How to Do Quadratic Regression on the TI-84 Evo

To do quadratic regression on the TI-84 Evo, put your x-values in L1 and your y-values in L2, then run QuadReg from the STAT menu's CALC tab. It gives you a, b and c for y = ax² + bx + c, plus R².

As an example, here's a ball tossed into the air, with its height measured once a second:

Time, seconds (x) 0 1 2 3 4
Height, feet (y) 4 55 69 51 6

Enter the data

If L1 or L2 already has numbers in it, empty it first: in the list editor, arrow up onto the list's name, press clear, then enter.

  1. Press stat, then enter. That opens the list editor, where each column is a list. The x-values go in L1 and the y-values in L2.
  2. Type the x-values down L1, pressing enter after each one. Here that's 0, 1, 2, 3 and 4.
  3. Press the right arrow and type the y-values down L2. Here that's 4, 55, 69, 51 and 6, with enter after each. Every y-value should sit in the same row as its x-value.
    The TI-84 Evo list editor with 0 to 4 in L1 and 4, 55, 69, 51, 6 in L2

Run QuadReg

  1. Press stat, then the right arrow. That opens the CALC tab, which holds all the regressions.
  2. Press the down arrow until QuadReg is highlighted. QuadReg is the quadratic one.
    The CALC tab of the TI-84 Evo STAT menu with QuadReg highlighted
  3. Press enter. A setup screen opens with XLIST on L1 and YLIST on L2, so the lists are already right.
    The QuadReg setup screen with XLIST L1, YLIST L2, an empty STORE RegEQ field and a CALCULATE button at the bottom
  4. Press the down arrow until the cursor reaches STORE RegEQ. Putting Y1 here saves the equation, so you can graph it afterward. If you only need the numbers, skip to the last step.
  5. Press alpha, then trace. A shortcut menu opens with Y1 at the top.
    The YVAR shortcut menu open over the QuadReg setup screen, with 1: Y1 highlighted
  6. Press enter. STORE RegEQ now reads Y1.
    The QuadReg setup screen with STORE RegEQ set to Y1
  7. Press zoom. The CALCULATE button at the bottom of the screen sits right above the zoom key, and pressing that key runs the regression. Pressing enter here only moves the cursor.

Read the results

QuadReg results on the TI-84 Evo: y equals ax squared plus bx plus c, a equals negative 16, b equals 64, c equals 5, R squared equals 0.9972175849
  • a, b and c go into y = ax² + bx + c. Here a = −16, b = 64 and c = 5, so the equation is y = −16x² + 64x + 5.
  • R² measures the fit. It runs from 0 to 1, and the closer it is to 1, the closer the curve passes to your points. Here it's about 0.997, a very close fit.
  • No R² on your screen? Diagnostics is turned off. Press mode, arrow down to DIAGNOSTICS ON, and press enter. Then run QuadReg again.

Graph the curve over your points

This part needs the equation saved in Y1, from the STORE RegEQ step.

  1. Press 2nd, then y=. That opens the STAT PLOTS menu.
    The TI-84 Evo STAT PLOTS menu with Plot1 Off highlighted
  2. Press enter twice. The first press opens Plot1, and the second turns it On. It's already set to a scatter plot of L1 and L2.
    The Plot1 setup screen with ON selected, the scatter type, XLIST L1 and YLIST L2
  3. Press zoom, then 9 for Zoom Stat. (On OS 7.0 it's spelled ZoomStat.) Zoom Stat fits the window to your data, then draws the points with the parabola running through them.
    The TI-84 Evo graph of the five data points with the quadratic regression curve drawn through them

Good to know

  • Use Y1 to predict. On the home screen, press alpha, trace, enter to paste Y1, then type ( and the x-value, and press enter. Y1(1.5) gives 65, the height after 1.5 seconds. More on this in evaluating functions on the TI-84 Evo.
    The TI-84 Evo home screen showing Y1 of 1.5 equals 65
  • Changed the data? Run QuadReg again. The results don't update on their own. The STORE RegEQ field starts empty every time you open QuadReg, so set it to Y1 again if you want the graph updated too.
  • CubicReg and QuartReg work the same way. They sit right below QuadReg in the CALC tab and use the same setup screen.
  • Data that looks like a straight line? Use linear regression instead.