Once a line is fitted, two questions remain. How much of y’s variation does the line actually explain? — that is r². And is a straight line even the right shape? — that is what a residual plot reveals. A residual is just the vertical gap between a point and the line. Pick a scenario, slide the scatter up and down, and watch both the explained-variation bar and the residual plot recompute from the dots on screen.
The scatterplot
Residual plot — every gap, replotted against x
R-squaredpick a scenario to begin
1.00×
Variation in y, split in two
Points n—
r² explained—
unexplained—
correlation r—
Two different questions.r² answers “how strong is the fit?” — a big number means the line predicts y well. The residual plot answers “is the line the right shape?” A trustworthy fit shows residuals in a formless horizontal band around zero, with no curve, no funnel, no drift. If you can see a shape in the residuals, the model is missing something — no matter how large r² looks.
Don’t confuse the two. The Weak scenario has a small r² but a perfectly patternless residual plot — a straight line is the correct shape, there is simply a lot of unexplained scatter. The Curved scenario can post a healthy-looking r² yet its residuals bow into an arch — the line is the wrong shape. Also note: r² measures variation the line accounts for, never proof that x causes y.