If you are trying to find the relationship between a dependent variable a 2 continuous predictor variables which you call covariates, then perform multiple regression analysis. Your dependent variable is flow and covariates are preflow and total rain. If you adopt multiple regression and want to compare means, you perform a 2-way analysis of variance; hoping that I understood you well.

Anand Nainar,

I like preserving as much of the original information as possible (first method in step 1). But, there may be a compelling reason to create the index—I'll default to your discretion on this.

I don't think you want to take the difference in flow (option 3), unless taking the difference in preflow has the same relationship and will you will not lose information when regressing. (This isn't a bad approach though; good thinking).

Options 1 and 2 are essentially the same, but 2 might be a little better for modeling and interpretation.

I wrote an R script (attached) for the approach I would take. This is a very preliminary analysis and should really only serve you as a comparison of method/approach. After reading in and wrangling the data, I built a "Global" multiple regression model using Box-Cox transformation and removing outliers—needed to do this to fit a decent linear model. The model included flow_id (A or B), total_rain, preflow_val, and the interaction of total_rain and preflow_val.

I then did model selection to compare fit of model with and without flow_id factor. The highest weighted model for best fit did not include the flow_id factor (interpreted by some to mean 'does not have an effect') and was able to explain about 83% of the variation. A scatterplot shows the best fitting model, with transformed flow on y-axis, total rain on x-axis, and point size the preflow value. I include the flow_id factor (A and B) and a color just for the extra info.

Hope this helps.

Cheers,

Caleb

Caleb A. Aldridge

Sorry for the late reply. I was reading and trying the code line by line.

That was extremely clear and elaborate. Sorry to put you through this, but thank you so much. Your kind of reply deserves to be in a textbook.

I clearly understood every explanation and line of code. However, i think i will need to include the outliers in my analysis.

See attached PDF.

Jochen Wilhelm Hi Sir. Sorry for the late response. Thank you for such elaborate steps. I understood everything!

One question - Why wouldn't you choose to model the differences between the two dependent variable against the predictors? Does that not have higher statistical power?

Anand Nainar, I am not sure what the results of such a model would tell me.