t+3] defined as the natural logarithm
of one plus the total number of nonself-citations received on the firm's patents filed (and eventually granted) scaled by the number of patents filed (and eventually granted) at year t + 3.
Price of borrowed funds = the natural logarithm
of the ratio of interest expenses to the sum of deposits
The coefficient on the natural logarithm
of total revenue is positive in each sample year, but is statistically significant in 2010, 2012, and 2013.
The outcome variables examined are the natural logarithm
of net premium written (NPW), the natural logarithm
of assets, the natural logarithm
of capital-to-assets, the fraction of premium ceded to reinsurers, and an indicator that the insurer is paying dividends.
The dependent variable of the second-stage regressions is the natural logarithm
of the duration between two rounds in months.
The estimated coefficients are in natural logarithm
form and thus show elasticities of wheat production with respect to various explanatory variables.
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.
By plotting the natural logarithm
of K(T) as a function of the inverse temperature, the slope of the graph is proportional to the activation energy of diffusion, and the intersection of the graph with the ordinate is the proportionality factor [K.
Since some of the initial results are less than 1, and the natural logarithm
of a number less than one returns a negative number, the value had to be increased a nominal amount.
The rate of return is the change in the natural logarithm
of the price index for a given time period.
dt is the natural logarithm
of the international food price index for a specific country, [gdp.
PBASt = a0 + a1ACTIVITYt + et where ACTIVITY indicates natural logarithm
of either the number of transactions (NT) or the trading volume (VO).