Question

1. For the data below (1) Determine the degree of relationship, and (2) the percent of variability accounted for. (3) Graph the data and (4) find the line of best fit (find the equation of the line and draw it on the graph).

X	Y
1	2
2	3
4	2
5	6
8	7

Answer 1

Ans:

	x	y	xy	x^2	y^2
1	1	2	2	1	4
2	2	3	6	4	9
3	4	2	8	16	4
4	5	6	30	25	36
5	8	7	56	64	49
Total	20	20	102	110	102

a)

correlation coefficient,r=(5*102-20*20)/SQRT((5*110-20^2)*(5*102-20^2))=0.856

There is strong positive relationship between x and y.

b)

percent of variability accounted for,R^2=0.856^2=0.733 or 73.3%

c)

d)

slope,b=(5*102-20*20)/(5*110-20^2)=0.733

intercept,a=(20-0.7333*20)/5=1.0667

Regression equation:

y'=0.7333 x+1.0667