Fitting Exponentials and Polynomials to Data Lesson 9.7

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 1970 1975 1980 1985 1990 1995 2000 t 5 10 15 20 25 30 35 Lobster 17 19 22 27 36 56

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 4th 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 regression 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 9.7 Page 431 Exercises 5, 13, 15, 17, 19