  
    Model = Equation_Regression_Linear
+-- Algorithm = Regression_Linear
    +-- Data
  

  
    Model = Equation_Regression_Linear
+--    y = + b_0 * x^0
           + b_1 * x^1

Calculate b_0
+-- mu_y = + b_0 * 1
           + b_1 * mu_x
+-- b_0 = mu_y - b_1 * mu_x

Calculate b_1
+-- b_1 = CORREL ( col_y_vals, col_x_vals )	
        = PEARSON( col_y_vals, col_x_vals )	
  

  
    count = Number of data points
SSE   = sum-squared error
MSE   = mean-squared error
      = SSE / count
RMSE  = root-mean-squared error

  

  
    Model = Equation_Regression_Linear
+-- Beta = Beta( y, x )

         = \frac
           { \sum_{i=1}^{n} (y_i - mu_y) \cdot (x_i - mu_x) }
           { \sum_{i=1}^{n} (x_i - mu_x) \cdot (x_i - mu_x) }

         =   Correlation       ( y, x ) 
           * Standard Deviation( y )
           / Standard Deviation( x )
  

Machine Learning - Excel - Model Algorithm Data - Linear Regression - Beta of y with respect to x

SGD 55.00

Excel worksheet with the simplest example of a machine learning:
Model: Linear Regression, which uses the
Algorithm: Ordinary Least Squares, on
Data: y vs x
Mean, Standard Deviation, Variance, Covariance, Correlation, Beta

D:\Dropbox\_\work\ML\_Theory\ML_XL_011_Model(Algo(Data))_Regression_Linear_Beta\ML_XL_011_Model(Algo(Data))_Regression_Linear_Beta.xlsm

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