Researchers recorded the resting heart rate $($RHR$)$ and number of hours of exercise per week of $18$ healthy adults. They fit a least$-$squares linear regression line relating RHR $($in bpm$)$ and exercise:

$($Estimated RHR$)=105-{7\mathrm{.}1}^{**}($Hours of Exercise$)$

with MSE $45\mathrm{.}9$

If necessary, round your answers to the nearest thousands place $(3$ decimal places$).$

$($a$)$ We know that the correlation between hours of exercise and RHR must be

Equal to $1$

Between $0$ and $1$

Equal to $0$

Between $-1$ and $0$

Equal to $-1$

Points possible: $2$

$($b$)$ What are the degrees of freedom for this model?

$18-t$

$18,1$

$18-2$

$18$

$($c$)$ The estimated standard error for the slope of the regression line is $0\mathrm{.}52.$ So$,$ the variance of the original $x($hours of exercise$)$ values is

Points possible: $3$

$($d$)$ One of the individuals exercises $3$ hours per week and has RHR $73.$

According to the linear model, their RHR is expected because the point $73$ is the regression line.