Hi there, I am attempting to predict a dependent variable from 3 independent variables. All 4 variables are log normaly distributed and so I have transformed all the variables (dependent and response) by adding a constant to bring the minimum value of each variables to 1 so that the natural logarithm of the variable and the coinstant can be taken.
I then regressed the results to get the following formua, shown below for just 1 independent variables:
ln(Y+K) = B*ln(x + a) + c , where a and k are the constants to bring the variables minimum above 1.
I then rearranged and solved for Y:
Y = exp(b1) * (x + a) + exp(c) - k
Is this correct?
When I compare the prediction of ln(Y + K) to ln(Y + K) for all predicted values I get very accurate results i.e. pearson correlation coefficient of 0.917, slope of .84 for prediction vs origional and the sum of predicted / sum of the origional equal to 1(roughly), however after solving for Y as shown above the predicted values are not as accurate, pearson correlation of 0.737, slope of 0.2 and quotient of sums = 2.67.
Really annoying as the prediction of ln(Y + K) is nearly perfect but after solving for Y the results really are not accurate anymore.
Any help would be absolutely fantastic