I have done a presentation where I have used regression equation to know the relationship between productivity and profitability. Now to get a certificate, I have been asked to criticize my work and create a one page study on what alternative method I could use to check the relationship other than regression equation. For now Google is not helping me. Can anyone help me suggest something?
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$\begingroup$ Alternates in what sense? Different loss function (/different error assumption)? Different relationship than linear? something else? $\endgroup$– Glen_bCommented Jan 20, 2016 at 7:05
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$\begingroup$ see e.g. section 5.2, 9.1, 12.3.6 and many other sections of web.stanford.edu/~hastie/local.ftp/Springer/OLD/… $\endgroup$– user83346Commented Jan 20, 2016 at 7:31
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3$\begingroup$ It is sort of an odd question. In statistics, you generally start with a problem and pick a good statistical method/model to solve it. Regression is popular for many reasons but it is not perfect. Before looking into different models, you first need to Identify where and for what reasons your regression model may not be performing well or does not seem ideal. I.e. non-linearity, outliers, invalid predictions, etc. Once you have can articulate the problem, it will be much easier to find an alternative method. $\endgroup$– Zachary BlumenfeldCommented Jan 20, 2016 at 8:52
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There are different ways to do a prediction analysis or a regression if you want and maybe the answer to your question is a bit too broad.
You can do a classical regression with linear or non-linear model, which i think is what you have done.
You can do a regression with a Bayesian approach if you want to weight more your "a-priori knowledge":Wiki
You can have a machine-learning approach:Wiki
You can apply non-parametric methods if you don't know the population distribution:Wiki
You can apply robust regression methods:Wiki
I think there is some material here to start investigating your answer
