# Activities

• • • ##### Subject Area

• Math: Statistics: Inferential Statistics

• ##### Author 9-12

60 Minutes

• ##### Device
• TI-83
• TI-83 Plus Family
• TI-84 Plus
• TI-84 Plus Silver Edition
• ##### Other Materials
This is Activity 3 from the EXPLORATIONS Book:
Statistics Handbook for the TI-83

• ##### Report an Issue

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.

• 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