Consider the targeted marketing campaign case of selling products through promotional catalogs. The following tables show the confusion matrices of the classification tree model and the logit regression model, which classifies customers into 'likely to respond' (positive) and 'not likely to respond' (negative).

Confusion Matrix of the Classification Tree Model:

p (actual) n (actual)
p (predicted) 10 4
n (predicted) 3 15

Confusion Matrix of the Logit Regression Model:

p (actual) n (actual)
p (predicted) 13 5
n (predicted) 2 12

Which model is more accurate (higher accuracy rate) based on the information given in these confusion matrices?

Question

Consider the targeted marketing campaign case of selling products through promotional catalogs. The following tables show the confusion matrices of the classification tree model and the logit regression model, which classifies customers into 'likely to respond' (positive) and 'not likely to respond' (negative).

Confusion Matrix of the Classification Tree Model:

p (actual)	n (actual)
p (predicted)	10	4
n (predicted)	3	15

Confusion Matrix of the Logit Regression Model:

p (actual)	n (actual)
p (predicted)	13	5
n (predicted)	2	12

Which model is more accurate (higher accuracy rate) based on the information given in these confusion matrices?

BlackTom AI · Accepted Answer

To evaluate accuracy from a confusion matrix, we add the true positives and true negatives, and divide by the total number of cases.
Option 1: 'The accuracy is the same for both models' – This is worth checking by computing each model's accuracy from its confusion matrix. For the classification tree, TP = 10, TN = 15, FP = 4, FN = 3, so accuracy = (TP + TN) / (TP + FP + FN + TN) = (10 + 15) / 32 = 25 / 32 ≈ 0.781. 
Option 2: 'Cannot answer based on the provided information.' – The confusion matrices give all four cells (TP, FP, FN, TN) for both models, so we can compute accuracy directly. There is enough information to determine which is more accurate, so this statement is incorrect.
Option 3: 'Classification tree' – If we compute the same way, the tree model has accuracy 25/32 ≈ 0.781. This option is suggesting that the tree is more accurate, which would require a higher value than the logit’s, but we’ll check the logit next.
Option 4: 'Logit regression' – For the logit model, TP = 13, TN = 12, FP = 5, FN = 2, so accuracy = (13 + 12) / 32 = 25 / 32 ≈ 0.781. This matches the tree’s accuracy.
Thus, both models have identical accuracy (25 correct out of 32 total cases). The core idea is that accuracy is the proportion of correct predictions, computed as (TP + TN) / (TP + FP + FN + TN). The key takeaway is that although the distributions of TP/FP/FN/TN differ between models, the resulting accuracy is the same in this scenario.
In short, the computed accuracies for the two models are equal, making the statement in Option 1 true and the other options incorrect for the reasons described above.

BU.330.780.T1.SP25 Quiz 2- Requires Respondus LockDown Browser

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