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I was going through the concept of Linear Regression and ran into the concept of deciding whether a Linear Regression Model is the best fit for your data by 5 assumptions:

  1. Linearity
  2. Homoscedasticity
  3. Multivariate normality
  4. Independence of errors
  5. Lack of multicollinearity

The following are a general introduction of the five assumptions, feel free to add more detail to these assumptions.

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    $\begingroup$ Perhaps you could explain in more detail what you're struggling with? I think any answer at the moment would essentially just be a general explanation on the topic. Could you edit to clarify (perhaps if there is a bit in a textbook you don't understand, etc)? $\endgroup$ – htl Apr 25 at 13:29
  • $\begingroup$ If you want a general overview, you'll probably find much better explanation in a good textbook on the subject than whatever we could supply here. You could look in the bibliography of the Wikipedia article for some books if you don't know any. $\endgroup$ – htl Apr 26 at 8:05
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Here are the meanings of these concepts:

  1. Linearity: There must be a linear relationship between the dependent variable and the independent variables. Scatterplots can show whether there is a linear or curvilinear relationship.
  2. Homoscedasticity: This assumption states that the variance of error terms is similar across the values of the independent variables. A plot of standardized residuals versus predicted values can show whether points are equally distributed across all values of the independent variables.
  3. Multivariate Normality: Multiple Linear Regression assumes that the residuals, the differences between the observed value of the dependent variable y, and the predicted value ŷ are normally distributed.
  4. Independence of errors: Multiple Linear Regression assumes that the residuals, the differences between the observed value of the dependent variable y, and the predicted value ŷ are independent.
  5. Lack of multicollinearity: Multiple Linear Regression assumes that the independent variables are not highly correlated with each other. This assumption is tested using Variance Inflation Factor (VIF) values.
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