How to Make a Residual Plot on a TI-84

A residual plot isn’t a different kind of graph — it’s a scatter plot of a specific quantity: the leftover error, or residual, at each data point after fitting a regression line. Its whole purpose is a visual check that a straight line was actually the right model to use.

What a residual is

For each point, the residual is observed y − predicted y — how far off the regression line was at that particular x. Plotting x against these residuals (instead of against the raw y values) turns a subtle pattern into an obvious one: if the residuals scatter randomly above and below zero with no shape, a linear model was a good fit; if they curve up and then down (or vice versa), the true relationship isn’t actually linear, no matter how high the regression’s r² looked.

The general workflow

1. Run a linear regression on your (x, y) data to get the equation ŷ = a + bx.
2. Compute the predicted ŷ for every x in your data set using that equation.
3. Subtract: residual = y − ŷ, for each point.
4. Plot x against the residuals as a scatter plot.

A real TI-84 automates step 2–3 by auto-populating a hidden RESID list right after LinReg runs, so you can plot it immediately without computing anything by hand.

Try it yourself

Run Regress (Linear) in Tools → Lists & Stats on the TI-84 Calculator to get the equation, then compute the predicted values for your x’s with it and use List operations → A − B → Dest to subtract them from your original y list into a spare list (e.g. L3). Switch to Graph → Stat Plots, set a plot’s type to Scatter with Xlist = L1 and Ylist = L3, and turn it on — that’s your residual plot, ready to check for any leftover pattern a straight line missed.