Page 148 - Statistics II for Dummies

132 Part II: Using Different Types of Regression to Make Predictions

The math magic used in these steps is courtesy of the definition of logarithm,
which says . Suppose you have the equation log y = 2 + 3x.
10
If you take ten to the power of each side, you get . By the definition
of logarithm, the tens cancel out on the left side and you get y = 10 2+3x . This
model is exponential because x is in the exponent. You can take step two
up another notch to include the general form of the straight line model
y = b + b x. Using the definition of logarithm on this line, you get
0 1
.
1. Make a scatterplot of the data and see whether the data appears to
have a curved pattern that resembles an exponential curve.
If the data follows an exponential curve, proceed to step two; otherwise,
consider alternative models (such as multiple regression in Chapter 5).
Chapter 4 tells you how to make a scatterplot in Minitab. For more
details on what shape to look for, refer to the previous section.
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. Here’s what Minitab does:
1. Minitab applies the log (base 10) to the y-values. For example, if y
is equal to 100, log 100 equals 2 (because 10 to the second power
10
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 leave you with a straight line.

2. Minitab fits a straight line to the log(y) values by using simple
linear regression (see Chapter 4). The equation of the best-fitting
straight line for the log(y) data is log(y) = b + b x. Minitab passes
0 1
this model on to you in its output, and you take it from there.
3. Transform the model back to an exponential model by starting with
the straight-line model, log(y) = b + b x, that was fit to the log (y)
0 1 10
data and then applying ten to the power of the left side of the equa-
tion 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 + b x on the right side. The resulting exponential
0 1
model for y is .
4. Use the exponential model 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.

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