If you type data into your calculator and it appears to be linear, it can find the equation of the line for you.  This process is called performing a linear regression.

Calculator Set Up

  1. Make sure that your calculator has the Plots Off, Y= functions cleared, the MODE and FORMAT are set at “stage left”, and the lists are cleared.
  2. Turn the Diagnostics on.
  • Press 2nd the CATALOG (2nd of 0).  Press the teal D button (ALPHA of x-1)  This brings you to the items in the catalog that start with D.
  • Arrow down until you reach the command DiagnosticOn and press ENTER.
  • Press ENTER a second time.  Later, when you perform a linear regression, you will see an “r” value.  If that value is close to a ±1 there’s a strong correlation to the data, meaning the data points can be modeled by the line well.

Enter the Data

Data for this lab will be stored in L1 and L2.

  • Press the STAT menu and choose option 1:Edit…Stat Edit has Lists cleared
  • Type the first value in the L1 table, then press ENTER, type the second value next, and so forth.
  • Arrow over to the L2 table and enter the corresponding dependent values
  • Make sure there is an equal amount of data in both L1 and L2 so you don’t get a “dim mismatch” error.

Performing a Linear Regression

  • To view your data, you must set up a stat plot. Press 2nd STAT PLOT (2nd of Y=).  Press
    Stat Plot OnENTER
    to set up Stat plot 1.  Set up your stat plot to look like the one at the right.  Then press the ZOOM key and choose option 9:ZoomStat.
  • To find an equation that matches the data you see, you need to perform a linear regression on the data. Press the STAT menu and arrow to the right to the CALC menu.  Choose option 4:LinReg (ax+b).  Type L1, a comma, L2, then the VARS button, arrow over to Y-VARS, choose 1:Function, the 1:Y1 option, then press ENTER.

When you press the GRAPH button a line that matches your data points will also be in your viewing window.  Pressing the Y= button will give you the equation of that line.

Let’s have the calculator find the line of best fit for wing length vs. wing-beat rate.

  Flamingo Shell Duck Velvet Scooter Fulmar Great Egret
Wing Length (mm) 400 375 281 321 437
Wing-Beat Rate (bps) 2.4 3.0 4.3 3.6 2.1

 

Equation of your line _________________________

Correlation Coefficient ________________

A printable version of this activity is available for classroom use. Linear Regressions on TI Graphing Calculators