Let x be per capita income in thousands of dollars. Let y be the number of medical doctors per 10,000 residents. Six small cities in Oregon gave the following information about x and y. x 8.7 9.2 9.8 8.0 8.3 8.7 y 9.9 18.1 20.2 10.2 11.4 13.1 Complete parts (a) through (e), given Σx = 52.7, Σy = 82.9, Σx2 = 464.95, Σy2 = 1239.27, Σxy = 740.8, and r ≈ 0.909. (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.)
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 per capita income in thousands of dollars. Let y be the number of medical doctors per 10,000 residents. Six small cities in Oregon gave the following information about x and y.
| x | 8.7 | 9.2 | 9.8 | 8.0 | 8.3 | 8.7 |
| y | 9.9 | 18.1 | 20.2 | 10.2 | 11.4 | 13.1 |
Complete parts (a) through (e), given Σx = 52.7, Σy = 82.9, Σx2 = 464.95, Σy2 = 1239.27, Σxy = 740.8, and r ≈ 0.909.
(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 |
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