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Statistics Week9 - Coggle Diagram

- - - - plot data separately and manually, get trendline for each
      - plot data together, encode category, create artificial variable (with its own new set of data), use data analysis toolkit, and then sub in values of encoding to get individual trendlines (refer to slide 7 week9.2)
- - - - sum of all ei^2
      - sum of (yi - yhat)^2
    - - sum of (yhat - ybar)^2
    - - derivation of SST
        
        trick: add and subtract y hat, then expand (a + b)^2
        
        how to proof??
      - SST = (n-1) * sample variance of y
      - total variation of y values ( yi - ybar)^2 sum up
    - - the sign of r corresponds to the slope of least square line
      - r^2 is also known as the coefficient of determination
      - r is known as the correlation coefficient --> use correl in Excel
    - - MSE = s^2 = SSE/(n-2)
        
        errors, ei, are iid normal with mean 0 and variance sigma^2
        
        note, sum of all the errors = 0
        
        note, sum of all the (error * the x coordinate) = 0
        
        because of the two noted constraints, thats why degree of freedom reduced by 2
    - - use data analysis toolpack and regression to do residuals plot
      - random residuals plot is good, error supposed to be random
      - if from the residuals plot we observe that the residuals follow a quadratic or a cubic pattern, then we need to transform the data
        
        y - y hat = cubic/quadratic
        
        model y = cubic/quadratic + a constant term
        
        take ln on both sides to make the data linear
        
        remember your final ans would be in quad/cubic form, NOT Linear
    - - any abs(error) > 2 s (2 sqrt of MSE)