Regression Analysis > Quadratic Regression

## What is Quadratic Regression?

Quadratic regression is finding the best fit equation for a set of data shaped like a parabola. The equation has the form:

y = ax

^{2}+ 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.

**Contents:**

## 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.

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

- Press [2nd] and then 1.
- Press the comma key.
- Press [2nd] and then 2.
- Press the comma key.
- Press VARS, right arrow to Y-VARS and press ENTER.
- 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=ab^{x}. The trigonometric regression equation will also appear in the y1= line of the Y= screen.

This particular quadratic regression equation is .34632*x^{2}+2.62653*x+31.51190.

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