I am working on a very large data set (n = 6.5 million) and I am trying to come up with a simple linear regression between two variables. I am working in R and using a monte carlo style simulation to estimate the true intercept and slope. I take a sample of 1000 and run the regression and store the corresponding beta0 and beta1 into vectors, and repeat this process 10,000 times. I am doing it this way because the data set is too large for me to effectively identify points as being outliers, etc. My question; When I do histograms of the 10,000 beta0's and beta1's, the distribution has a very distinct bimodal shape (one large peak, and a smaller peak). What does this tell me about my data and the relationship between the two variables? Can I assume the 'true' coefficients lie in the center of each of the bigger peaks?
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This might mean that there is not a single relationship between the two variables, and that subsets of the data follow different relationships, ie. that the true model is a mixture.
