Simple Linear Regression Interpretation help I am supposed to analyze a relationship and model of two variables. Here's what I got. the p-value indicates a relationship but the R-squared is tiny. The model does not look linear at all. How would you analyze this? Do I need a polynomial? Do I need to do anything to this model?


 A: It depends how sophisticated you want to be. If you're only interested in the linear association (i.e., correlation) between these variables, what you have done is enough. A significant F-value means there is evidence of a relationship between the variables. A small R2 means there is much variability in the outcome that is not explained by the linear effect of the predictor, or equivalently that the linear effect of the predictor explains only a small portion of the variability in the outcome. Because your sample is so large, you have enough evidence to claim that there is a relationship in the population, though it would seem this relationship is weak.
If you want to be more sophisticated and really see if a non-linear relationship between the variables would fit the data better, you can try one of many flexible regression models like cubic splines, kernel regression, or loess regression models. These attempt to squeeze more information about the outcome from the predictor. In all of these, you won't be able to read off a parameter estimate that can be interpretable, but you will be able to plot the predictions against the observed values, as you have done, and you can interpret that graph.
A: I agree with @Noah 's answer. Additionally, which is seems beyond the task at hand, is there are likely better explanatory variable at play which were a part of the data generating process, which are likely not discernible given data engineering of WindSpeed. I mention this given the orthogonal mass of observations at around WindSpeed = 8, above the slope. That or WindSpeed would have to be a sharp polynomial around that space area than plateau off.  
