Tests

> ifemale <- which(data$group==0)

> data_female <- data[ifemale,]

> imale <- which(data$group==1)

> data_male <- data[imale,]

• Rule of thumb: observation has high influence if Cook’s distance exceeds 4/(n - p - 1)

  • n <- dim(data)[1]

  • p <- dim(data)[2]-1

  • plot(linreg_clean) -> eventhough points are most leveraged, it does not mean they are outliers

• Multicollinearity

• anova(reg)

• Depending on siginficance level

  • Variable is significant

  • Variable is not significant

• Normality

• jarque.bera.test(summary(reg)$residuals)

• Hypothesis test

  • H0: Errors follow a normal distribution

  • H1: Errors dont follow a normal distribution

• Multicollinearity

• var.test(x,y,data)

• Hypothesis test

  • H0: population variances are equal

  • H1: population variances are not equal

  • Interpretation

• Autocorrelation

• durbinWatsonTest(reg)

• Hypothesis tests

  • H0: residuals are not autocorrelated

  • H1: residuals are positively autocorrelated

• Heteroscedasticity

• bptest(reg)

• Hypothesis test

  • H0: data is not heterocedastic

  • H1: data is heteroscedastic

boxplot(data)

cor(data)

pairs(data) <- pairwise correlation plots

• Multicollinearity

• vif(reg)

• value that exceeds 5 or 10 indicates a problematic amount of collinearity

• barplot(vif(mreg), horiz = TRUE)

• abline(v = 5, lwd = 3, lty = 2)

  • v: add vertical line at x = 5

  • lwd: define linewidth

  • lty: define line type

1. Option: Boxplot

   • hout <- boxplot(data)$out

   • iout <- which(data$variable==hout)

   • data_clean <- data[-iout,]

2. Option: Scatterplot - Maximum point

   • iout <- which.max(data$variable)

   • dataclean <- data[-iout,]

• Variable selection

• stepAIC(reg, direction="backward")

  • backward: removes predictors sequentially from the given model with decreasing complexity

  • forward: adds predictors sequentially to the given mode with increasing complexity

  • both: a forward-backward search that, at each step, decides whether to include or exclude a predictor

• last displayed model shows all significant variables and removed variables, that do not improve the validity of the dataset

1. Transform data & plot in transformed space

   > logreg=lm(log(sales)∼log(price),data)

   > plot(log(data$price),log(data$sales), pch = 16, col = "blue") > abline(linreg,col="red")

2. Plot in original space

   > plot(data$price,data$sales, pch = 16, col = "blue")

   > x=seq(from=min(data$price),to=max(data$price),by=0.01)

   > y=predict(logreg,list(price=x))

   > matlines(x,y,col="red")

3. Plot the residuals

4. Analyize R²

plot(x,y,col=data$x2+3)

> data$x2: data which should be seperated by color

> predict(lm,newdata <- data.frame(income=50, competitor=3,

mallvisitors=2000),interval=’confidence’)

> predict(lm,newdata <- data.frame(income=50, competitor=3,

mallvisitors=2000),interval=’prediction’)

• ci.plot(lm,conf.level=0.90)

• Prediction is too optimistic

1. Linearity

2. Strict Exogenitiy

3. No Correlation of X and the Errors

4. No Correlation of the Errors

5. Heteroscedasticity

6. Normality

7. No Perfect Multicollinearity

• VIF

• F-Test

• Anova

• analyze the QQ-Plot

• Jarque-Bera Test

• Breusch-Pagan Test

• Durbin Watson Test