The following table presents the mean cost of a hospital stay, in \(\$ 1000\) s, and the number of hospital stays, in millions, in the United States for each of 15 years.

a. Compute the least-squares line for predicting the number of stays \((y)\) from the cost \((x)\).

b. Compute the coefficient of determination \(r^{2}\).

c. Construct a residual plot. Does the relationship appear to be linear?

d. True or false: If the coefficient of determination is large, the relationship must be linear.

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Cost 9.8 10.3 10.3 10.6 11.3 11.8 12.5 13.7 Number 34.3 34.1 34.2 34.2 34.7 34.9 35.5 36.4 Cost 15.0 17.3 19.7 20.5 22.3 24.0 26.1 Number 37.2 37.8 38.2 38.7 39.2 39.5 39.5