Assignment 7

1. What is LDA

• LDA reduces dimensions and it focuses on maximizing the separability among the categories so we can make the best decision.

2a. What is/are the requirement(s)of LDA?

• Once the data is projected onto a new axis, we want to:
  • 1. Maximize the distance between the two means.
  • 2. Minimize the variation (which LDA calls scatter) within each category.

2b. How LDA is different from Logistic Regression?

• LDA uses least square estimation while logistic regression relies on maximum likelihood estimation.
• LDA works best when predicted and predictor variables are continuous (not categorical) and follow a normal distribution. In logistic regression, a predictor is a binary variable and it works well with categorical variables as predictors.

2c. What is ROC?

• The ROC curve, an acronym for receiver operating characteristic curve, is a graph showing the performance of a classification model at all classification thresholds. This curve plots two parameters: true positive rate and false positive rate. An ideal ROC curve hugs the upper left corner, so the larger the area under the curve the better the classifier.

2d. What is sensitivity and specificity? Which is more important in your opinion?

• Sensitivity and specificity are statistical measures of the performance of a classification test or screening test, which is often used in medicine.

  Sensitivity measures the proportion of actual positives which are correctly identified (e.g. the percentage of sick people who are correctly identified as having the condition), and is complementary to the false negative rate.

  Specificity measures the proportion of negatives which are correctly identified (e.g. the percentage of healthy people who are correctly identified as not having the condition), and is complementary to the false positive rate.

  I believe that sensitivity is more important because it is complementary to false negative (falsely identifying a sick patient as healthy can potentially endanger someone’s life).

2e. From the following chart, for the purpose of prediction, which is more critical?

• In line with the above, false negative seems most critical. Also, false positive can have serious psychological consequences on a (healthy) person.

3. Calculate the prediction error

• 23/9,667=0.2% false positives and 252/333=75.7% false negatives