Least Squares

The Fitted Line and Zero-Sum Residuals

The fitted line and residual table are locked to the same shown data. The zero-sum residual check is visible, exact, and limited to this fit.

highlighted = computed this step

The fitted line

The fitted line is y=11/10 plus 11/10x. The fit plot and residual table carry the same fit lock.

y^=11/10+11/10x\hat y=11/10+{}11/10x
Fit with residual certificateThe fitted line and residual table share the same exact data.Least-squares fitExact data points and the exact fitted line in one coordinate plot.fitABCDVisible residual certificatexyfitresid0111/10-1/101311/54/52233/10-13/103522/53/5sum residuals = 0

What zero-sum means

The residuals -1/10, 4/5, -13/10, and 3/5 sum to 0. Positive and negative misses balance vertically.

∑r=0\sum r=0
Fit with residual certificateThe fitted line and residual table share the same exact data.Least-squares fitExact data points and the exact fitted line in one coordinate plot.fitABCDVisible residual certificatexyfitresid0111/10-1/101311/54/52233/10-13/103522/53/5sum residuals = 0

Summary

The fitted SSE is 27/10, below the trial SSE 3. Zero-sum is a checkable property of this fit with an intercept, not a quality claim.

SSE=27/10<3SSE=27/10<3
Fit with residual certificateThe fitted line and residual table share the same exact data.Least-squares fitExact data points and the exact fitted line in one coordinate plot.fitABCDVisible residual certificatexyfitresid0111/10-1/101311/54/52233/10-13/103522/53/5sum residuals = 0