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What is regression analysis used for?

Regression analysis is used for 

  • explaining the impact of changes in independent variables on the dependent variable.
  • predicting the value of a dependent varibale based on the value of independent variable.

Dependent variable --> the variable we wish to predict or explain. --> Y

Independent variable --> the variable used to predict or explain the dependent variable. --> X

 

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How is variation measued in regression?

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What is the coefficiont of determination and howw can we calculate it?

The coeffision of determination is the portion of the total veariation in the dependet varibale that is explained by variation in the independent variable

the coefficient of determination is also called r-squared and is denoted as r^2

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What are the assuptions of regression/diagnostics of regression? --> When these are not satisfied we probably missed something in the model.

Linearity: the relationship between x and y is linear 

  • Plot the residuals and check if the residual are linear distributed.

Independent:

  • Error values are statistically independent
  • Durbin-Watson test (dwtest()) p < 5% must be satisfied.

Normality

  • Error values are normally distributed for any given value of x
  • Examine the Histogram of the residuals
  • Construct a Normal Probability Plot of the residuals
    • In Normal Probability Plot, if the QQ plot approximately 
      follows a straight line, the residuals can be regarded as
      normally distributed
  • Use Shapiro-Wilk normality test --> p < 5% must be satisfied.

Equal variance (homoscedasticity)

  • Use Breusch-Pagan test against heteroskedasticity: e.g. 
    bptest() {lmtest} in R
  •