# Explaining the predictive capacity of the logistic regression model

The given logistic regression is run in two steps. The initial step can be called the beginning block or Step 0 or Block 0. It is considered as a nonmodel and it only gives the value of the constant. Block 0 or the initial step output is for a model that includes only the intercept (which is taken as constant). It includes no predictors and just the intercept. The final step, or Step 1, includes all the predictors/independent variables (Table 6.2).

Table 6.3 describes the variables for the intercept (constant) for binary logistic in Step 0 (initial step).

Under the variables in the equation, we see that the intercept (only) model is in (odds) = 369. If we exponentiate both sides of this expression, we find that our predicted odds [Exp(B)] = 1.446. That is, the predicted odds of deciding the WTP monthly premium for green insurance are 1.446.

Table 6.2 Classification table for binary logistic in Step 0 (initial step)

 Classification Table0- b Observed Predicted WTP premium for green insurance on monthly basis Percentage correct No Yes Step 0 WTP No 0 368 0.0 Yes 0 532 100.0 Overall percentage 59.1

’ Constant is included in the model.

bThe cut value is. S00.Source: Primary survey

Table 6.3 Variables in the equation

 В S.E. Wald df s'i■ Exp(B) Step 0 Constant 0.369 0.068 29.548 1 0.000 1.446

Source: Primary survey

# Variables not in the equation

Table 6.4 Variables not in the equation

 Variables Score df s'i- Step 0 AGE 366.959 1 0.000 GENDER 48.860 1 0.000 EDUCATION 664.433 1 0.000 MARRIAGE 50.286 1 0.000 FAMILY TYPE 388.936 1 0.000 NOFM 365.071 1 0.000 OWN HOUSE 120.714 1 0.000 FAMILY INCOME 31 1.185 1 0.000 NOEMF 12.131 1 0.000 EPYA 526.823 1 0.000 DYA 424.690 1 0.000 DISEFREQ 2.339 1 0.126 HOSPITALTY 42.679 1 0.000 ICGB 626.394 1 0.000 WTPBID 15.873 1 0.000 Overall Statistics 763.1 13 15 0.000

Source: Primary survey

# Step 1 (model) omnibus tests of model coefficient is the final step which includes all variables together in the study

Table 6.5 shows Step 1 (model) omnibus tests of model coefficient

Block 1: Method = Enter

Now at the Block 1 (final step) output, SPSS has added the variables as a predictor. The omnibus tests of model coefficients give us a chi-square of 1,150.585, significant beyond the.001 level.

The given logistic regression is run in two steps (Table 6.5). The initial step, called Step 0, includes no predictors and just the intercept. The final step, called Step 1, includes all the predictors/independent variables. As we move from the initial step to the final step, which includes all variables, predictive accuracy moves from 59.1 per cent in the initial step (Step 0) to 99.1 per cent accuracy in the final step (Step 1), when the full regression model is applied to the data. This 40 per cent jump represents a major improvement in the predictive capability of the model. The best level of predictability is now 99.1 per cent. Therefore, there is an improvement of 40 percentage points in the predictive capacity by using the logistic regression model (Table 6.6).

Table 6.5 Omnibus tests of model coefficients

 Chi-square Df % Step 1 Step 1,150.585 15 0.000 Block 1,150.585 15 0.000 Model 1,150.585 15 0.000

Source: Primary survey

Table 6.6 Classification table for binary logistic WTP for green insurance

 Observed Predicted WTP Percentage correct No Yes Step 1 WTP No 366 2 99.5 Yes 6 526 98.9 Overall percentage 99.1

a.The cut value is. S00 Source: Primary survey

Table b.l Model summary of binary logistic regression

 Model summary Step -2 Log likelihood Cox & Snell R Square Nagelkerke R Square 1 67.028a .722 .973

1 Estimation terminated at iteration number I I because parameter estimates changed by less than .001.

Source: Primary survey

# Model summary of the binary logistic model result

The result shows that the -2 Log Likelihood statistic measures how poorly the model predicts the decisions. The smaller the statistic, the better the model. In this model, we see that the -2 Log Likelihood statistic is 67.028, which is quite satisfactory.

The Cox 8c Snell R square can be interpreted like R square in a multiple regression; its maximum value is .75. In the given model, Cox 8c Snell R square is .722, which is acceptable for the model.

The value of Nagelkerke R square is on a scale of 0-1. This value can reach a maximum of 1 and is an indication that the regression model constructed has added a major contribution to the prediction of WTP for green insurance or not. Here, the Nagelkerke R square figure for the 'goodness of fit' of the model is good at .973; this suggests that the model is strong and it improves the level of predictability of the given model. In the study, the given binary model the value of Nagelkerke R square is .973, which implies that 97 per cent of the variability in dependent variable WTP for green insurance is explained by the independent variables.