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...

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, Σx
²
= 1420, Σy
²
= 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
r
². 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
r
²
to three decimal places. Round your answers for the percentages to one decimal place.)

r ² =
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

Jun 01, 2022

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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...

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