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What is a loss function? How can we relate the slope of Linear Regression with Sum of Squared Errors?

bedanta madhab gogoi
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    Those are three questions. Could you bring it back to a single one? – Sextus Empiricus Mar 14 '19 at 13:33
  • https://stats.stackexchange.com/search?q=what+is+a+loss+function – Sextus Empiricus Mar 14 '19 at 13:34
  • Have you tried googling what's a loss function? Fot the SSE, check [this](https://stats.stackexchange.com/questions/118/why-square-the-difference-instead-of-taking-the-absolute-value-in-standard-devia). – Lucas Farias Mar 14 '19 at 13:34
  • https://stats.stackexchange.com/search?q=why+sum+of+squares – Sextus Empiricus Mar 14 '19 at 13:34
  • I gave a similar answer here: https://datascience.stackexchange.com/a/46823/10372 – gented Mar 14 '19 at 13:47
  • I think you will find the information you need in the linked threads. Please read them. If it isn't what you want / you still have a question afterwards, come back here & edit your question to state what you learned & what you still need to know. Then we can provide the information you need without just duplicating material elsewhere that already didn't help you. – gung - Reinstate Monica Mar 14 '19 at 14:03

1 Answers1

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A loss function is a (real-valued) function which typically takes a data set and a certain fitted model.

It is typically used as a measurement to determine goodness-of-fit of the model. Multiple techniques are based on finding the model that minimizes such loss function.

SSE is used in linear regression because it directly relates to the portion of the variance of outcome $Y$ that is not explained (cannot be contributed) to the difference is the values of (the) predictor(s) $X$. It is a measure of 'predicability' of the $X$'s for the value of $Y$.

The SSE directly relates to the slope of a linear regression model because it is the sum of the squared deviations of a given $(X,Y)$ from $(X,\hat{Y})$ where $\hat{Y}$ is the predicted value based on the model and the given $X$.

Peter Leopold
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Mathijs
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