The resting heart rate, \(h\) beats per minute (bpm), and average length of daily exercise, \(t\) minutes, of a random sample of 8 teachers are shown in the table below.
\(t\)
20
35
40
25
45
70
75
90
\(h\)
88
85
77
75
71
66
60
54
State, with a reason, which variable is the response variable.
The equation of the least squares regression line of \(h\) on \(t\) is
$$h = 93.5 - 0.43 t$$
Give an interpretation of the gradient of this regression line.
Find the value of \(\bar { t }\) and the value of \(\bar { h }\)
Show that the point \(( \bar { t } , \bar { h } )\) lies on the regression line.
Estimate the resting heart rate of a teacher with an average length of daily exercise of 1 hour.
Comment, giving a reason, on the reliability of the estimate in part (e).
The resting heart rate of teachers is assumed to be normally distributed with mean 73 bpm and standard deviation 8 bpm .
The middle \(95 \%\) of resting heart rates of teachers lies between \(a\) and \(b\)