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 1.5 1.5 1.4 1.0 0.7 Complete parts (a) through (e), given Σx = 90, Σy = 7.9, Σx2 = 1420, Σy2 = 11.19, Σxy = 111.4, and r ≈ −0.956. (c) Find x, and y. Then find the equation of the least-squares line = a + bx. (Round your answers for x and y to two decimal places. Round your answers for a and b to three decimal places.) x = y =   = + x  (e) 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? (Round your answer for r2 to three decimal places. Round your answers for the percentages to one decimal place.) r2 =   explained     % unexplained     % (f) Suppose a pharmaceutical company has 14 different research programs. What does the least-squares equation forecast for y = mean number of patents per program? (Round your answer to two decimal places.) patents per program

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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 1.5 1.5 1.4 1.0 0.7

Complete parts (a) through (e), given Σx = 90, Σy = 7.9, Σx2 = 1420, Σy2 = 11.19, Σxy = 111.4, and

r ≈ −0.956.
(c) Find x, and y. Then find the equation of the least-squares line = a + bx. (Round your answers for x and y to two decimal places. Round your answers for a and b to three decimal places.)
x =
y =
  = + x
 
(e) 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? (Round your answer for r2 to three decimal places. Round your answers for the percentages to one decimal place.)
r2 =  
explained     %
unexplained     %

(f) Suppose a pharmaceutical company has 14 different research programs. What does the least-squares equation forecast for y = mean number of patents per program? (Round your answer to two decimal places.)
patents per program

 

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