Take log of your data for regression Analysis

Logarithmic transformations are very popular in econometrics, for several reasons. First, many economic time series exhibits a strong upward and downward trend. When this is caused by some underlying growth process, a plot of the series will reveal an exponential curve. In such cases, the exponential component dominates other features of the series like cyclical and irregular components of time series, and may thus obscure the more interesting relationship between this variable and another growing variable. Taking the natural logarithm of such a series effectively linearizes the exponential trend.

For example, one may want to work with the log of macroeconomic variables, which will appear on a graph roughly a straight line, rather than the exponential curve exhibited by the raw series.

Second, logs •nay also be used to linearize a model that is non-linear in the parameters.

All examples are the Cobb-Douglas production function:

Y = AL^αK^βe^µ 

Taking logs of both sides we obtain:

ln(Y) = ln(A) +a ln(K) + b ln(L) + u

so that the transformed model becomes:

y = a + ak + bl + u

Which is linear in the parameters and hence can easily be estimated using ordinary least

squares (OLS) regression.

The third advantage of using logarithmic transformations are that it allows the regression

Coefficients to be interpreted as elasticities since for small changes in any variable x, change in log x relative change in x itself. (This follows from elementary

differentiation: d(ln x)/dx = 1/x and thus d(ln x) = dx/x.)

In the log-linear production function above measures the change in In( Y)

Associated with a small change in ln (K), i.e. it represents the elasticity of output with

respect to capital.