For the intercept term, a multiple regression's estimated regression coefficients are interpreted similarly to a basic linear regression, but differently for the slope coefficients:
When all of the independent variables are equal to zero, the dependent variable's value is what is known as the intercept term.
The estimated change in the dependent variable for a one-unit change in each independent variable, while holding the other independent variables constant, is represented by a slope coefficient.
The slope coefficients in a multiple regression are frequently referred to as partial slope coefficients because of this.
I have made a table for you:
| Aspect | Simple Linear Regression | Multiple Regression |
|---|---|---|
| Intercept Term | Represents the expected value of the dependent variable when the independent variable is zero. | Represents the expected value of the dependent variable when all independent variables are zero. |
| Slope Coefficient | Represents the estimated change in the dependent variable for a one-unit change in the independent variable. | Represents the estimated change in the dependent variable for a one-unit change in a specific independent variable, while holding other independent variables constant. Often referred to as partial slope coefficients. |