Answered: Let x be the number of different…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

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	1.7	1.7	1.5	1.4	1.0	0.7

Complete parts (a) through (e), given Σx = 90, Σy = 8, Σx² = 1420, Σy² = 11.48, Σxy = 112.8, and

r ≈ −0.9542.

(a) Draw a scatter diagram displaying the data.

(b) Verify the given sums Σx, Σy, Σx², Σy², Σxy, and the value of the sample correlation coefficient r. (Round your value for r to four decimal places.)

Σx =
Σy =
Σx² =
Σy² =
Σxy =
r =

(c) Find x, and y. Then find the equation of the least-squares line = a + bx. (Round your answer to four decimal places.)

x	=
y	=
	=	+ x

(d) Graph the least-squares line. Be sure to plot the point (x, y) as a point on the line.

(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 four decimal places. Round your answers for the percentages to two decimal place.)

r² =
explained	%
unexplained	%

(f) Suppose a pharmaceutical company has 18 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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