where all variables are defined the same as in Equation (2), except [IE.sub.i.t] is the

natural logarithm of one plus one of the four patent and citation innovative efficiency measures in time t for firm i--used as the dependent variable in the previous sections.

Considering the aforementioned exclusion, correlations between variables transformed to

natural logarithm showed that the largest correlation coefficient of LN_TBCOEF10 was with LN_PEROOM (0.578), implying that the average number of people per room was the factor of greatest influence on TB prevalence in Belem.

Along with three variables described above, in the second model specification we add the

natural logarithm of the stock of FDI (FSR) to equation 1 to test the FDI-specific impact on exports with impact of increased supply capacity held constant.

Finally, the multiple linear model in terms of

natural logarithm of total phosphorus (TP') is

Leonard (1975) described a Bayesian hierarchical model with multivariate normal structure for means and for

natural logarithms of variances that clearly demonstrates important properties of shrinkage estimators when applied to both means and variances.

Mathematical operations involving

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

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

natural logarithm of the inflation-adjusted average hourly earnings (i.e., the slope of the regression of the

natural logarithm of the inflation-adjusted average hourly earnings on the year of observation) on the rate of change of the fatality rate and rate of change of the injury and illness.

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

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

For each year I took the

natural logarithms of the following variables:

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.