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, Σx2 = 1420, Σy2 = 11.19, Σxy = 111.4, and r ≈ −0.956. (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 three 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 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 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 three decimal places. Round your answers for the percentages to one decimal place.) r2 = 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
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
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, Σx2 = 1420, Σy2 = 11.19, Σxy = 111.4, and
(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 answers for x and y to two decimal places. Round your answers for a and b to three decimal places.)
| x | = | |
| y | = | |
| = | + x |
| r2 = | |
| 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
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