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I have a variable (weight of 400 pieces of meat in Kgs) that is measured before and after a thermal process. The explanatory variable is the weight before processing and the response is the weight after it. The standard deviation of the response variable around twice the explanatory variable. It’s common sense that larger weights should produce larger weight after the thermal process (response). However, there seems to be a weak linear relationship between them, for instance, the Pearson correlation coefficient is 0.30. I tried including other variables in the model without much success. I'm aiming at building a more effective model for prediction. What would be the standard/recommended procedure in cases like this?

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    $\begingroup$ You need subject matter knowledge about what variables to try in a regression model. Then you can apply one of the many possible variable selection procedures. I might recommend a stepwise technique where AIC or BIC should be used as a criteria for choosing the final model. I would not use a form of R-square. Our friend and regression expert Frank Harrell would probably suggest something else and strenuously object to stepwise regression. Maybe he will see this post and make some comments. $\endgroup$ – Michael R. Chernick Jan 4 '17 at 5:31
  • $\begingroup$ Can you edit your question to show us a plot of before versus after? $\endgroup$ – mdewey Jul 6 '17 at 7:15
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Just want to make sure that the weak linear relationship has been established visually as well?

See post on datasaurus package in R that uses the anscombe data to show that it's possible to get same summary statistics on completely different data.

If from domain knowledge or by intuition you know some variables should impact the outcome and yet the model performance does not improve I would suggest a couple of things:

  1. Feature engineering: In one of the famous R datasets - heightweight, a square interaction term of weightLb describes the heightIn better than the column without an transform
  2. Model selection: vary say linear model to linear mixed effects model or GAM etc
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