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Chapter 5: Multiple Regression with Two X Variables 93

so you can use the resulting equation to estimate y. This specific model is
the best-fitting multiple linear regression model. This section tells you how to
get, interpret, and test those coefficients in order to complete step five in the
multiple regression analysis.

Finding the best-fitting linear equation is like finding the best-fitting line in
simple linear regression, except that you’re not finding a line. When you have
two x variables in multiple regression, for example, you’re estimating a best-
fitting plane for the data.

Getting the multiple regression

coefficients

In the simple linear regression model, you have the straight line y = b + b x;
0 1
the coefficient of x is the slope, and it represents the change in y per unit
change in x. In a multiple linear regression model, the coefficients b , b ,
1 2
and so on quantify in a similar matter the sole contribution that each
corresponding x variable (x , x ) makes in predicting y. The coefficient b
1 2 0
indicates the amount by which to adjust all these values in order to provide
a final fit to the data (like the y-intercept does in simple linear regression).

Computer software does all the nitty-gritty work for you to find the proper
coefficients (b , b , and so on) that fit the data best. The coefficients that
0 1
Minitab settles on to create the best-fitting model are the ones that, as a
group, minimize the sum of the squared residuals (sort of like the variance
in the data around the selected model). The equations for finding these
coefficients by hand are too unwieldy to include in this book; a computer
can do all the work for you. The results appear in the regression output in
Minitab. You can find the multiple regression coefficients (b , b , b , . . . , b )
0 1 2 k
on the computer output under the column labeled COEF.
To run a multiple regression analysis in Minitab, click on Stat>Regression>
Regression. Then choose the response variable (y) and click on Select. Then
choose your predictor variables (x variables), and click Select. Click on OK,
and the computer will carry out the analysis.

For the plasma TV sales example from the previous sections, Figure 5-3
shows the multiple regression coefficients in the COEF column for the
multiple regression model. The first coefficient (5.257) is just the constant
term (or b term) in the model and isn’t affiliated with any x variable. This
0
constant just sort of goes along for the ride in the analysis; it’s the number
that you tack on the end to make the numbers work out right. The second
coefficient in the COEF column is 0.162; this value is the coefficient of the
x (TV ad amount) term, also known as b . The third coefficient in the COEF
1 1
column is 0.249, which is the value for b in the multiple regression model
2
and is the coefficient that goes with x (newspaper ad amount).
2

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