Education Technology

Fitting an Equation to Bivariate Data

Activity Overview

In this activity, students fit a linear least-square regression line to a population data. They explore various functions to model the given data.

Before the Activity

  • See the attached PDF file for detailed instructions for this activity
  • Print pages 27 - 36 from the attached PDF file for your class
  • During the Activity

    Distribute the pages to your class.

    Follow the Activity procedures:

  • Enter the data for the year and population as a list
  • Set up a scatter plot and try to fit the data by a linear least-square regression line
  • Calculate the fit equation
  • Plot the data scatter and fit equation
  • Plot the residuals
  • Verify whether the data follows a linear regression
  • Observe that the residuals trace a parabola
  • Measure the sum of squared residual errors to determine the closeness of the fit
  • Predict the population for a given year
  • Calculate r and r2 as measure of linearity
  • Repeat steps to model fits for quadratic, logarithmic, exponential, and power regressions for the population data
  • Compare the various fits
  • After the Activity

    Review student results:

  • As a class, discuss questions that appeared to be more challenging
  • Re-teach concepts as necessary