text: Summarise these lecture notes from an advanced statistics class. Insert the correct formulas where appropriate:  Influential observations 
  
  
  large change in fit can be seen visually but how do we actually measure 
  it? For each observation y we ca look at yhat -yhati where yhat is vector 
  fitted value with all observations and yhati is vector of predictions with 
  ith observation excluded. Cook's distance can be used the formula is:.
  
  Large values of cooks distance are influential and small are less 
  influential. When plotting observations that have large leverages we can 
  be led to believe they need to be removed. But when looking at cooks we 
  can see which are influential as well. 
  
  dfbeta can be used to see hov it affects the coefficient for a certain 
  predictor. Identify can be used to write out the names of the countries 
  for example that greatly affect that coefficient.
  
  Plot y against all xi's to get a good feeling of the relationships. But it 
  does not give a completely clear picture as there might be a need for it 
  in addition to another variable to get the whole picture.
  
  Added variable plots are better tool for outliers and influential values 
  detection. Partial residual plot are goot at capturing non-linearity. It's 
  important to plot as it can be hard to spot things purely with numerical 
  analysis.
  
  
  Detecting collinearity
  We can use the correlation matrix c where C_ij = Corr( X_i,X_j) It will 
  however not detect X_i = X_j + X_k. We want to detect collinearity when 
  one predictor is almost linear com