Linear regression results: How to interpret the plot? I have a dataset where I am comparing two variables, activity is dependent and days_existed is independent. The correlation between the two variables is 0.41 and I ran an OLS linear regression analysis then plotted the results.
R-squared is 0.15 and p-value for dependent variable is 0.000, the intercept coefficient is negative. 
What else should I be looking at that could be important in determining is there is a relationship between the two variables?
Here is the plotted regression line, it looks like the model is wrong to me.

 A: I perceive a number of potential problems.


*

*Your response appears to be a count, and in any case cannot be negative; ordinary linear regression will necessarily be negative somewhere, so something like a negative intercept shouldn't be a surprise. 

*Further, the assumption of constant variance won't hold - if the mean is close to 0, non-negative data will tend to squish up near the axis (have low variability), while where the mean is large there will tend to be more variability.

*As the mean becomes smaller, the true mean relationship cannot plow down through 0; you would therefore expect it to curve so that the mean doesn't enter an impossible region.

*The plot seems to hint that there's a degree of clumpiness in the distribution that might perhaps suggest other important predictors.

*If these are observations over time, there may be dependence over time (autocorrelation)
These observations suggest ordinary linear regression is unsuitable.
It may be that something more like a GLM with a log-link would be more suitable; perhaps a negative binomial wouldn't be too poor, possibly zero-inflated.  (I wouldn't try a Poisson GLM - the variation looks to be much too large relative to the mean.) However, I don't think that can deal with the apparent clumpiness nor with time dependence; some additional investigation (and likely, larger models) would be needed to address those adequately. 
