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Unit 3 - Coggle Diagram

- - - - trend - the tendancy for values to generally increase or decrease over a significant period of time
      - Cycles - a periodic movement in time series data, must be in a period of greater than 1 year
      - Seasonality - periodic movement with a calendar-related period. EG per year, month or week
      - structual change - a sudden change in the established pattern
      - Outliers - individual values that stand out from the general body of data
      - irregular fluctuations - something that cannot be associated to a systematic change
    - - 3 moving mean
        
        smoothed y_2 = (y_1 +y_2 +y_3)/3
      - 5 moving mean
        
        Smothed y_3 = (y_1 + y_2 + y_3 + y_4 + y_5)/5
      - even number smoothing
        
        break into smaller chunks of moving means, then average those
  - - - Explainatory value is x value
      - response value is y axis
      - Direction of association and outliers
        
        Positive
        
        Negative
      - Form of association
        
        Linear
        
        Non-linear
      - strength of association
        
        strong = 0.75 - 1
        
        Moderate = 0.5 - 0.75
        
        Weak = 0.25 - 0.5
        
        no association = 0 - 0.25
        
        Correlation coefficient = r = S_xy/S_x * S_y
      - variable prediction
        
        Coefficient of determination
        
        is equal to r^2
        
        "##% of variations in y can be explained by variations in x"
    - - Least-squares regression line
        
        the line where the sum of the squares of the residuals is the smallest
        
        a can be found through the equation a = y(BAR) - Bx(BAR)
        
        a can be found through the equation b = (r*s_y)/s_x
        
        Calc steps
        
        mode > 2 > 2
        
        input data > AC
        
        SHFT+1 > 5
        
        all linear relationships follow the rule for linear lines, y=mx+c
        
        From the regression line, future predictions can be made based off the equation of said line
      - Residual plots
        
        residual plots are a graph of the residuals found in linear regression
        
        Residual value = Actual - predicted
        
        If there is a pattern in the residual plot, then a non-linear association is present
        
        If the residual data is seemingly random then a linear association is present
    - - Correlation =/= causation
      - Common response - meaning the two variables are linked through an external, third variable
      - Confounding variables - meaning that the two variables may be related, however it is to difficult to disentangle them from what causes them
      - purely coincidence
  - - - Seasonal average = sum of seasons/number of seasons
    - - Deseasonalised = actual/seasonal index
      - reseasonalised = deseasonalised * seasonal index
- - - - T_n = T_0*d(n-1)
    - - T_n = T_n-1 + d
  - - - T_n = T_0*r^(n-1)
    - - T_n = T_n-1 * r
- - - - Eq = 111.2cos(/theta)Angular Distance
    - - Eq = 111.2*Angular Distance