Considering the aforementioned exclusion, correlations between variables transformed to

natural logarithm showed that the largest correlation coefficient of LN_TBCOEF10 was with LN_PEROOM (0.

For these models we removed the CPI variable from our base estimations and replaced it with the

natural logarithm of the food price index and the core price index mentioned in the previous section.

All explanatory variables except initial income are country averages for the 1980-2000 period; all are entered as

natural logarithms.

Figure 1 shows the results (outputs) of the simulation model as a probability distribution function of

natural logarithm of total phosphorus (TP') for each trophic level.

Proportional 95% upper and lower bounds for variance components as a function of the variance of

natural logarithms of the component.

Mathematical operations involving

natural logarithms are the same as shown in Table 1-4.

The mean gonad weight at a constant carapace width for each sex in each month in each water body was determined by using analysis of covariance (ANCOVA) of the

natural logarithm of the gonad weight as the dependent variable, month as a fixed factor, and the

natural logarithm of the carapace width as a covariate.

Finally, we ran a regression of the rate of change of the

natural logarithm of the inflation-adjusted average hourly earnings (i.

The standard ma th functions include power, square root, square,

natural logarithms and exponential, fractional, integer, reciprocal, factorial, and rounding.

I also took the

natural logarithms of the control variables (discussed below).

From 1938 to 1946, 37 volumes of the NBS Math Tables Series were issued, containing tables of trigonometric functions, the exponential function,

natural logarithms, probability functions, and related interpolation formulae (23).

All variables are converted into

natural logarithms, and their first differences are taken.