Fitting Exponentials and Polynomials to Data Lesson 11.7

Linear Regression Used in section 1.6 to find equation for a line of best fit Used in section 4.4 to find equations of logarithmic models Other types of regression are available

Problem … Which Regression? Not always obvious which type of regression to use Consider the lobster catch (in millions of lbs.) in the last 30 some years  Enter into Data Matrix Year t Lobster

Viewing the Data Points Specify the plot F2,  X's from C1, Y's from C2 View the graph  Check Y= screen, use Zoom-Data

Which Regression? The graph could suggest different modeling functions  To find a modeling function which includes the third point makes us think of a polynomial function  To let that point be off the modeling line, it could be a power function or an exponential

Try Different Regressions Try for a quadratic function Try for power function

Try Different Regressions Try for 4 th degree polynomial

Try Different Regressions What about exponential regression?

Which is Best? Issues  Which best fits data?  Which gives best predictions for years of given data?  Which gives best predictions for future?  Might there be one that gives us an idea of what was done in the past (where we have no records)?

Other Technology Tools Excel will also do regressionExcel Plot data as (x,y) ordered pairs Right click on data series  Choose Add Trend Line

Other Technology Tools Use dialog box to specify regression Try Others

Assignment Lesson 11.7 Page 477 Exercises 5, 13, 15, 17, 19