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Exponential Regression

            Suppose we want to find a model for the data given in the following table:

x

4

6

8

10

12

y

0.2

0.7

1.4

2.8

5.8

Figure 1 below shows a plot of the points.

Figure 1

Notice that the points appear to have the shape of an exponential function. That is, they are increasing and concave upward. We can use the Exponential Regression Applet to calculate the exponential regression equation for the data. The exponential regression equation is the equation of the form , which provides the best fit for the data. Using the Exponential Regression applet enter the data in the x and y columns. Then click the Plot button to plot the points and the Analyze button to find the equation. See Figure 2.

Figure 2

We see that the exponential regression equation for the data is  (coefficients are rounded to four decimal places).