Database Reference
In-Depth Information
“OK,” Dangle says cautiously. “I
think
it's a plan. Don't forget to add the 'how
much would you spend' question. When can we see some results?”
“Well, I have to construct the survey, post it in various forums online, and then
process the results. Two weeks should do, soup to nuts.”
“I love it!” Nick says. “Wow, we'd really impress the new owners if we could
crack this one!”
Dangle waves off Bonavich, indicating she believes he's just spouted nonsense.
She's still sceptical. Tapping her hands together using her ingertips, she delivers
her parting shot, glaring at you: “Well, I hope this so-called research isn't a colossal
waste of time.”
“Nothing ventured, nothing gained, right?” you reply good-naturedly.
Dangle utters something under her breath as she heads out the door, but you don't
catch it.
At least you have some marching orders.
11.3
LOGISTIC REGRESSION
In this section, we introduce details of
binary
logistic regression. This is the
regression method we use when the Y (dependent) variable is a categorical vari-
able with
two
categories. If the Y variable is categorical with more than two
categories (e.g., willing to buy, not sure, not willing to buy), we refer to the
analysis as
multinomial
logistic regression; we are covering only the case of
binary
logistic regression. Your independent variables can be either categorical
or continuous, or a mix of both.
For the dependent variable, we adopt the “1” and “0” notation, where “1” stands
for one category and “0” stands for the other category. Traditionally, if the two cat-
egories are analogous to “buy” versus “didn't buy,” we usually let the “1” stand for
the “buy,” or positive result, and the “0” for the “not buy,” or negative result. Given
this customary choice of notation, the predicted Y, which we have been notating
by Yc, stands for
the predicted probability that the result is a “1.”
And, of course,
a probability must be between 0 and 1 (or, 0-100%), by deinition. In a “regular”
simple linear regression, our regression line is
Yc=a+b*X.
Our logistic model is a complicated expression, but results in an equivalent
regression line,
Yc=a+b*X.
However, the Yc is no longer itself, the probability that the result is a
“1.” Instead, it is the natural logarithm of the odds of obtaining a “1.” (See the
sidebar.)
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