Linear Regression or Spline Fit? I have data with 2 variables: X - Area Size of a field, Y - Average Production Rate. I need to check the relation between the two. I have plotted the data, and got the following two graphs:

and

Now I have a dilemma. Should I fit a linear regression model, or should I take into account all the little fluctuations in the trend, as shows in the smoothed curve. Which model is better, linear regression or spline fit (which I am not too familiar with).  Won't I get overfitting by using the spline model here?
 A: Polynomials are notoriously bad at extrapolating trends. They are mathematically bound to go to $\pm \infty$ whereas our intuition of trends does not. This should be a cautionary tale for anyone considering splines for inference or prediction.  Looking at your graphic, I am certain that is displaying overfitting, which applies to your question whether it is for inferential or predictive statistics. 
You can penalize your splines, like with a LOESS smoother, if your desire is to generate a descriptive non-parametric summary of a possibly non-linear trend.
In your comments you note you transform $Y$ to log and the trend is non-linear. It seems to me your visual inspection of these data is heavily weighted by the high influence/leverage points in the tails. It seems less than 5% of the data lie in the right 2/3rds of the graphic. I would suggest graphing these data with a log transform applied to the $X$ axis. If you would like to find a single polynomial function which relates $X$ to $Y$ in this graphic, consider the use of fractional polynomials, rather than fitting scads of models higgledy piggledy.
