Chapter 3.2, Problem 72E

To determine

To find: The regression line

Answer to Problem 72E

The regression line is $\widehat{y}=3.60+0.835x$

Explanation of Solution

Given:

  $\overline{y}=55.1,s_y=12.3,\overline{x}=61.7,s_x=14,r=0.95$

Calculation:

The slope could be calculated as:

  $\begin{array}{c}b=r\times \frac{s_y}{s_x}\\ =0.95\left(\frac{12.3}{14.0}\right)\\ =0.835\end{array}$

The intercept could be calculated as:

  $\begin{array}{c}a=\overline{y}-b\overline{x}\\ =55.1-0.835\left(61.7\right)\\ =3.60\end{array}$

Thus, the equation of the regression line is:

  $\begin{array}{c}\widehat{y}=a+bx\\ =3.60+0.835x\end{array}$

Hence, the correct option is (a).