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In the preceding section we observed that the exponential trend curve is determined by doing a linear regression with data points of the form . We can, of course, do that linear regression directly by taking natural logarithms of the y data. Furthermore, it is often more revealing to work with the logarithm of data than the data itself. The CPI rose from 2.3 in 1913 to 179.9 in 2002, a change of two orders of magnitude. The standard xy-graph does not do justice to the details of change over such a large range. But if we work with logarithms of the CPI, our graph can show details of the entire history. Here is the way to calculate natural logarithms of a data column in Excel:
To graph the logarithmic data, follow these steps:
In the preceding section we saw that the exponential trend curve has the formula . If we take the natural log of the right-hand side of this formula, we find that
.
This last expression is the formula for the regression line in Figure 10 -- which confirms that the exponential trend curve is actually derived from the regression line.
Another way to see a logarithmic plot of the data is to use a logarithmic scale on the vertical axis. To do so, go to the original graph in your worksheet (see Figure 6 or Figure 7). Double-click the vertical axis. Choose Scale and Logarithmic scale
Elizabeth B. Appelbaum, "The Consumer Price Index and Inflation - Calculate and Graph the Logarithm of the CPI," Loci (December 2004)
Journal of Online Mathematics and its Applications