Page 174 - Intermediate Statistics for Dummies

13_045206 ch08.qxd 2/1/07 9:58 AM Page 153
Chapter 8: Yes, No, Maybe So: Making Predictions by Using Logistic Regression
3. Plug the coefficients from step one into the logistic regression model:
b x
b 0 +
e
1
/
p =
b 0 +
b x
e
1 +
1
This equation is your best-fitting logistic regression model for the data.
Its graph is an S-curve (for more on the S-curve, see the section “Using
an S-curve to estimate probabilities” earlier in this chapter).
In the sections that follow, you see how to ask Minitab to do the above steps
for you. You also see how to interpret the resulting computer output, find the
equation of the best-fitting logistic regression model, and use that model to
make predictions (being ever mindful that all conditions are met).
Running the analysis in Minitab
Using Minitab, here’s how to perform a logistic regression (other statistical
software packages are similar): 153
1. Input your data in the spreadsheet as a table that lists each value of
the x variable in column one, the number of yeses for that value of x
in column two and the total number of trials at that x-value in column
three.
These last two columns represent the outcome of the response variable
y. (For an example of how to enter your data, see Table 8-1 based on the
movie-age data.)
2. Go to Stat>Regression>Binary Logistic Regression.
3. Beside the Success option, select your variable name from column
two, and beside Trial, select your variable name for column three.
4. Under Model, select your variable name from column one, because
that’s the column containing the explanatory (x) variable in your model.
5. Click OK, and you get your logistic regression output.
When you fit a logistic regression model to your data, the computer output is
composed of two major portions:
The model-building portion: In this part of the output, you can find the
coefficients b 0 and b 1 (I describe coefficients in the section “Finding the
coefficients and making the model”).
The model-fitting portion: You can see the results of a Chi-square
goodness-of-fit test (see Chapter 15) as well as the percentage of con-
cordant and discordant pairs in this section of the output. (A concordant
pair means the predicted outcome from the model matches the observed
outcome from the data. A discordant pair is one that doesn’t match.)