Statistics How To

Quadratic Regression

Regression Analysis > Quadratic Regression

What is Quadratic Regression?

quadratic regression TI 89 2

BradBeattie|Wikimedia Commons

Quadratic regression is finding the best fit equation for a set of data shaped like a parabola. The equation has the form:
y = ax2 + bx + c, where a≠0.

The first step in regression is to make a scatter plot. If your scatter plot is in a “U” shape, either concave up (like the letter U) or concave down (an upside down U), you’re probably looking at some type of quadratic equation as the best fit for your data.


  1. TI-83 Instructions
  2. TI-89 Instructions

TI-83 Instructions

Step 1: Press STAT, then press ENTER to enter the lists screen. If you already have data in L1 or L2, clear the data: move the cursor onto L1, press CLEAR and then ENTER. Repeat for L2.

Step 2: Enter your x-variables, one at a time into the L1 column. Press the ENTER key after each entry.

Step 3: Use the arrow keys to scroll across to L2 (the next column to the right).

Step 4: Enter your y-variables, one at a time. Press ENTER after each number.

Step 5: Press the STAT button, then use the scroll key to highlight “CALC.”

Step 6: Arrow right to calc and then arrow down to QuadReg. Press ENTER.
quadratic regression ti 83 2

Step 7: Type in the following parameters: L1, L2, Y1. Here’s the steps to do that:
quadratic regression ti 83

  1. Press [2nd] and then 1.
  2. Press the comma key.
  3. Press [2nd] and then 2.
  4. Press the comma key.
  5. Press VARS, right arrow to Y-VARS and press ENTER.
  6. Choose Y1 and press ENTER.

Step 8: Press ENTER to calculate the regression.

Tip: Press GRAPH to graph the parabola. From there, you can determine if the equation is a good fit for the data.

TI-89 Instructions

Sample Problem: Perform a quadratic regression TI 89 for the following data set:

x: 1,2,3,4,5,6,7,8,9
y: 32.5,35.9,37.3,37.9,36.4,32.7, 32.4,29.5,28.5

Step 1: Press APPS and then use the cursor keys to scroll to the Data/Matrix Editor. Press ENTER.

Step 2: Select 1 for “Current.”

Step 3: Type your x-values into the c1 list and then type your y-values into the c2 list.

Step 4: Press F5 for Calc. A new screen will appear.

Step 5: Type your x-values into column c1 and your y-values into column c2.

Step 6: Move your cursor to the Calculation Type box, press the right-cursor key and select “9:QuadRegReg.”

Step 7: Type the location of your x-data into the “x” box. For example, if your x-values are in list c1 then type “c1.”

Step 8: Type the location of your y-data into the “y” box. For example, if your y-values are in list c2 then type “c2.”

Step 9: Move the cursor to the Store ReqEQ line and then press the right cursor key. Move the cursor to y1(x) and then press ENTER. A window will pop up with the data for the quadratic regression equation y=abx. The trigonometric regression equation will also appear in the y1= line of the Y= screen.

This particular quadratic regression equation is .34632*x2+2.62653*x+31.51190.


If you prefer an online interactive environment to learn R and statistics, this free R Tutorial by Datacamp is a great way to get started. If you're are somewhat comfortable with R and are interested in going deeper into Statistics, try this Statistics with R track.

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Quadratic Regression was last modified: November 13th, 2017 by Stephanie Glen