How to Graph a Quadratic Regression

A quadratic regression is the plot of a quadratic function of the form f(x)=ax^2+bx+c for fixed constants a, b, and c. Quadratic regression models are often used in economics cases such as cost-benefit analyses, forecasting and utility functions. The parabola-shaped regression line measures the amount of variation in the data around the mathematical curve. Regression lines can illustrate the ups and downs of a function in ways that linear models cannot. Learning how to graph regression charts is an essential skill in statistics.

Things You'll Need

  • Pencil
  • Graph paper
  • Applet
  • Spreadsheet software
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Instructions

  1. Using an Applet

    • 1

      Access the quadratic regression applet.

    • 2

      Input data for the independent variable in the first column. Enter data for the dependent, complementing values in the second column. Rename the columns for your convenience.

    • 3

      Click on the "Plot" button and a quadratic function will appear.

    • 4

      Click on "Analyze" to graph a quadratic regression line. Observe the equation of the regression function as well as the percentage error and correlation coefficient.

    • 5

      Click on the numerical tab between "Results" and "Precision" to denote the decimal place of your results.

    • 6

      Press "Clear" to graph another quadratic regression.

    Using a Software Spreadsheet

    • 7

      Click on "New" to create a new spreadsheet in a statistics program such as Microsoft Excel.

    • 8

      Input the independent variable data points in the first column. Insert the data points of the dependent variable in the second column.

    • 9

      Highlight both columns and select the "Chart Wizard" button.

    • 10

      Select the "XY (Scatter) Plot." Choose the "Only True Sub-Type" scatter plot.

    • 11

      Click on "Next," "Finish". View your graph and modify its font, color and background, if necessary.

    • 12

      Right-click on the graph, click on "Chart" and drag down to "Add Trendline."

    • 13

      Choose "quadratic" under the "Type" tab and select "Display equation on chart" under the "Options" tab. View the results of your quadratic regression analysis.

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