Chapter 13, Problem 1PS

a.

To determine

Interpret the $Y$ intercept.

Explanation of Solution

The given prediction line is ${\widehat{Y}}_i=2+5X_i$ .

The general prediction line is given by:

${\widehat{Y}}_i=b_o+b_1{X}_i$

Here, ${\widehat{Y}}_i$ is the predicted value of dependent variable $Y$ for the number of observations $i$ , $X_i$ is the value of independent variable $X$ for observations $i$ , $b_o$ is the sample $Y$ intercept and $b_1$ is the sample slope.

Comparing the given equation with general equation, the intercept is, $b_0=2$ . It can be interpreted as the predicted value of $Y$ is 2, when $X=0$ .

b.

To determine

Interpret the slope coefficient.

Explanation of Solution

In the given prediction line, the slope is $b_1=5$ .

Slope coefficient gives the change in $Y$ for a unit change in $X$ . Here, slope $b_1=5$ means that for an unit increase in $X$ , the predicted value of $Y$ increases by a mean of $5$ units.

c.

To determine

Find the predicted value of $Y$ , when $X=3$

Answer to Problem 1PS

The predicted value is 17.

Explanation of Solution

The prediction line is given by ${\widehat{Y}}_i=2+5X_i$ .

Now, substitute $X_i=3$ in the above prediction line.

$\begin{array}{c}{\widehat{Y}}_i=2+5\times 3\\ =17\end{array}$

Thus, the required value is ${\widehat{Y}}_i=17$ .