Question

The term "Residual" is defined as:

• A. Fraction of all the test data's variance that is accounted for by the model.
• B. The difference between the value predicted for a data point and the actual observed value.
• C. A regression method where we tune our model parameters so as to minimize sum of the distances between data points.
• D. Actual predicted value.

Hint:

Residuals are used to assess how well a regression model fits the data, with smaller residuals indicating better fit.

Answer 1

The Correct Option is B

Step 1: Residual Definition.
A residual in regression analysis quantifies the discrepancy between an observed dependent variable value and its predicted value from the model, signifying prediction error.

Step 2: Option Evaluation.
- (A) Fraction of test data variance explained by the model: Incorrect; this is R-squared.
- (B) The discrepancy between a data point's predicted value and its actual observed value: Correct; this is the definition of a residual.
- (C) A regression technique minimizing the sum of distances between data points: Incorrect; this describes methods like least squares, not residuals themselves.
- (D) Actual predicted value: Incorrect; this is the model's forecast, not the residual.

Step 3: Final Answer.
The correct definition is (B) The difference between the value predicted for a data point and the actual observed value.