Regression Analysis — Process

Sequence of steps to be followed in the development of a regression model.

  1. Sample: The sample size should be adequately large to ensure statistical power and generalizability of the regression.
  2. Model design: Choose the dependent and plausible explanatory variables. Check assumptions:
    • Normality
    • Linearity
    • Homoscedasticity
    • Independence of the error terms.
    Often there is also the need to create additional variables to meet some of the below requirements:
    • Transformations, in case some assumptions are not met.
    • Dummy variables to cater for nonmetric variables.
    • Polynomials required if curvilinear relationships exist.
    • Interaction terms required if there are moderator effects.
  3. Run the model. Variable Selection is usually a combination of methods such as confirmatory, stepwise estimation, forward regression and backward regression.
  4. Examine Results: Output need to be thoroughly examined in the context of the following:
    • Issues: Influential observations. Check for multicollinearity.
    • Practical Significance: Is it theoretically sound? Are the signs and magnitude of coefficient meaningful?
    • Statistical Significance:
      1. Radj2: Adjusted coefficient of determination.
      2. F-ratio: Standard error of estimation.
      3. t-test: Statistical significance of regression coefficients.
      4. Residuals: Ensure that residuals meet required criteria.
      If model lacks practical/statistical significance or there are modelling issues, the model design must be revised (i.e., back to stage 3).
  5. Validation: Cross-validate the regression to assess how well the model can be generalized.
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