Microsoft Office Tutorials and References

In Depth Information

**Chapter 11: Rolling the Dice on Predictions and Probability**

Linear model

In a linear model, the mathematical formula that models the data is as

follows:

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.

Exponential model

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.

Figure 11-1:

An

exponential

curve.