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 0.234 and the equation of the regression line is ^y = 17.5 + 0.850x, where x represents height. The mean of the 60 heights is 63.4 in and the mean of the 60 pulse rates is 75.6 beats per minute. Find the best predicted pulse rate of a woman who is 74 inches tall. Use a significance level of a=0.01.

Question

Mathematics

Chaya Lucas

17 February, 08:54

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 0.234 and the equation of the regression line is ^y = 17.5 + 0.850x, where x represents height. The mean of the 60 heights is 63.4 in and the mean of the 60 pulse rates is 75.6 beats per minute. Find the best predicted pulse rate of a woman who is 74 inches tall. Use a significance level of a=0.01.

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Yogi · Answer 1

The best predicted pulse rate of a woman who is 74 inches tall is 80.4 (beats per minute).

Step-by-step explanation:

The best predicted pulse rate of a woman who is 74 inches tall is obtained below:

Let x denotes height (in inches) and y denotes pulse rates (in beats per minute).

From the information, the regression equation is, the total number of women is 60 and the linear correlation coefficient between height and pulse rates is 0.234 and the mean of heights is 63.4 and the mean of pulse rates is 75.6. The estimated regression line is

^y = 17.5 + 0.850x

The required best predicted pulse rates is,

=17.5 + (0.850*74)

=17.5 + 62.9

= 80.4 beats per minute