2.6 Lines of Best Fit

Using linear regression features on graphing calculators.

Step 1: Enter the data into two lists. Press STAT, EDIT and in the L1 column, enter all the x-values from the ordered pairs. In the L2 column, enter all the y-values from the ordered pairs

Example: The table shows the number y (in thousands) of alternative-fueled vehicles in the US, x years after 1997. Approximate the line of best fit by using a calculator.

x 0 1 2 3 4 5 6 7

y 280 295 322 395 425 471 511 548

Another way to enter data is from the main screen; use the curly brackets (above parentheses) and input each x-value list with commas in between, store to L1, then do the same for y-values, store to L2.

Step 2: Find an equation of best fitting (linear regression) line.Press STAT, choose CALC, and then LinReg(ax + b). Your screen should look like this:

Select Calculate and up will come this screen:

If your correlation coefficient doesn’t show up, in CATALOG, select DiagnosticOn.

OR If this one, you might need to make sure it is using L1 and L2 by inputting after this command

Write down equation. To graph, you also could have stored this equation in the previous step.

Step 3: (optional in some problems) Make a scatter plot to see how well the regression equation models the data. Select an appropriate window. Press 2ND STATPLOT to set up your plot. Hit enter to select Plot1. Make sure ON is highlighted, the Type is SCATTERPLOT (look for bunch of points) and where Data is coming from: Xlist: L1 Ylist: L2Select what kind of mark you want showing .

Step 4: Graph the data and the regression equation and see how it looks with data.

You can use this Line of BEST FIT to predict values in regions where you don’t have data. This is called Forecasting , and is used extensively in business and scientific applications

For example, use the equation in our example to predict how many alternative-fueled cars there are in 2014.

Solution: Since t = 0 represented 1997, and 2014 represents t = 17, we would take our equation and input t = 17You could do this with trace, but might need to change your window to include x = 17. Make sure you are paying attention to which graph you are tracing on.If x = 17, y = 957.6, which is in thousands of cars.

HOW DID WE DO?