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covariance convergence - Coggle Diagram

- - - - margin frquency
        
        ni. = ni1 + ni2 + ... + nil j = 1, ..., l
        
        n.j = n1j + n2j + ... + nkj i = 1, ..., k
      - total n = sum(nij) = sum(ni.) + sum(n.j)
      - percentage
        
        column percentage nij/n.j
        
        relative freq hij = nij/n
        
        row percentage nij/ni.
      - absolute frequency nij: number of observations simutaneously showing values ai and bj
- - - - deterministics
      - stochastic
      - no observable
    - - center of mass
        
        (mean x, mean y)
      - covariance
        
        positive correlation -> positive covariance
        
        negative correlation -> negative covariance
        
        no correlation -> covariance = 0
        
        disadvantage: covariance depends on dimensions and cannot tell strength of relationship
      - correlation coefficient
        
        r = sxy/(sx * sy)
        
        r has no dimension
        
        measure of strength and direction of linear relationship, but not a proof of relationship or causality
        
        eg: parabola has correlation, but not linear, so r = 0
        
        coef does not describe a linear relationship (slope, intercept, etc
  - - - criterion
        
        make the distance parallel to the fitting curve smallest
        
        sum(y-bx-a)^2 = minimum
        
        result
        
        a = mean y - b* mean x
        
        regression from x to y direction
        
        reversal of the prediction direction
        
        both regression are the same
        
        linear relationship
        
        both lines are perpendicular to each other
        
        no linear relationship
        
        the smaller angle between 2 lines, the stronger linear correlation
        
        not prove causality
      - why not orthogonal regression :question: