View
222
Download
0
Category
Preview:
Citation preview
MORE ON TWO VARIABLE DATANon-Linear Data
Get That ProgramFish
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
Attack of the Rockfish!!!
Run the FISH 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
HOMEWORK
17-19,24,25Exponential M&M’s?
Recommended