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OLS Linear Regression is appropriate when Scientific Question(s) have…

- - - - determine any confounders and precision variables between explanatory variable of interest and response variable
        
        Plot numeric explanatory variables against response to do a "pre check" for functional form, obvious groups, extreme outliers, etc. Create side-by-side boxplots or stacked histograms for categorical explantory variables Create a "Table 1" with summary statistics for the variables you will use in your regression.
        
        Pick initial model to answer question(s). Do scientific questions require an interaction? Be sure to include confounders and precision variables
        
        fit model
        
        \[\hat{\beta}=(X^TX)^{-1}X^TY\]
        
        lm(yvar~xvar1+xvar2+...+xvark, datasetname)
        for interaction replace + with *
        
        Do you have non-constant variance?
        Plot residuals against fitted values
        spread of residuals change with fitted values?
        
        2 more items...
- - - - search and assess models
        (Assuming goal is to minimize out of sample MSE)
        
        Ways to assess model
        
        In sample estimates
        
        Adjusted \(R^2\)
        
        mallows \(C_p\)
        
        BIC
        
        \(R^2\)
        
        AIC
        
        in sample MSE
        
        x-validation/ leave n-out + MSE
        
        divide into validation and training +MSE
        
        Ways to search possible models
        
        Stepwise fwd/backward
        
        Best subsets
        
        informed guessing
- - - - D
    - - B
- - - - is n large?
        
        yes
        
        C
        
        no
        
        D
    - - A