In constructing a confidence interval for the mean value of y for a mathematical model based on a natural log transformation of y, the initial confidence interval is:
- E + E which we can then
Which we can then transform back to the original units:
e{ - E) + E)
In the example of the wood density being used to predict stiffness, we reproduce the data:

In that example, it was shown that a natural log transformation of stiffness had r1 = 91.41 %. If we construct a mathematical model based on this transformation, for a density of 20, construct a 95% confidence interval of the mean stiffness, rounding the transformed limits to the nearest hundred.

Density 21.7 15.2 23.4 154 4.5 16.7 25.6 15 24.4 7 Stiffness 47,661 28.028 104,170 25,312 22,148 49,499 25,319 96,305 26,222 72,594 5304