On the other hand, if the difference between actual and predicted doesnвЂ™t matter from a physical standpoint then IвЂ™d note the fact of the poor fit to those points in my report and get on with whatever it is that I was trying to do.ДЄt the end of the day the real test of your equation is its ability to predict, within its margin of error, the performance of your system. If they have something in common (same level of one of the variables for example) then there might be something worth investigating by doing something like dropping them from the data set and re-running the analysis. Once you have identified them you need to decide if the poor fit to those points matters from the standpoint of what you are trying to do. Ok, so who are the bad boys? That is, which points are driving the significance for lack-of-fit? What you need to do is look at the difference between actual and predicted for these point and identify them on the plots you have provided. Which points have the worst fit? Find those and look at them and then re-run the analysis with those points removed and see what you see вЂ“ again with graphs as well as summary statistics. The normal probability plot looks good if all you look at is the overall trend but what bothers me is the lack of scatter above and below the normal line вЂ“ particularly those points to the extreme right вЂ“ they are all below the line вЂ“ who are they and what happens when you run the analysis without them? Are they the ones with the worst fit?Д¦.

Look at the observation order вЂ“ something happened between about 10 and 30 вЂ“ whatвЂ™s the story on those data points?ДҐ. As you move from 0 out to around 1,000,000 or so notice how, within a given interval, the pattern of residuals as you move along either has a number of clusters mostly above the 0 line or below the 0 line.Д¤. What happens if you log the Y value and re-run the analysis?ДЈ. The residual plot gives the sense of trending toward a funnel shape and given the size of the fitted values this isnвЂ™t too surprising. The three extreme points to the right on the residual plot could be the tail wagging the dog вЂ“ what does the analysis look like with those removed?Дў. The normal plot, the residuals against predicted and the time order all appear to have some issues.ДЎ. The summary stats look great вЂ“ the plots donвЂ™t. You should be able to get these books through inter-library loan. Introduction to Linear Regression Analysis вЂ“ Montgomery In order to understand what your graphs are telling you you will need to get a good book on regression analysis and read the chapters on residual analysis.ДЄ couple of references вЂ“ Regression Analysis вЂ“ Draper and Smith then you will need to go back and investigate. If you have trends/shapes/clustering/influential data points/etc. Pay particular attention to the way your replicate responses plot over time. Next you should look at the residuals vs the levels of the independent variables and ask the same questions.ДЇinally, you should look at the residuals in time order of experimental run to see if there are any trends.

If all is well, and given that you have a significant lack of fit it probably isnвЂ™t, then your residual plot should look like a shotgun blast with no obvious trending/clustering/patterns. You should first look at a plot of residuals against predicted to see if there are any important trends/shapes. The first order of business is plot the data.

What you, as an investigator, need to do is run regression analysis and that requires far more than just looking at some summary statistics on a printout.

In short, you, or rather the machine, took some data and ran a regression. IвЂ™m not trying to be mean spirited or snarky but you appear to have done nothing more than build a central composite design, dump the results into a program and hit run.

Minitab express residual plots