(X - Mx)(Y - My) = 2216.625

R Calculation
r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))

r = 2216.625 / √((2715.75)(3045.938)) = 0.7707

c. As we see that there is increasing trend and value is near 1 so there is strong positive correlation between x and y.

d.

Sum of X = 618
Sum of Y = 631
Mean X = 38.625
Mean Y = 39.4375
Sum of squares (SSX) = 2715.75
Sum of products (SP) = 2216.625

Regression Equation = ŷ = bX + a

b = SP/SSX = 2216.63/2715.75 = 0.8162

a = MY - bMX = 39.44 - (0.82*38.63) = 7.9114

ŷ = 0.8162X + 7.9114

e.

f. For x=50, ŷ = (0.8162*50)+ 7.9114=48.7214

For x=70, ŷ = (0.8162*70)+ 7.9114=65.0454