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.x101214161820y1.71.71.51.41.00.7Complete parts e and f please. given Σx = 90, Σy = 8, Σx2 = 1420, Σy2 = 11.48, Σxy = 112.8, and r ≈ −0.9542.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 %(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

e) r ≈ −0.9542. The coefficient of determination r2: r^2=(-0.9542)^2=0.9105 The percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line is, r^2=0.9105*100%=91.05% The percentage is unexplained is, 1-r2=1-0.9105=0.0895*100%=8.95%. r2 = 0.9105 explained 91.05 % unexplained 8.95%f From the previous parts, The regression equation is, y^=2.876-0.103x. Suppose a pharmaceutical company has 18 different research programs. The least-squares equation forecast for y = mean number of patents per program is, y^=2.876-(0.103*18) = 1.02 patents per program

Answered: Let x be the number of different…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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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	1.7	1.7	1.5	1.4	1.0	0.7

Complete parts e and f please. given Σx = 90, Σy = 8, Σx² = 1420, Σy² = 11.48, Σxy = 112.8, and

r ≈ −0.9542.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	%

(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

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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