8. 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 th many research programs might lead to a decline in overall research productivity. The following data are for a collection of pharmaceutical companies and their rese 10 y 1.8 12 1.5 14 16 20 1.0 0.7 18 1.7 1.4 n USE SALT Complete parts (a) through (e), given Ex = 90, Ey = 8.1, Ex² = 1420, Ey? = 11.83, Exy = 114.2, and r= -0.9223. (c) Find x, and y. Then find the equation of the least-squares line ŷ= a + bx. (Round your answer to four decimal places.)

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**Question 8:**

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; 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 activities:

| \( x \) | 10 | 12 | 14 | 16 | 18 | 20 |
|---|---|---|---|---|---|---|
| \( y \) | 1.8 | 1.5 | 1.7 | 1.4 | 1.0 | 0.7 |

Complete parts (a) through (e), given \( \Sigma x = 90 \), \( \Sigma y = 8.1 \), \( \Sigma x^2 = 1420 \), \( \Sigma y^2 = 11.83 \), \( \Sigma xy = 114.2 \), and \( r = -0.9223 \).

(c) Find \( \bar{x} \) and \( \bar{y} \). Then find the equation of the least-squares line \( \hat{y} = a + bx \). (Round your answer to four decimal places.)
Transcribed Image Text:**Question 8:** 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; 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 activities: | \( x \) | 10 | 12 | 14 | 16 | 18 | 20 | |---|---|---|---|---|---|---| | \( y \) | 1.8 | 1.5 | 1.7 | 1.4 | 1.0 | 0.7 | Complete parts (a) through (e), given \( \Sigma x = 90 \), \( \Sigma y = 8.1 \), \( \Sigma x^2 = 1420 \), \( \Sigma y^2 = 11.83 \), \( \Sigma xy = 114.2 \), and \( r = -0.9223 \). (c) Find \( \bar{x} \) and \( \bar{y} \). Then find the equation of the least-squares line \( \hat{y} = a + bx \). (Round your answer to four decimal places.)
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