Residual Plot Interpretation

[t.searls]

I'm fairly new to statistics as a whole so you'll have to excuse my ignorance if this is an easier answer than I've been making it to be... I have an OLS regression. The fitted-observed and fitted-residuals plots are below. Needless to say the data is non-normal. Is there anything I can do to meet the '6 OLS assumptions'. I have been avoiding transforming the model dependents because the study this OLS applies to looks more at the relationships between variables and their significance versus the model fit itself...


Thanks,
Tyler

 

[Karabiner]

What is your dependent variable? There exist phenomena where non-transformation
has to be justified rather than transformation. And what are your predictor variables?

With kind regards

Karabiner

 

[t.searls]

The dependent is a growth increment and the predictors represent various climate, stand and environmental conditions.

There are species and regional categoric variables included. These predictors are used only in interaction terms with other climate predictors.

Kind regards,
Tyler

 

[Karabiner]

Can you assume that growth is linear with respect to your predictor variables?
Growth increment can be better modeled after its natural logarithm is taken,
as far as I know.

With kind regards

Karabiner

 

[t.searls]

It's possible the relationship may be non-linear. I had thought the distribution of the fitted-observed plot almost looked exponential. My concern with any transformation of the dependent or predictors is that my ability to quantify the relationship between the transformed variables becomes muddied.

In the case of a transformed dependent, predictor coefficients are now related to a log-transformed dependent rather than the dependent itself.
That is to say the coefficient for mean temperature can no longer be interpreted as 0.9 degrees to each centimeter growth increment?

This would be problematic since, as I've said, the intent of the study is to explore these relationships more than establish a idealistic fit. Still, in order to explore these relationships, the model needs to have merit. This is my dilemma.

Thanks again,
Tyler

 

[Karabiner]

the intent of the study is to explore these relationships more than establish a idealistic fit. Still, in order to explore these relationships, the model needs to have merit.

Personally, I would never suggest to transform data just in order to achieve a perfect fit or
to meet some more or less sensible model assumptions. Here we have a substantial
argument in fovour of a transformation. Since growth is exponential, a linear model makes
only limited sense

That is to say the coefficient for mean temperature can no longer be interpreted as 0.9 degrees to each centimeter growth increment?

If the transformation was LOG(10), then you would have % increment instead of cm increment.
Although Ln would be the more appropriate choice for biological processes, at least so I was told.
Moreover, you could plot relationships on a logarithmic rather than a linear scale

With kind regards

Karabiner