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 whether they had children and what their annual household income is.
Because the response is binary, the consultant uses binary logistic regression to determine how the advertisement, having children, and annual household income are related to whether or not the adults sampled bought the cereal.
Choose Stat > Regression > Binary Logistic Regression > Fit Binary Logistic Model.
From the drop-down list, select Response in binary response/frequency
format.
In Response, enter Bought.
In Continuous
predictors, enter Income.
In Categorical
predictors, enter ChildrenViewAd.
Click Options. Under Confidence level for all
intervals, enter 90.
Click OK in each dialog box.
Interpret the results
The Analysis of variance 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 predictors Children and ViewAd have a statistically significant relationship with the response. Income does not have a statistically significant relationship with the response because the p-value is greater than 0.10. The consultant may want to refit the model without the income variable.
The odds ratio indicates that adults with children are approximately 4.2 times more likely to purchase the cereal than adults without children. The odds ratio for adults that saw the ad indicates that they are 2.8 times more likely to purchase the cereal than adults who have not seen the ad.
The goodness-of-fit 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 R2 value indicates that the model explains approximately 12.7% of the deviance in the response.
Binary Logistic Regression: Bought versus Income, Children, ViewAd
Method
Link function Logit
Categorical predictor coding (1, 0)
Rows used 71
Response Information
Variable Value Count
Bought 1 22 (Event)
0 49
Total 71
Regression Equation
P(1) = exp(Y')/(1 + exp(Y'))
Children ViewAd
No No Y' = -3.016 + 0.01374 Income
No Yes Y' = -1.982 + 0.01374 Income
Yes No Y' = -1.583 + 0.01374 Income
Yes Yes Y' = -0.5490 + 0.01374 Income
Coefficients
Term Coef SE Coef VIF
Constant -3.016 0.939
Income 0.0137 0.0195 1.15
Children
Yes 1.433 0.856 1.12
ViewAd
Yes 1.034 0.572 1.03
Odds Ratios for Continuous Predictors
Odds Ratio 90% CI
Income 1.0138 (0.9819, 1.0469)
Odds Ratios for Categorical Predictors
Level A Level B Odds Ratio 90% CI
Children
Yes No 4.1902 (1.0245, 17.1386)
ViewAd
Yes No 2.8128 (1.0982, 7.2044)
Odds ratio for level A relative to level B
Model Summary
Deviance Deviance Area Under
R-Sq R-Sq(adj) AIC AICc BIC ROC Curve
12.66% 9.25% 84.77 85.37 93.82 0.7333
Analysis of Variance
Wald Test
Source DF Chi-Square P-Value
Regression 3 8.79 0.032
Income 1 0.50 0.481
Children 1 2.80 0.094
ViewAd 1 3.27 0.070
Fits and Diagnostics for Unusual Observations
Observed
Obs Probability Fit Resid Std Resid
50 1.000 0.062 2.357 2.40 R
68 1.000 0.091 2.189 2.28 R
R Large residual
By using this site you agree to the use of cookies for analytics and personalized content. Read our policy