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I am currently working with a few different regression models (regression trees, GBT, linear, etc) in the platform KNIME and now that I have computed the following statistical measures: $R^2$, mean squared and mean absolute error (MSE and MAE respectively), root MSE, and mean signed difference.

This site explains things, however there is a part where the author states:

"In conclusion, R² is the ratio between how good our model is vs how good is the naive mean model."

What is meant by the "naive mean model" and how significant is it in model comparison?

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  • $\begingroup$ Welcome to the site, Angela. It's best to post questions separately here, because it allows more specific titles (helps makes the site more searchable) and also because people who may know the answer to one of your questions but not others are less likely to post answers. $\endgroup$
    – mkt
    Sep 28 '19 at 17:34
  • $\begingroup$ @mkt Thanks for the advice! So should I edit this question and repost an extra two in separate questions? (3 posts total) $\endgroup$
    – Angela S.
    Sep 28 '19 at 17:59
  • $\begingroup$ Yes, I think that would be a good idea $\endgroup$
    – mkt
    Sep 28 '19 at 18:01
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    $\begingroup$ @mkt I will do just that then. I really appreciate you taking the time to help me get acclimated on here :) One last thing: would it be beneficial at all if I link the other questions to this question? (Thinking in the event that one person answers this query, they might also be knowledgable on the rest) $\endgroup$
    – Angela S.
    Sep 28 '19 at 18:10
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    $\begingroup$ @mkt Awesome. Well I know I've said it already, but third time's the charm, so thank you once again! $\endgroup$
    – Angela S.
    Sep 28 '19 at 18:19
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The 'naïve mean model' refers to a model where the prediction is just the average of the dependent/target variable for the whole dataset. Think of a regression where the slope is zero and the intercept is just the mean of all the data points - a horizontal line.

This very simple reference model is what you compare a more complex model against. The $R^2$ then compares the new model against this simple/naïve reference model.

This is why it's possible for a model to have a negative $R^2$, if it makes predictions that are worse than just predicting the mean (see the linked answer for a good example).

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Briefly, the naive mean model is guessing the average $y$ value no matter what the values of your predictor variables are.

Longer answer:

The goal of regression is to predict a conditional mean. In other words, for given values of the predictor variables, you might sometimes get 2.1, sometimes 1.9, sometimes 2.2, sometimes 1.8, etc, but, on average, you expect to get 2. Then 2 is your predicted value.

The most naive way to do this prediction is to ignore the predictor variables and always guess the average value of your response variables. This results in high variance, and we use regression to tighten up our estimates. For instance, we expect adults to be taller than toddlers, so if we were to guess the height of an adult, we would want to account for the fact that they ought to be taller. By including this toddler/adult variable, we make fair comparisons to other adults instead of letting many 2-foot-tall toddlers stretch out the distribution and cause less precision in our estimate.

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