Let x be the age of a licensed driver in years. Let y be the percentage of all fatal accidents (for a given age) due to failure to yield the right of way. For example, the first data pair states that 5% of all fatal accidents of 37-year-olds are due to failure to yield the right of way. x 37 47 57 67 77 87 y 5 8 10 15 27 44 Complete parts (a) through (e), given Σx = 372, Σy = 109, Σx2 = 24814, Σy2 = 3079, Σxy = 8043, and r ≈ 0.927. (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) Predict the percentage of all fatal accidents due to failing to yield the right of way for 75-year-olds. (Round your answer to two 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 the age of a licensed driver in years. Let y be the percentage of all fatal accidents (for a given age) due to failure to yield the right of way. For example, the first data pair states that 5% of all fatal accidents of 37-year-olds are due to failure to yield the right of way.
| x | 37 | 47 | 57 | 67 | 77 | 87 |
| y | 5 | 8 | 10 | 15 | 27 | 44 |
Complete parts (a) through (e), given Σx = 372, Σy = 109, Σx2 = 24814, Σy2 = 3079, Σxy = 8043, and r ≈ 0.927.
(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) Predict the percentage of all fatal accidents due to failing to yield the right of way for 75-year-olds. (Round your answer to two decimal places.)
%
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