Regression Analysis

Step 1: Understanding residuals.
In regression analysis, a residual is the difference between the observed value of the dependent variable and the value predicted by the model. It represents the error in the model's predictions.

Step 2: Analysis of options.
- (A) Fraction of all the test data's variance that is accounted for by the model: Incorrect, this describes the R-squared value, not residuals.
- (B) The difference between the value predicted for a data point and the actual observed value: Correct, this is the definition of a residual.
- (C) A regression method where we tune our model parameters so as to minimize sum of the distances between data points: Incorrect, this refers to techniques like least squares, but not residuals.
- (D) Actual predicted value: Incorrect, the predicted value is the value the model forecasts, not the residual.

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