Chapter 9.2, Problem 8P

For Problems 7–18, please do the following.

1. (a) Draw a scatter diagram displaying the data.
2. (b) Verify the given sums ∑x, ∑y, ∑x², ∑y², and ∑xy and the value of the sample correlation coefficient r.
3. (c) Find $\bar{x}$, $\bar{y}$, a, and b. Then find the equation of the least-squares line $\hat{y}=a+bx$.
4. (d) Graph the least-squares line on your scatter diagram. Be sure to use the point $\left(\bar{x},\bar{y}\right)$ as one of the points on the line.
5. (e) Interpretation Find the value of the coefficient of determination r². What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? What percentage is unexplained?

8. Ranching: Cattle You are the foreman of the Bar-S cattle ranch in Colorado. A neighboring ranch has calves for sale, and you are going to buy some to add to the Bar-S herd. How much should a healthy calf weigh? Let x be the age of the calf (in weeks), and let y be the weight of the calf (in kilograms). The following information is based on data taken from The Merck Veterinary Manual (a reference used by many ranchers).

Complete parts (a) through (e), given ∑x = 92, ∑y = 617, ∑x² = 2338, ∑y² = 82,389, ∑xy = 13,642, and r ≈ 0.998.

1. (f) The calves you want to buy are 12 weeks old. What does the least-squares line predict for a healthy weight?