Question

How much should a healthy Shetland pony weigh? Let x be the age of the pony (in months), and let y be the average weight of the pony (in kilograms).

x3,6,12,17,23

y60,95,140,168,177

(a) Make a scatter diagram of the data and visualize the line you think best fits the data.

(b) Would you say the correlation is low, moderate, or strong?

Would you say the correlation is positive or negative?

    

(c)

Use a calculator to verify that x = 61,

x² = 1007,

y = 640,

y² = 91,778,

and xy = 9,357.

Compute r. (Round your answer to three decimal places.)

As x increases from 3 to 23 months, does the value of r imply that y should tend to increase or decrease? Explain your answer.

Given our value of r, y should tend to remain constant as x increases.

Given our value of r, we can not draw any conclusions for the behavior of y as x increases.

Given our value of r, y should tend to increase as x increases.

Given our value of r, y should tend to decrease as x increases.

Answer 1

a.

b. If we draw line through the points, mostly all will fall on the line

Hence it is strong

And as it is increasing trend so it is positive

c.

	x	y	x^2	y^2	xy
	3	60	9	3600	180
	6	95	36	9025	570
	12	140	144	19600	1680
	17	168	289	28224	2856
	23	177	529	31329	4071
Total	61	640	1007	91778	9357

X Values
∑ = 61
Mean = 12.2
∑(X - M_x)² = SS_x = 262.8

Y Values
∑ = 640
Mean = 128
∑(Y - M_y)² = SS_y = 9858

X and Y Combined
N = 5
∑(X - M_x)(Y - M_y) = 1549

R Calculation
r = ∑((X - M_y)(Y - M_x)) / √((SS_x)(SS_y))

r = 1549 / √((262.8)(9858)) = 0.962

As we see r is positive so slope is also positive, and hence as x increases y will increase

Given our value of r, y should tend to increase as x increases.