Parameters

The three parameters in an equation of the form

y  =  b0 + b1 x + b2 z

are interpreted in a similar way to the corresponding parameters for an equation with one explanatory variable.

Intercept
The parameter b0 is called the intercept and is the y-value when both x and z are zero.
Slopes
The other two parameters are slope parameters. The value of each is the expected increase in the response when the corresponding explanatory variable increases by 1. For example, when x increases by 1, y increases by b1.

Illustration

The diagram below represents a linear model. The diagonal grey line that is initially visible shows how y is related to x only.

The two red arrows that are initially visible represent the parameters b0 and b1. Adjust these parameters by dragging the arrows vertically. Observe that b0 is the y-value when x=0, and that b1 is the increase in y when x increases by 1.

Now drag the centre of the diagram a little towards the bottom right to rotate the diagram (or click the x-y-z button). A third arrow becomes visible that allows you to change the third parameter. Adjust all three parameters and observe how they affect the positioning of the plane.