Chapter 14, Problem 1PS

For this problem, use the following multiple regression equation:

${\hat{Y}}_i=10+5X_{\text{1}i}+3X_{\text{2}i}$

a. Interpret the meaning of the slopes.

b. Interpret the meaning of the $Y$ intercept.

To determine

Interpret the meaning of slopes.

Explanation of Solution

The given multiple regression is:

$\widehat{Y_i}=10+5X_{1i}+3X_{2i}$

The coefficients of $X_{1i}$ and $X_{2i}$ represent the slope of the equation. The coefficient of $X_{1i}$ is 5 . It means that holding the independent variable $X_{2i}$ constant , one unit increase in $X_{1i}$ leads to an increase of 5 units in the response variable Y.

Similarly, the coefficient of $X_{2i}$ represents the 3 unit increase in the response variable Y for a unit increase in $X_{2i}$ while keeping other independent variable constant.

To determine

Interpret the meaning of the Y intercept.

Explanation of Solution

The Y-intercept of given regression line is 10. It represents the value of response variable Y when the both the independent variables $X_1$ and $X_2$ are zero.