Question

The age x of a pony (in months) and the weight y (in kg) is given in the following pairs (x,y):

(3,60), (6,95), (12,140), (18,170), (24,185)

(that is, at 3 months it weighed 60 kg, at 6 months it weighed 95 kg, etc.)

a) Find the value of r for this data.

b) Is there strong, moderate or weak correlation? Is this positive or negative?

c) Find the least squares line and use it to predict the weight of the pony at age x=15 months.

Question 1 options:

Answer 1

a)

The formula of r is

n = 5

	x	y	xy	x^2	y^2
	3	60	180	9	3600
	6	95	570	36	9025
	12	140	1680	144	19600
	18	170	3060	324	28900
	24	185	4440	576	34225
Total	63	650	9930	1089	95350

b) There is a strong correlation.

There is a positive correlation.

c) We have to find the least squares line.

The line is y = a + b*x

Here a is intercept and b is the slope.

= 12.6

= 130

	x	y	xy	x^2
	3	60	180	9
	6	95	570	36
	12	140	1680	144
	18	170	3060	324
	24	185	4440	576
Total	63	650	9930	1089

y = 55.7317 + 5.8943*x

x = 15

y = 55.7317 + 5.8943*15 = 144.1463