Residuals ($y - \hat{y}$): A residual is the vertical distance between an actual data point and the predicted line.
Least Squares Method (LSRL): The "Line of Best Fit" isn't just an ocular guess. It is the specific mathematical line that MINIMIZES the total sum of all squared residual areas!
Influence of Outliers: Because residuals are SQUARED, a point extremely far away from the line pulls the line drastically towards it to minimize its massive area penalty.
Tags
RegressionResidualsLSRLOutliers
LEAST SQUARES REGRESSION LINE
$\hat{y} = a + bx$
CLICK GRAPH TO ADD POINTS
Data Control
Interactive Fitting
Slope ($b$) = 1.0
Intercept ($a$) = 0
LSRL EQUATION
Points $n$:5
Eq $\hat{y}$:10.5 + 2.3x
PENALTY METRIC
Total SSR ($\sum e^2$):85.4
Visualizing Squares: The algorithm calculates the vertical distance ($e$) from each point to the line, and physically SQUARES it. The mathematically perfect line is the one that forces the total combined area of these red squares to be as small as possible!