#======================================================
# Analyze activation energy etc by Arrhenius plot
#======================================================
infile : D:/git/tkProg/tkprog_COE/electrical/Hall/Hall-SnSe.xlsx
model  : simple Arrhenius
Tlabel : T (K), Plabel: n (cm-3)
Ttype  : T(K), Ptype: P
Fitting x range: -1e+100 - 1e+100
Fitting T range: -1e+100 - 1e+100
Read [D:/git/tkProg/tkprog_COE/electrical/Hall/Hall-SnSe.xlsx]
T(K)=[249.8715, 274.44749, 297.0, 325.0, 370.0, 428.0, 472.0, 523.0, 572.0, 625.0, 672.0]
P   =[101783000000000.0, 365955000000000.0, 1000000000000000.0, 2000000000000000.0, 8000000000000000.0, 3e+16, 8.5e+16, 1.8e+17, 4e+17, 9e+17, 2.8e+18]

Least-squares fitting with 1-th order polynomial of 1000/T
Data to be fitted:
  1000/T       log10(P)    
         4.002        14.01
         3.644        14.56
         3.367           15
         3.077         15.3
         2.703         15.9
         2.336        16.48
         2.119        16.93
         1.912        17.26
         1.748         17.6
           1.6        17.95
         1.488        18.45
Fitted polynomial coefficients:
  c0 = 20.5713 +- 0.165882
  c1 = -1.67324 +- 0.061963
  Residual variance sigma2_resid =      0.02912
Save parameters and stds to D:\git\tkProg\tkprog_COE\electrical\Hall\Hall-SnSe-parameters.xlsx
Save to [D:\git\tkProg\tkprog_COE\electrical\Hall\Hall-SnSe-parameters.xlsx]
Estimated measurement error sigma_meas = 1.46616

Scores between P(input) and P(fit)
  Mean values = <y1> = sum(y1) / n                 :    4.006e+17
                <y2> = sum(y2) / n                 :    2.577e+17
  Variance    = sum((y1 - <y1>)^2) / n             :    6.441e+35
              = sum((y2 - <y2>)^2) / n             :    1.457e+35
  Standard deviation = sqrt(Variance(y1))          :    8.026e+17
                       sqrt(Variance(y2))          :    3.817e+17
  Sample std  = sqrt(sum(y1 - <y1>)^2 / (n-1)      :    8.417e+17
                sqrt(sum(y1 - <y1>)^2 / (n-1)      :    4.004e+17
  MAE  (mean absolute error) = sum(|y1 - y2|) / n  :    1.682e+17
  MSE  (mean squared error)  = sum((y1 - y2)^2) / n:    2.327e+35
  RMSE (root MSE)            = sqrt(MSE)           :    4.824e+17
  R^2  (coefficient of determnation)
           = 1 - sum((y1 - y2)^2 / sum(y1 - <y2>)^2:       0.6387
  r    (correlation coefficient)                   :       0.9489

Scores between log10(P(input)) and log10(P(fit))
  Mean values = <y1> = sum(y1) / n                 :        16.31
                <y2> = sum(y2) / n                 :        16.31
  Variance    = sum((y1 - <y1>)^2) / n             :        1.954
              = sum((y2 - <y2>)^2) / n             :         1.93
  Standard deviation = sqrt(Variance(y1))          :        1.398
                       sqrt(Variance(y2))          :        1.389
  Sample std  = sqrt(sum(y1 - <y1>)^2 / (n-1)      :        1.466
                sqrt(sum(y1 - <y1>)^2 / (n-1)      :        1.457
  MAE  (mean absolute error) = sum(|y1 - y2|) / n  :       0.1291
  MSE  (mean squared error)  = sum((y1 - y2)^2) / n:      0.02383
  RMSE (root MSE)            = sqrt(MSE)           :       0.1544
  R^2  (coefficient of determnation)
           = 1 - sum((y1 - y2)^2 / sum(y1 - <y2>)^2:       0.9878
  r    (correlation coefficient)                   :            1
Save results to [D:\git\tkProg\tkprog_COE\electrical\Hall/Hall-SnSe-fit.xlsm]
tkVariousData.to_excel(): Use Excel template [D:\git\tkProg\tkprog_COE\excel\template\StandardGraph.xlsm] to save to [D:\git\tkProg\tkprog_COE\electrical\Hall/Hall-SnSe-fit.xlsm]
Save to [D:\git\tkProg\tkprog_COE\electrical\Hall/Hall-SnSe-fit.xlsm]
time at startup:25/06/21 14:05:38
time at end:25/06/21 14:05:39
Elapsed time from startup to end:    1.09148 sec