Page 110 - Statistics II for Dummies

94 Part II: Using Different Types of Regression to Make Predictions

The regression equation is
Figure 5-3:
Sales = 5.267 + 0.162 TV ads + 0.249 Newsp ads
Regression
output for Predictor Coef SE Coef T P
the ads Constant 5.2574 0.4984 10.55 0.000
and plasma TV ads 0.16211 0.01319 12.29 0.000
Newsp ads 0.24887 0.02792 8.91 0.000
TV sales
example. S = 0.976613 R-Sq = 92.8% R-Sq(adj) = 92.0%

Putting these coefficients into the multiple regression equation, you see the
regression equation is Sales = 5.267 + 0.162 (TV ads) + 0.249 (Newspaper ads),
where sales are in millions of dollars and ad spending is in thousands of
dollars.

So you have your coefficients (no sweat, right?), but where do you go
from here? What does it all mean? The next section guides you through
interpretation.

Interpreting the coefficients

In simple linear regression (covered in Chapter 4), the coefficients represent
the slope and y-intercept of the best-fitting line and are straightforward to
interpret. The slope in particular represents the change in y due to a one-unit
increase in x because you can write any slope as a number over one (and
slope is rise over run).

In the multiple regression model, the interpretation’s a little more complicated.
Due to all the mathematical underpinnings of the model and how it’s finalized
(believe me, you don’t want to go there unless you’re looking for a PhD in
statistics), the coefficients have a different meaning.

The coefficient of an x variable in a multiple regression model is the amount
by which y changes if that x variable increases by one unit and the values of
all other x variables in the model don’t change. So basically, you’re looking
at the marginal contribution of each x variable when you hold the other vari-
ables in the model constant.

In the ads and sales regression analysis (see Figure 5-3), the coefficient of x
1
(TV ad spending) equals 0.16211. So y (plasma TV sales) increases by 0.16211
million dollars when TV ad spending increases by 1.0 thousand dollars and
spending on newspaper ads doesn’t change. (Note that keeping more digits
after the decimal point reduces rounding error when in units of millions.)

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