A marketing consultant for a cereal company investigates the effectiveness of a TV advertisement for a new cereal product. The consultant shows the advertisement in a specific community for one week. Then the consultant randomly samples adults as they leave a local supermarket to ask whether they saw the advertisements and bought the new cereal. The consultant also asks adults what their annual household income is.
Because the response is binary, the consultant uses binary logistic regression to determine how the advertisement and income are related to whether or not the adults sampled bought the cereal.
 Open the sample data, CerealPurchase.MTW.
 Open the Binary Logistic Regression dialog box.
 From the dropdown list, select Response in binary response/frequency format.
 In Response, enter Bought.
 In Continuous predictors, enter Income.
 In Categorical predictor, enter ViewAd.
 Click Options. In Confidence level, enter 90.
 Click OK.
Interpret the results
The Deviance table shows which predictors have a statistically significant relationship with the response. The consultant uses a 0.10 significance level and the results indicate that the predictor ViewAd has a statistically significant relationship with the response. Income does not have a statistically significant relationship with the response because the pvalue is greater than 0.10. The consultant may want to refit the model without the income variable.
The odds ratio for adults that saw the ad indicates that they are about 3 times more likely to purchase the cereal than adults who have not seen the ad.
The goodnessoffit tests are all greater than the significance level of 0.05, which indicates that there is not enough evidence to conclude that the model does not fit the data. The deviance R^{2} value indicates that the model explains approximately 8.8% of the deviance in the response.

P(1) = exp(Y')/(1 + exp(Y')) 



No  Y' = −2.4148 + 0.02656 Income  Yes  Y' = −1.2946 + 0.02656 Income 



Bought  1  22  (Event)   0  49    Total  71  


Regression  2  7.7412  3.87058  7.74  0.0208  Income  1  2.4005  2.40054  2.40  0.1213  ViewAd  1  4.2686  4.26858  4.27  0.0388  Error  68  80.1551  1.17875    Total  70  87.8963    


Constant  2.4148  0.7874  (3.7099, 1.1197)  3.07  0.0022  Income  0.02656  0.01751  (0.00224, 0.05535)  1.52  0.1292  ViewAd       Yes  1.1203  0.5543  (0.2085, 2.0320)  2.02  0.0433 

Odds Ratios for Continuous Predictor 

Income  1.02691  (0.998, 1.057) 

Odds Ratios for Categorical Predictor 

ViewAd     Yes  No  3.06566  (1.232, 7.630) 


Deviance  68  80.16  0.1486  Pearson  68  71.96  0.3483  HosmerLemeshow  8  9.71  0.2859 

Fits and Diagnostics for Unusual Observations 

48  1  0.106913  2.11459  2.16  R  50  1  0.138176  1.98959  2.02  R 
