First we take the first model η=e^(β0+ β1X) and try the transformed data ln(y) given in table two, where η= y. The scatter diagram for this data, exhibits approximate linear relations.

Table 2. Data transformed using Ln(y)

Figure 2. Scatter diagram of the transformed data given in table 2

With the aid of a standard computer program for regression analysis the following results are obtained by transforming the original data.

Regression Analysis: ln(y) versus X

Analysis of Variance

Thus, the equation of the fitted line is

The proportion of the ln(y) variation that is explained by the straight line model is

which means that the model used to fit the data of table one is accurate, because the result of R^2 and a standard deviation of 0.192228, using a 95% confidence interval.