I have 1 continuous dependent and 1 continuous predictor variable that I've logarithmically transformed to normalise their residuals for simple linear regression. Can someone give me some pointers on how to relate these transformed variables to their original context?
I want to use linear regression to predict the number of days of school that pupils missed in 2011 based on the number of days they missed in 2010. Because most pupils miss 0 days or just a few days the data is positively skewed to the left hence the need for transformation to use linear regression. I've used log10(var+1) for both variables (I used +1 for pupils who had missed 0 days school). I'm looking to use regression because I want to add in categorical factors - gender/ethnicity etc too.
The audience I want to feed back to wouldn't understand log10(y) = log(constant) + log(var2)x (and frankly neither do I). Are there better ways of interpreting transformed variables in regression? I.e. for ever 1 day missed in 2010 they will miss 2 days in 2011 as opposed to for ever 1 log unit change in 2010 there will be x log units change in 2011?
I'm using SPSS v20.
Actually I suppose my specific question is this.
Looking at the following website
it quotes that:
"This is the negative binomial regression estimate for a one unit increase in math standardized test score, given the other variables are held constant in the model. If a student were to increase her mathnce test score by one point, the difference in the logs of expected counts would be expected to decrease by 0.0016 unit, while holding the other variables in the model constant."
Is this saying that for every one unit increase in the score of the UNTRANSFORMED variable math leads to a 0.0016 decrease from the constant (a)? So, if UNTRANSFORMED maths score goes up by two points, I subtract 0.0016*2 from the constant a? Therefore, to model the effect, I get the geometric means by using exponential(a)) and exponential(a+beta*2) and calculate the percentage difference between these two to say what effect the predictor variable(s) has/have on the dependent variable?
Or have I got that totally wrong? Sorry for framing this in a long question.