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 thousanddollars age of householder monthly mortgage size of family householdDV: whether the householder would take or decline theoffer. Take the offer was coded as 1 and decline the offerwas 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 TESTEDThere 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 SPSS1) Click Analyze2) Select Regression3) Select Binary Logistic4) 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 offer5) Enter the predictors (IVs) that you want to test into the Covariates Box. In this case, Household Income and Monthly Mortgage6) Leave Enter as the default method
CONTINUATION OF SPSS STEPS7) If there is any categorical IV, click on Categorical buttonand 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 iterations9) Continue, then, OK
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, however, this paper only considered two independent variables.