Question

Given the following data:

x	2	8	5	12	9
y	6	11	7	14	10

a) draw/graph a scatter plot.

b) by hand, find the correlation coefficient r.

c) by hand, find b0 and b1.

d) write the regression equation.

Answer 1

Solution(a)
Scatter plot can be constructed as follows

Solution(b)
Correlation coefficient r can be calculated as
Correlation coefficient = ((n*Xi*Yi)-(Xi*Yi))/sqrt(((n*Xi^2)-(Xi)^2))*((n*Yi^2)-(Yi)^2)))

X	Y	X^2	Y^2	XY
2	6	4	36	12
8	11	64	121	88
5	7	25	49	35
12	14	144	196	168
9	10	81	100	90
36	48	318	502	393

Correlation coefficient = ((5*393)-(36*48))/sqrt(((5*318)-(36*36))*((5*502)-(48*48))) = 237/sqrt(294*206) = 0.9630
Solution(c)
The slope of regression line b1 can be calculated as
Slope b1 = ((n*Xi*Yi)-(Xi*Yi))/((n*Xi^2)-(Xi)^2)) = ((5*393)-(36*48))/((5*318)-(36*36)) = 237/294 = 0.8061

The intercept of the regression line can be calculated as
Intercept b0 = ((Yi - Slope * Xi))/n = (48-0.8061*36)/5 = 18.98/5= 3.7959
Solution(d)
Regression equation can be written as
Y = b0+b1*X
Y = 3.7959 + 0.8061*X