The series was transformed into natural logarithms
and found to be first-order integrated, I(1).
Notably, the transformation of the original values of the variables in natural logarithms
increased the correlation coefficients with TBCOEF10, which was favorable for the development of the model.
Subsequently, all the series have been transformed in billion lei and in natural logarithms
Thus, in Figure 11, natural logarithms
are used instead of common logarithms, while a calculator that provides logarithms to bases other than 10, such as Casio fx-991ES PLUS, is used to demonstrate that the idea of halving the logarithm to find a square root (previously illustrated in Figure 6) is a feature of logarithms in general, not only of common logarithms: the numerical square root of 52 can be found with logarithms to any base.
The authors have also include tables of common (Briggsian) logarithms, natural logarithms
, exponential functions, and trigonometric functions.
1991:120; see also Morris and Doak 2002:68 and Mills 2007:109) in which natural logarithms
of the ratios of successive raw counts are regressed on the intervals between surveys, forced through the origin.
Log (TNA), Log (Family Size), Log (Tenure), and Log (Fund Age) are the natural logarithms
of fund total net assets in the month prior to the quarter, the number of funds in the family, the length of manager tenure, and the fund age since the first offer, respectively.
Thus, [mu] is the overall mean for the natural logarithms
of the expected frequencies, [lambda] terms each represent "effect" which the variables have on the cell frequencies S, Z, and Y are the variables i, j and k refer to the categories within the variables.
To estimate the parameters ([beta], v, [gamma]) in (2), the data for continuous variables: yield, seed, fertiliser, herbicides/fungicides, traction, manure and hired labour except gross profit margin were transformed into natural logarithms
to normalise data as well ease the interpretation of the estimated coefficients as elasticities .
By plotting the natural logarithms
of the slopes of the trend lines from Fig.
Because of too large margins revealed by profitability and company size (total assets) values of the companies natural logarithms
were preferred in order to harmonize the data.
4 Variable N BC Job rotation 25,862 WC Job rotation 25,862 Total Job rotation 25,862 BC Wage-diff (isic 2) 27,987 WC Wage-diff (isic 2) 27,835 Total Wage-diff (isic 2) 27,767 Output growth 26,360 Unempl (City) 28,589 Elect cons (KWh) 27,991 Note: All variables are expressed in natural logarithms