Chapter 3.2, Problem 64E

(a)

To determine

To find the equation of the least squares line for predicting full year change from January change.

Answer to Problem 64E

  $\widehat{y}=6.0831+1.7068x$ .

Explanation of Solution

It is given that,

  $\begin{array}{l}r=0.596\\ \overline{x}=1.75\\ s_x=5.36\\ \overline{y}=9.07\\ s_y=15.35\end{array}$

The general equation of the regression line is:

  $\widehat{y}=a+bx$

The slope of the regression line is:

  $\begin{array}{l}b=r\frac{s_y}{s_x}\\ =0.596\times \frac{15.35}{5.36}\\ =1.7068\end{array}$

And the intercept is as:

  $\begin{array}{l}a=\overline{y}-b\overline{x}\\ =9.07-1.7068(1.75)\\ =6.0831\end{array}$

Thus, the equation of the regression line is:

  $\begin{array}{l}\widehat{y}=a+bx\\ \Rightarrow \widehat{y}=6.0831+1.7068x\end{array}$

(b)

To determine

To predict the percentage change the entire year without using the least square line.

Answer to Problem 64E

The predicted height is $9.07\%$ ..

Explanation of Solution

It is given that,

  $\begin{array}{l}r=0.596\\ \overline{x}=1.75\\ s_x=5.36\\ \overline{y}=9.07\\ s_y=15.35\end{array}$

Thus, we have,

  $\begin{array}{l}\widehat{y}=6.0831+1.7068x\\ =6.0831+1.7068(1.75)\\ =9.07\end{array}$

Thus the predicted height is $9.07\%$ .