Chapter 9.2, Problem 13P

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?

13. Income: Medical Care Let x be per capita income in thousands of dollars. Let y be the number of medical doctors per 10,000 residents. Six small cities in Oregon gave the following information about x and y (based on information from Life in America’s Small Cities by G. S. Thomas, Prometheus Books).

Complete parts (a) through (e), given ∑x = 53, ∑y = 83.7, ∑x² = 471.04, ∑y² = 1276.83, ∑xy = 755.89, and r ≈ 0.934.

1. (f) Suppose a small city in Oregon has a per capita income of 10 thousand dollars. What is the predicted number of M.D.s per 10,000 residents?