Setting up your study and collecting the data is a time intensive process. It’s definitely worth the effort to find the model that provides the best fit. Working days are defined as Monday-Friday 8am-7pm inclusive, excluding Saturday, Sunday and Public Holidays. Next Day & Named Day Delivery

is a line with slope a. A line will connect any two points, so a first degree polynomial equation is an exact fit through any two points with distinct x coordinates. If you are dealing with count data, you might look into zero inflated models. I discuss those a bit in my post about choosing the correct type of regression analysis. You’ll find that in the count data section at the end.Coope [23] approaches the problem of trying to find the best visual fit of circle to a set of 2D data points. The method elegantly transforms the ordinarily non-linear problem into a linear problem that can be solved without using iterative numerical methods, and is hence much faster than previous techniques. In this post, all the models that I indicate are biased in the table have portions along the fitted value lines where it systematically over and under predicts. You can see that in the graph for each model throughout this post.

You can also select a convenient day to receive your delivery by choosing a named day delivery (delivery on working days only). On the fitted line plots, the quadratic reciprocal model has a higher R-squared value (good) and a lower S-value (good) than the quadratic model. It also doesn’t display biased fitted values. This model provides the best fit to the data so far! Curve Fitting with Log Functions in Linear Regression

Curve Fitting using Polynomial Terms in Linear Regression

Your model can take logs on both sides of the equation, which is the double-log form shown above. Or, you can use a semi-log form which is where you take the log of only one side. If you take logs on the independent variable side of the model, it can be for all or a subset of the variables. The effect of averaging out questionable data points in a sample, rather than distorting the curve to fit them exactly, may be desirable. Let’s apply this to our example curve. A semi-log model can fit curves that flatten as the independent variable increases. Let’s see how a semi-log model fits our data! Your general process sounds correct. Although, I have a few suggestions. For one thing, be sure to assess the residual plots for the model without the squared variables. If there is curvature that you need to fit, you’ll often see it in the residual plots. And, those plots are a great way to verify that you’re fitting any curvature adequately.