Chapter 4.2, Problem 16P

Research: Patents The following data are based on information from the Harvard Business Review (Vol. 72, No. 1). Let x be the number of different research programs, and let y be the mean number of patents per program. As in any business, a company can spread itself too thin. For example, too many research programs might lead to a decline in overall research productivity. The following data are for a collection of pharmaceutical companies and their research programs:

x	10	12	14	16	18	20
y	1.8	1.7	1.5	1.4	1.0	0.7

Complete parts (a) through (e), given $\Sigma x=90,\Sigma y=8.1,\Sigma x^2=1420,\Sigma y^2=11.83,\Sigma xy=113.8,\text{ and }r\approx -\text{0}\text{.973}$.

(f) Suppose a pharmaceutical company has 15 different research programs. What does the least-squares equation forecast for y = mean number of patents per program?