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
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
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section4.5: Correlation And Causation
Problem 24PFA
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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 (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
| 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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