Linear regression presentation

• Variable type: outcome must be continuous. Predictors can be continuous or dichotomous
• Non-zero variance: Predictors MUST NOT HAVE zero variance
• Independent errors: For any pair of observation, the error terms are uncorrelated
• Linear relationship between x and y (check with scatterplot)
• No or little multicollinearity: Predictors x1, x2.. xn must not be highly correlated - corr ()
• Homoscedasticity: For each value of the predictors the variance of the error term should be constant
• Normally-distributed Errors

In Linear regression the sample size rule of thumb is that the regression analysis requires at least 20 or 30 cases/observations per independent variable in the analysis.

• Correlation matrices: corr()

• Variance Inflation Factor (VIF): - The inverse of the tolerance statistic (higher values indicate that a predictor is redundant): Should be less then 10 or 20. In R vif(lmodel) is in the car package

• Tolerance statistic: The % of variance in the independent variable that cannot be accounted for by the other predictors (smaller values indicate that a predictor is redundant). It should be at least higher than 0.1 or 0.2
  vif_values <- vif(model)
tolerance <- 1 / vif_values
tolerance

• Standardized residuals:

  • 95% ofstandardized residuals should lie between +-2
  • 99% should lie between +-2.5
  • standardized residuals of 3 or more are outliers
    rstandard(lmmodel)
    

• Cook's distance: measures the influence of a single case on the model as a whole

  • values higher than 4/n may be cause for concern plot(lmmodel,which=4,id.n = 5)

• Homoscedasticity/indipendence of errors:
  • residual versus fittet plot; plots standardized residuals against standardized predicted values

plot(lmmodel,which=1) which=1 odnosi se na residuals vs fitted

• ovjde istrazujemo homoscedasticity or heteroscedasity
• gledamo linear concept of data. Ako je linija zakrivljena nije linearni model.
• ovaj plot mora biti homeoscedastic.
• na ovom plotu vidimo i outlayere. Izbaci nam broj reda i onda odlucimo da li trebmo da ga izbacimo.

residuals <- resid(lmmodel)

QQ plot

qqnorm(residuals) qqline(residuals, col = "red")

Shapiro-Wilk test

shapiro.test(residuals)

confint(model, level = 0.90)