Database Reference
In-Depth Information
SIDEBAR: HOLD ON! WHAT HAPPENED TO THE HIGHER R SQUARE I HAD
WITH GOOD OLD-FASHIONED MULTIPLE REGRESSION?
We might recall that the value of
r
2
was 0.493 when we used all 15 variables, most of which were
not signiicant. Now we have a value of “only” 0.469.
We reiterate what we noted earlier: What you need to realize is that the 0.493 is a bit misleading in
that it includes the sum of a bunch of small values added to the
r
2
based on variables that really cannot be
said to add value to predicting Y. When we eliminate all these small “fake” additions to
r
2
, we end up with
0.469, or 46.9%. If this sounds subtle, we sympathize, but do not apologize. Regression analysis is a fairly
complex topic and has many subtle areas, most of which, fortunately, you do not have to be concerned with.
Yc=0
.
528+0
.
311*X15+0
.
177*X7+0
.
121*X11+0
.
153*X1+0
.
106*X3
+0
.
106*X2+0
.
055*X6,
or, if we order the variables by subscript,
Yc=528+0
.
153*X1+0
.
106*X2+0
.
106*X3+0
.
055*X6+0
.
177*X7
+0
.
121*X11+0
.
311*X15
.
In other words, this equation says that if we plug in a person's value for X1, X2,
X3, X6, X7, X11, and X15, we get our best prediction for what the person will put
for Y, the likelihood on the 5-point scale that he/she will adopt the search engine. For
example, if we arbitrarily assume a person gives a “4” to each of the seven X's in the
equation, the Yc comes out 4.64. Of course, an individual responder cannot respond
4.64, since the value chosen must be an integer. The right way to think of this is that
if we had a large number of people who answered “4” for each of the variables, the
mean response
for the Y,
likelihood to adopt the search engine
, is predicted to be 4.64.
We want to add one more piece of potentially useful information about interpreting
the bottom portion of
Figure 10.16
. You will notice that there is a column (right-hand-
most column shown in the bottom portion of
Figure 10.16
) called “Coeficients Beta.” In
a stepwise regression, where there is relatively little overlap among the X variables in the
equation (remember: the way [and a strength] of how stepwise regression works is that if
there were a lot of overlap between two variables, one of the two variables would not be in
the equation!), the magnitude of these “Beta values” roughly (not exactly, but likely close
enough) relect, in some sense, the relative importance of the variables. Here, the order is:
Ability to perform a Boolean search
Ability to search by skills
Ability to search by job title
Ability to search candidates by companies in which they have worked
Ability to search by location
Ability to search by years of experience
Ability to search candidates by level of education
This order is reasonably close to the order that is considered by many to be the
true order of importance. Of course, these results are based on a sample, and not the
total population, so you should not expect that the order would come out “perfectly.”
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