Page 165 - Intermediate Statistics for Dummies

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Part II: Making Predictions by Using Regression
If the data follows an exponential curve, proceed on to the next step;
otherwise, consider alternative models (such as multiple regression in
Chapter 5).
To see how to make a scatterplot in Minitab, check out Chapter 4. For
more details on what shape to look for, see the section “Recollecting
exponential models.”
2. Use Minitab to fit a line to the log(y) data.
In Minitab, you go to the regression model (curve fit). Under Options,
select Logten of y. Then select Using scale of logten to give you the
proper units for the graph.
Understanding the basic idea of what Minitab does during this step is
important; being able to calculate it by hand isn’t. You can see what
Minitab does during this step in the following:
• Minitab applies the log (base 10) to the y-values. For example, if y
is equal to 100, log 10 100 equals 2 (because 10 to the second power
equals 100). Note that if the y-values fell close to an exponential
model before, the log(y) values will fall close to a straight-line
model. This phenomenon occurs because the logarithm is the
inverse of the exponential function, so they basically cancel each
other out, and you’re left with a straight line.
• Minitab fits a straight line to the log(y) values by using simple
linear regression (from Chapter 4). The equation of the best-fitting
straight line for the log(y) data is log(y) = b 0 + b 1 x. Then Minitab
passes this model on to you in its output; you take it from here.
3. Transform the model back to an exponential model by starting with
the straight-line model, log(y) = b 0 + b 1 x, that was fit to the log 10 (y) data
and then applying ten to the power of the left side of equation and ten
to the power of the right side.
By the definition of logarithm, you get y on the left side of the model and
ten to the power of b 0 + b 1 x on the right side. The resulting exponential
model for y is y = 10 b 0 + b 1 x .
4. Use the exponential model found in step three to make predictions for
y (your original variable) by plugging your desired value of x into the
model.
Only plug in values for x that are in the range of where the data are
located.
5. Assess the fit of the model by looking at the scatterplot of the log(y)
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data, checking out the value of R adjusted for the straight-line model
for log(y), and checking the residual plots for the log(y) data.