#16 Research: Patents The following data are based on information from the Harvard Business Review. Let x be the number 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 1.8 1.7 1.5 1.4 1.0 0.7 (a) Draw a scatter diagram displaying the data. (b) Verify the given Ex = 90, Ey = 8.1, Ex? = 1420, Ey² = 11.83, Exy = 113.8, and r = -0.973 %3D (c) Find x, y,a, and b. Then find the equation of the least-squares line ŷ = a + bx. (d) Graph the least-squares line on your scatter diagram. Be sure to use the point (x,y) as one of the points 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? (f) Suppose a pharmaceutical company has 15 different research programs, what does the least-squares equation forecast for y = mean number of patents per program?

#16 Research: Patents The following data are based on information from the Harvard Business Review. Let x be the number 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 1.8 1.7 1.5 1.4 1.0 0.7 (a) Draw a scatter diagram displaying the data. (b) Verify the given Ex = 90, Ey = 8.1, Ex? = 1420, Ey² = 11.83, Exy = 113.8, and r = -0.973 %3D (c) Find x, y,a, and b. Then find the equation of the least-squares line ŷ = a + bx. (d) Graph the least-squares line on your scatter diagram. Be sure to use the point (x,y) as one of the points 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? (f) Suppose a pharmaceutical company has 15 different research programs, what does the least-squares equation forecast for y = mean number of patents per program?

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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