What does a high residual error mean in regression model ( error value 65.89%)

Question

kindly guide me. I am stuck in the middle of my MS Research. I have 3D printed 9 samples of PLA material with process parameters of flow rate, extrusion temperature and print speed for 3D Printing. After getting results for Ultimate Tensile Testing (UTS) and Impact Testing, I put those values in Minitab Taguchi design and conclude regression models for both UTS and Impact Strength. See below pictures of Regression models for UTS and Impact Strength. The error value for UTS is 13.49% and that for Impact Strength is 65.89%. What does this high error of 65.89% mean? Kindly help me out in this case. Thank you

Answer 1

This is an analysis of variance table. It tells you how much of the variance in your outcome variable can be explained by each of your predictors. In the first table, the the predictors together explain 34% of the variance, leaving 66% unexplained (which for reasons beyond the scope of your question, we call the "error variance").

Note however that although 34% might sound ok, you have only 9 data points, and 3 predictors. Indeed, the first row shows that the p-value for these 3 predictors combined is .518, well above the usual significance threshold of <.05. This means you can't reject the null hypothesis that these predictors are unrelated to the outcome (and that you only explained 34% of the variance by chance).

Answer 2

In terms of statistics, the contribution column tells you that the predictors flow rate, extrusion temperature and print speed explain more of the variability in UTS (81% + 4% + 1.6% = 86.6%) than the variability in impact energy (27% + 0.5% + 6% = 33.5%). It might be more helpful, however, to think in terms of the science. Presumably, UTS and impact energy measure different aspects of the phenomenon your MS research is about.

You might get more insight by plotting the response variables against the predictor variables. Plotting the data is usually the best place to start in general.

In particular, extrusion temperature and print speed doen't make much difference, at least not in the range observed in this experiment. So start by plotting UTS & impact energy against flow rate and investigate why flow rate explains 81% of the variability in UTS but only 27% of the variance in impact energy.