2. M ORE ON T WO V ARIABLE D ATA Non-Linear Data Get That Program Fishy Moths

3. Exponential N ON -L INEAR D ATA 1 st : Scatterplot 2 nd : Linear Regression Stats 3 rd : Examine r, r 2, and RESIDUAL Plot If the residual plot shows a pattern… It’s NOT LINEAR DATA!! At this point we have 2 choices… Power But how do I know which one it is? Man, He’s buff!!!

4. H OW DO W E D ECIDE The Easiest Way Try one Not good Enough? Try the Other 1: (log) the y data to “straighten” it out 2: Once you (log) the y’s, Run LinReg again to get your new equation 3: Log(y) = a + bx (log) the y AND x data to “straighten” it out Exponential Once you (log) the y AND x data, Run LinReg again to get your new equation Log(y) = a + bLog(x) One of these methods will have“linearized” your data and have new Equations to go with it!!! Then, Look at the Scatter & Residual Plots to see if your data’s “linear” Power If Not…

5. H OW D O I M AKE P REDICTIONS W ITH M Y N EW E QUATIONS ? Exponential Power Log(y) = 23 +.345x Log(y) = 23 +.345Log(x) You can still make predictions! You just have to “adjust” your equations! Let’s Look at the Math to see how!! Now that we can make “straighten things out” and make predictions, let’s do some practice!!

6. The Attack of the Gypsy Moth’s!!! YearAcres 197863042 1979226260 1980907075 19812826095 The Gypsy Moth Outbreak came to fruition in 1978. The Moths invaded and DESTROYED America’s Fields at an astonishing rate!! Use the data below to help scientists make some gutsy predictions!! 1)Scatterplot 2)Eq & Residual Plot 3)Log y’s 4)Eq & Residual Plot 5)Write the Equation 6)Fix it and Predict Predict The # of Acres Decimated by 1982… 1990…

7. Log y = -1094.507084 +.5557705737x y-hat = 10^ (-1094.507084 +.5557705737x) 1982… = 10719957.74 acres 1990… = 2.99e11 acres Do your Math Magic to “fix” this Equation Now, Plug in 1982 & 1990 to predict…

8. Attack of the Rockfish!!! Run the FISHY program to get your data… 1)Scatterplot 2)Eq & Residual Plot 3)Log y’s 4)Eq & Residual Plot 5)Write the Equation 6)Fix it and Predict Until he was eaten by the great beast, Alber Fishstien devoted his life to studying a Green River Rockfish he called, Rocky. He collected data comparing Rocky’s length in cm (L1) and weight in grams (L2) over a 20 year maturation period. You were out fishing and snagged a 36 cm Rockfish. Since you left your trusty scale at home, use regression to estimate your fishy’s weight.

10. Log (y) = -1.899397207 + 3.049417866 Log (x) y-hat = 10 ^(-1.899397207 + 3.049417866 Log (x)) y-hat = 10^ (-1.899397207 + Log (x^ 3.049417866) y-hat = 10^ (-1.899397207) x^ (3.049417866) 702.133 grams