I am doing RSM and the results gave a low R-square model (both full quadratic and reduced model) but the lack-of-fit P-value is high (>0.05) how is it that R-square says the model does not fit but the lack-of-fit statistics says it does? For additional info, I am using nature-based polymers (alginate and hydroxypropyl cellulose), is it because I'm using these?
Dear Isaac,
For having an acceptable modeling result with RSM, you should obtain a greater Correlation coefficient (R2) to be sure that high variation is explained by your model. In another word, a higher R-square (up to 1.0) means the better fit between your model and observations.
P-value should be less than the significance level (usually 0.05), otherwise, your model did not meet the requirement of the null hypothesis.
So, try to keep the low P-value and increase the R2 by ignoring some high variance data and/or select another kind of model rather than quadratic (more fit to your observations).
Mohamad-Javad Mehrani Hello sir, I'm a little confused. According to this site which uses the same program I am using, the P-value of the Lack-of-Fit statistics should be greater than the significance level to accept the null hypothesis (which is "The relationship assumed in the model is reasonable, i.e., there is no lack of fit in the model"). But mine is greater than the 0.05 which means my model is reasonable and there is no lack of fit. however, my R2 is 49% and 60% for each response model which says my model does not fit the data. If I keep the low P-value and increase R2, wouldn't that mean that my model is not reasonable even though there is high correlation coefficient?
link of site: https://online.stat.psu.edu/stat501/lesson/2/2.11#:~:text=Analysis%20of%20Variance,-Source&text=value%20is%200.006.-,The%20P%2Dvalue%20is%20smaller%20than%20the%20significance%20level%20%CE%B1,the%20simple%20linear%20regression%20model.
Isaac Marvin Santos Patubo P-value is a probability indicator and somehow difficult to explain it. A smaller p-value (smaller than 0.05) means that there is stronger evidence in favor of the alternative hypothesis. In this way, you reject the null hypothesis and its good for your model.
So try to decrease the p-value (< 0.05) and increase the R2 as high as you can with different scenarios (up to 100%).
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