Question

Asked Jul 18, 2019

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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).

x |
3 | 6 | 12 | 20 | 26 |

y |
60 | 95 | 140 | 160 | 189 |

(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 = 67,

x^{2} = 1265,

y = 644,

y^{2} = 93,546,
and

xy = 10,544.

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

As*x* increases from 3 to 26 months, does the value of *r* imply that *y* should tend to increase or decrease? Explain your answer.

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

low

moderate

strong

Would you say the correlation is positive or negative?

positive

negative

(c) Use a calculator to verify that

Compute

As

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

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

Step 1

**Part (a):**

The scatter diagram, along with the best fitted line (least-squares regression line) for the data is as follows:

Step 2

**Part (b):**

All the points fall very close to the straight line in the graph, in such a way, that as *x* increases, *y* also increases.

Thus, the correlation is **strong** and **positive**.

Step 3

**Part (c):**

Here, *x*, *x*2, *y*, *y*2, and *xy* are the sums of *X*, *X*2 *Y*, *Y*2, and *XY*, respectively.

Using calculator, it is verified that:

*x* = (3 + 6 + 12 + 20 + 26) = 67.

*x*2 = (32 + 62 + 122 + 202 + 262) = 1,265.

*y* = (60 + 95 + 140 + 160 + 189) = 644.

*y*2 = (602 + 952 + 1402 + 1602 + 1892) = 93,546.

*xy* = (3×60) + (6×95) + (12×140) + (20×160) + (26×189) = 10...

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