MORE ON TWO VARIABLE DATANon-Linear Data

Get That ProgramFishyMoths

Exponential

NON-LINEAR DATA

1st: Scatterplot 2nd: Linear Regression Stats 3rd: Examine r, r2 , 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!!!

HOW DO WE DECIDE

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…

HOW DO I MAKE PREDICTIONS WITH MY NEW EQUATIONS?

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!!

The Attack of the Gypsy Moth’s!!!

Year Acres

1978 63042

1979 226260

1980 907075

1981 2826095

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) Scatterplot2) Eq & Residual Plot3) Log y’s4) Eq & Residual Plot5) Write the Equation6) Fix it and Predict

Predict The # of Acres Decimated by 1982…

1990…

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

…

Attack of the Rockfish!!!

Run the FISHY program to get your

data…

1) Scatterplot2) Eq & Residual Plot3) Log y’s4) Eq & Residual Plot5) Write the Equation6) 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.

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