A sample of 60 women is obtained, and their heights (in inches) and pulse rates
ID: 3254433 • Letter: A
Question
A sample of 60 women is obtained, and their heights (in inches) and pulse rates (in beats per minute) are measured. The linear correlation coefficient is 0.291 and the equation of the regression line is y = 8.2 + 0.930x, where x represents height. The mean of the 60 heights is 62.9 in and the mean of the 60 pulse rates is 74.9 beats per minute. Find the best predicted pulse rate of a woman who is 68 in tall. Use a significance level of alpha = 0.01. The best predicted pulse rate of a woman who is 68 in tall is 81.44 beats per minute.Explanation / Answer
Solution:-
Regression line: y = 18.2 + 0.93x. If x = 68, then the predicted height is 18.2 + 0.93(68) = 81.44, which is close but not exactly the given answer 74.9.
The regression line should go through the center of the data cloud. Let's check that: 18.2 + 0.93(62.9) = 76.697, not 74.9. Strange.