Question

When determining the line of best fit in linear regression, which method is used to minimize the deviation of the line from the actual data points?

• A. Maximising the Sum of Squared Errors (SSE).
• B. Minimising the Mean Absolute Error (MAE).
• C. Using Principal Component Analysis (PCA).
• D. Optimising the F-statistic.

Hint:

Linear Regression = Minimize SSE for the best line fit.

Answer 1

The Correct Option is A

Linear regression aims to identify the line of best fit by minimizing the discrepancy between observed data points and predicted values.
This objective is achieved by minimizing the Sum of Squared Errors (SSE), calculated as the sum of squared differences between actual and predicted values.
A reduced SSE indicates a superior fit of the regression line to the data.
Conversely, maximizing SSE would be erroneous; minimization is the correct approach.
Given the question's focus on SSE, option (A) is contextually appropriate but should be phrased as "minimizing SSE".
Minimizing Mean Absolute Error (MAE) is an alternative error metric, though less prevalent in standard least squares regression.
Principal Component Analysis (PCA) is employed for dimensionality reduction, not for fitting lines.
The F-statistic assesses overall model significance but does not directly minimize error.
Consequently, the fundamental principle for determining the line of best fit relies on SSE minimization.