WHAT IS LOGISTIC REGRESSION?

Logit for short, a specialized form of regression

used when the dependent variable is dichotomous (has

only two values 0 and 1) and categorical while the

independent variable(s) could be any type

There are many variables in the business world that are

dichotomous, for example: male or female, to buy or not

to buy, good credit risk or poor credit risks, to take offer

or decline offer, student will succeed or fail, etc.

ASSUMPTIONS OF LOGISTIC REGRESSION

Does not assume a linear relationship between DV and IV

Dependent variable must be a dichotomy (2 categories)

Independent variables need not be interval, nor normally distributed, nor linearly related, nor of equal variance within each group

The categories of the DV must be mutually exclusive and exhaustive such that a case can only be in one group and every case must be a member of one of the groups

GOAL OF LOGISTIC REGRESSION

logistic regression determines the impact of

multiple independent variables presented

simultaneously to predict membership of one or

other of the two dependent variable categories

DESCRIPTION OF THE DATA

The data used to conduct logistic regression is from a

survey of 30 homeowners conducted by an electricity

company about an offer of roof solar panels with a 50%

subsidy from the state government as part of the state’s

environmental policy.

The variables are:

IVs: household income measured in units of a thousand

dollars age of householder

monthly mortgage

size of family household

DV: whether the householder would take or decline the

offer. Take the offer was coded as 1 and decline the offer

was coded as 0.

WHAT IS THE RESEARCH QUESTION?

to determine whether household income and monthly

mortgage will predict taking or declining the solar panel

offer

Independent Variables: household income and monthly

mortgage

Dependent Variables: Take the offer or decline the offer

TWO HYPOTHESES TO BE TESTED

There are two hypotheses to test in relation to the

overall fit of the model:

H0: The model is a good fitting model

H1: The model is not a good fitting model (i.e.

the predictors have a significant effect)

HOW TO PERFORM LOGISTIC REGRESSION IN

SPSS

1) Click Analyze

2) Select Regression

3) Select Binary Logistic

4) Select the dependent variable, the one which is a

grouping variable (0 and 1) and place it into the

Dependent Box, in this case, take or decline offer

5) Enter the predictors (IVs) that you want to test into the

Covariates Box. In this case, Household Income and

Monthly Mortgage

6) Leave Enter as the default method

CONTINUATION OF SPSS STEPS

7) If there is any categorical IV, click on Categorical button

and enter it. There is none in this case.

8) In the Options button, select Classification Plots, Hosmer-

Lemeshow goodness-of-fit, Casewise Listing of residuals.

Retain default entries for probability of stepwise,

classification cutoff, and maximum iterations

9) Continue, then, OK

TABLE 1. CLASSIFICATION TABLE

TABLE 2. VARIABLES IN THE EQUATION TABLE

TABLE 3. VARIABLES NOT IN THE EQUATION

TABLE 4. OMNIBUS TEST OF COEFFICIENTS

TABLE 5. MODEL SUMMARY

TABLE 6. HOSMER AND LEMESHOW TEST

TABLE 7. CONTINGENCY TABLE FOR HOSMER AND

LEMESHOW TEST

TABLE 8. CLASSIFICATION TABLE

TABLE 9. VARIABLES IN THE EQUATION

A logistic regression analysis was conducted to predict if householders will take up or decline the offer of a solar panel subsidy.

Predictors --household income and mortgage payment

A test of the full model against the constant model was statistically significant, indicating that the predictors as a set differentiated between acceptors and decliners of the offer (chi-square=29, p<.000 with df=2).

Nagelkerke’s R2 of .83 indicated a moderately

strong relationship between prediction and

grouping. Prediction success overall was 83.3%

(85.7% for decline and 81.3% for accept).

The Wald criterion showed that both predictors

were not significant predictors. ExpB value

indicates that when household income is raised

by one unit ($1,000), the odds ratio is 1.33 times

as large and therefore householders are 1.33

more times likely to take the offer.

Since the predictors did not have a significant effect (p>.005), we fail to reject the null hypothesis that there is no difference between observed and model-predicted values, thus, the model is a good fitting model. Even if the two predictors did not show significant effect, they were able to distinguished between acceptors and decliners of the offer as the Chi-square table (Table 4) show.

Perhaps, other predictors such as age and family size may have significant effect, or perhaps adding one more predictor will improve the model, however, this paper only considered two independent variables.