write me a problem statement with answer on evaluation f1 score

Problem Statement:

In a binary classification problem, you have developed a machine learning model to predict whether an email is spam or not. After testing your model on a validation set, you obtained the following results:

• True Positives (TP): 100
• True Negatives (TN): 900
• False Positives (FP): 50
• False Negatives (FN): 150

Calculate the F1 score for this model.

Solution:

Step 1: Calculate Precision and Recall

Precision is the ratio of correctly predicted positive observations to the total predicted positive observations. The formula is:

Precision = TP/(TP+FP)

Recall (Sensitivity) - the ratio of correctly predicted positive observations to the all observations in actual class. The formula is:

Recall = TP/(TP+FN)

Step 2: Calculate F1 Score

The F1 Score is the weighted average of Precision and Recall. Therefore, this score takes both false positives and false negatives into account. The formula is:

F1 Score = 2*(Recall * Precision) / (Recall + Precision)

Let's calculate:

Precision = 100 / (100 + 50) = 0.6667 Recall = 100 / (100 + 150) = 0.4

F1 Score = 2*(0.4 * 0.6667) / (0.4 + 0.6667) = 0.5

So, the F1 score of the model is 0.5.