Question

The distance traveled in an hour by a Kentucky Horse rider is –1 miles plus 7 miles per hour on gravel (Distance = 7 * hours – 2). The correlation coefficient between distance and miles is

Answer 1

the correlation coefficient between distace and time will be 1.

why?

because they are linearly related.

lets take an example,

time(X)	distance(Y)	x=X-6	y=Y-40	xy	x^2	y^2
1	5	-5	-35	175	25	1225
4	26	-2	-14	28	4	196
5	33	-1	-7	7	1	49
6	40	0	0	0	0	0
9	61	3	21	63	9	441
12	82	6	42	252	36	1764
5	33	-1	-7	7	1	49
mean of X=6	mean of Y=40			sum of xy=532	sum of x^2=76	sum of y^2=3724

putting the values well get r=1