You are the foreman of the Happy Cows cattle ranch in Colorado. A neighboring ranch has calves for sale, and you are going to buy some to add to the Happy Cows herd. How much should a healthy calf weigh?

Let \( o \) be the age of the calf (in weeks), and let \( y \) be the weight of the calf (in kilograms). To answer your question, you select a random sample of calves in Colorado and collect the data presented in the file Calves.xlsx. (You may download this file from the "Files" section of the Canvas course webpage).

Tasks:

a) Make a scatter diagram of these data.

b) According to the scatter diagram obtained in (a), would you say there seems to be a correlation between the age of the calf and the weight of the calf? Explain your reasoning clearly. Does it seem to be positive or negative?

c) Compute the correlation coefficient \( r \).

d) Does the value of \( r \) support your conclusion in (b)? Explain your reasoning clearly.

Note: You have to answer this question using the Excel commands shown in class. The answers to this question must be submitted in Excel.

Data for reference (for visualization purposes, not part of the question):

\[
\begin{align*}
X: & \quad 10, 18, 34, 30, 24, 25, 18, 18, 4, 10, 22, 34, 30, 35, 23, 1, 35, 4, 11, 3, 8, 9, 29, 27, 4, 4, 25, 13, 25, 36, 31, 15, 20, 14, 32 \\
Y: & \quad 78.1, 118.2, 176.4, 168.1, 137, 147.4, 118.7, 117.1, 61.6, 86.6, 131.8, 184.4, 165.4, 193.8, 135.8, 39.4, 182.6, 52.2, 93.4, 41.5, 71.5, 77.9, 172.8, 156.5, 47.8, 51.7, 140, 88.7, 149.1, 189.7, 169, 108.5, 125.1, 100.9, 168.3 \\
\end{align*}
\]

(Additional sets of data omitted for brevity)