Page 118 - Intermediate Statistics for Dummies

10_045206 ch05.qxd 2/1/07 9:49 AM Page 97
Chapter 5: When Two Variables Are Better than One: Multiple Regression
coefficients (numbers) to put in for b 0 , b 1 , and b 2 , so you can use the resulting
equation to estimate y. This specific model is the best-fitting multiple linear
regression model. In this section, you see 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 0 + b 1 x;
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 1 , b 2 , and 97
so on quantify in a similar matter the sole contribution that each correspond-
ing x variable (x 1, x 2) makes in predicting y. The coefficient b 0 indicates the
amount by which to adjust all of 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 0 , b 1 , and so on) that fit the data best. The coefficients that
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 coeffi-
cients 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 0 , b 1 , b 2 , . . . , b 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) in Figure 5-3 is just the constant
term (or b 0 term) in the model and isn’t affiliated with any x variable. This
constant just sort of goes along for the ride in the analysis — the number
that you tack on the end to make the numbers work out right. The second