Question

 Let X be the weight of bikes (Ibs) and Y be the cost of bikes ($) as in the table below. Find the sample correlation coefficient and describe; find prediction equation and predict the cost of a bike with the weight of 30 Ibs.

Answer 1

X	Y	XY	X^2	Y^2
24	740	17760	576	547600
32	420	13440	1024	176400
35	400	14000	1225	160000
22	880	19360	484	774400
40	250	10000	1600	62500
28	610	17080	784	372100

From the above table and formula we get the value are as;

n	6
sum(XY)	91640.00
sum(X)	181.00
sum(Y)	3300.00
sum(X^2)	5693.00
sum(Y^2)	2093000.00
Numerator	-47460.00
Denominator	48272.10
r	-0.9832

Sample correlation coefficient = -0.9832

b = -33.9728
a = 1574.8461

Prediction equation = 1574.8461 - 33.9728x

when x = 30

y = 1574.8461 - 33.9728*30

= 555.6621