Here the outcome variable is continuous and bi-modally distributed with clustering at the both extreme ends of histogram. The predictor is a categorical variable which has three categories such as wild type (no polymorphic allele), heterozygous (one mutant allele) and homozygous (two polymorphic alleles). I guess such categorical variable is an ordinal variable. What kind of regression should i do in such a situation?
In linear regression for continuous response, it is the distribution of the residual which needs to be normally distributed (not necessarily the distribution of the response itself). If the assumption of normally distributed residuals is not satisfied (even after applying transformation to your response variable) then you may have to try alternative approaches, probably one suggested by Derek.
Here is a thread which is relevant to your question:
http://stats.stackexchange.com/questions/12262/what-if-residuals-are-normally-distributed-but-y-is-not
You can try logistic regressio analysis. If you use the online webserver SNPstats you can do this I hope
Logistic regression can be used if the outcome variable is binary. However, in this case the outcome variable is continous, hence a linear regression would be okay and multiple linear regression if there are other co variates.
First, we need to assume log additive model to call the three genotypes as ordinal (http://en.wikipedia.org/wiki/Ordinal_data). If we are uncertain, then it will be safe to keep the genotypes as indicator (i. genotype) variables.
Second, try linear regression and save the residuals. Check whether the residuals follow Gaussian distribution. If not, you may try one of the following fixes,
1. log transformation of the outcome variable; repeat linear regression, and then check whether the residuals follow Gaussian distribution
2. Try to fit a quadratic equation
3. Employ nonparametric robust regression models.
Good luck
In linear regression for continuous response, it is the distribution of the residual which needs to be normally distributed (not necessarily the distribution of the response itself). If the assumption of normally distributed residuals is not satisfied (even after applying transformation to your response variable) then you may have to try alternative approaches, probably one suggested by Derek.
Here is a thread which is relevant to your question:
http://stats.stackexchange.com/questions/12262/what-if-residuals-are-normally-distributed-but-y-is-not
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