An aerobic exercise instructor remembers the data given in the following table, which shows the recommended maximum exercise heart rates for individuals of the given ages. (A graphing calculator is recommended.) Age (x years) 20 40 60 Maximum heart rate (y beats per minute) 166 150 134 (a) Find the linear correlation coefficient for the data. (Round your answer to two decimal places.) (b) What is the significance of the value found in part (a)? The graph of the regression points passes through all three data points.One of the data points is the y-intercept. The linear correlation coefficient should always be positive.The graph of the regression points passes through none of the data points.The slope of the regression is about half of what the expected value is. (c) Find the equation of the least-squares regression line. (Round your answers to two decimal places.) ŷ = (d) Use the equation of the least-squares line from part (c) to predict the maximum exercise heart rate for a person who is 70. (Round your answer to the nearest whole number.) beats per minute (e) Is the procedure in part (d) an example of interpolation or extrapolation? extrapolationinterpolation?
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.
An aerobic exercise instructor remembers the data given in the following table, which shows the recommended maximum exercise heart rates for individuals of the given ages. (A graphing calculator is recommended.)
| Age (x years) | 20 40 60 |
|---|---|
| Maximum heart rate (y beats per minute) |
166 150 134 |
(b) What is the significance of the value found in part (a)?
(c) Find the equation of the least-squares regression line. (Round your answers to two decimal places.)
ŷ =
(d) Use the equation of the least-squares line from part (c) to predict the maximum exercise heart rate for a person who is 70. (Round your answer to the nearest whole number.)
beats per minute
(e) Is the procedure in part (d) an example of interpolation or extrapolation?
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