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Chapter 11: Rolling the Dice on Predictions and Probability
In a linear model, the mathematical formula that models the data is as
Y = mX + b
This tells you that for any X value, you calculate the Y value by multiplying X
by a constant m, and then adding another constant b. The value m is called the
line’s slope and b is the Y intercept (the value of Y when X = 0). This formula
gives a perfectly straight line, and real-world data doesn’t fall right on such a
line. The point is that the line, called the linear regression line, is the best fit
for the data. The constants m and b are different for each data set.
In an exponential model, the following formula models the data:
Y = bmX
The values b and m are, again, constants. Many natural processes,
including bacterial growth and temperature change, are modeled by exponential
curves. Figure 11-1 shows an example of an exponential curve. This curve is
the result of the preceding formula when b = 2 and m = 1.03.
Again, b and m are constants that are different for each data set.