{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## STEPDISC LDA - heart dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "#disable warnings\n",
    "from warnings import simplefilter, filterwarnings\n",
    "simplefilter(action='ignore', category=FutureWarning)\n",
    "filterwarnings(\"ignore\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### heart dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "Index: 150 entries, 0 to 149\n",
      "Data columns (total 14 columns):\n",
      " #   Column          Non-Null Count  Dtype  \n",
      "---  ------          --------------  -----  \n",
      " 0   disease         150 non-null    object \n",
      " 1   age             150 non-null    int64  \n",
      " 2   sex             150 non-null    object \n",
      " 3   chestpain       150 non-null    object \n",
      " 4   restbpress      150 non-null    int64  \n",
      " 5   cholesteral     150 non-null    int64  \n",
      " 6   sugar           150 non-null    object \n",
      " 7   electro         150 non-null    object \n",
      " 8   maxHeartRate    150 non-null    int64  \n",
      " 9   ExerciseAngina  150 non-null    object \n",
      " 10  oldpeak         150 non-null    float64\n",
      " 11  slope           150 non-null    object \n",
      " 12  vesselsColored  150 non-null    int64  \n",
      " 13  thal            150 non-null    object \n",
      "dtypes: float64(1), int64(5), object(8)\n",
      "memory usage: 17.6+ KB\n",
      "None\n"
     ]
    }
   ],
   "source": [
    "#vins dataset\n",
    "from discrimintools.datasets import load_heart\n",
    "D = load_heart(\"train\")\n",
    "print(D.info())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### instanciation and training"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Categorical features have been encoded into binary variables.\n",
      "\n",
      "\n",
      "====================== Step 1 backward selection results =======================\n",
      "                           Wilks' Lambda  Partial R-Square    F Value  Num DF  \\\n",
      "age                             0.390537          0.000287   0.037556       1   \n",
      "sexmale                         0.406288          0.039044   5.322618       1   \n",
      "chestpainatypicalAngina         0.410195          0.048197   6.633471       1   \n",
      "chestpainnonAnginal             0.407635          0.042220   5.774636       1   \n",
      "chestpaintypicalAngina          0.435333          0.103158  15.068044       1   \n",
      "restbpress                      0.395178          0.012029   1.595002       1   \n",
      "cholesteral                     0.391386          0.002455   0.322413       1   \n",
      "sugarlow                        0.397899          0.018784   2.507857       1   \n",
      "electrosttAbnormality           0.392351          0.004911   0.646455       1   \n",
      "electroventricHypertrophy       0.393479          0.007763   1.024876       1   \n",
      "maxHeartRate                    0.400177          0.024369   3.272082       1   \n",
      "ExerciseAnginayes               0.396484          0.015283   2.033088       1   \n",
      "oldpeak                         0.404146          0.033951   4.603833       1   \n",
      "slopeflat                       0.393651          0.008197   1.082665       1   \n",
      "slopeupsloping                  0.390878          0.001159   0.151970       1   \n",
      "vesselsColored                  0.442917          0.118515  17.612864       1   \n",
      "thalnormal                      0.392200          0.004525   0.595495       1   \n",
      "thalreversableEffect            0.393379          0.007510   0.991197       1   \n",
      "\n",
      "                           Den DF      Pr>F  \n",
      "age                           131  0.846637  \n",
      "sexmale                       131  0.022619  \n",
      "chestpainatypicalAngina       131  0.011118  \n",
      "chestpainnonAnginal           131  0.017660  \n",
      "chestpaintypicalAngina        131  0.000164  \n",
      "restbpress                    131  0.208856  \n",
      "cholesteral                   131  0.571133  \n",
      "sugarlow                      131  0.115691  \n",
      "electrosttAbnormality         131  0.422839  \n",
      "electroventricHypertrophy     131  0.313231  \n",
      "maxHeartRate                  131  0.072761  \n",
      "ExerciseAnginayes             131  0.156286  \n",
      "oldpeak                       131  0.033745  \n",
      "slopeflat                     131  0.300019  \n",
      "slopeupsloping                131  0.697293  \n",
      "vesselsColored                131  0.000050  \n",
      "thalnormal                    131  0.441692  \n",
      "thalreversableEffect          131  0.321286  \n",
      "\n",
      "Variable age will be removed\n",
      "\n",
      "\n",
      "====================== Step 2 backward selection results =======================\n",
      "                           Wilks' Lambda  Partial R-Square    F Value  Num DF  \\\n",
      "sexmale                         0.406288          0.038769   5.323891       1   \n",
      "chestpainatypicalAngina         0.410504          0.048642   6.749045       1   \n",
      "chestpainnonAnginal             0.407779          0.042283   5.827703       1   \n",
      "chestpaintypicalAngina          0.435344          0.102923  15.144637       1   \n",
      "restbpress                      0.396076          0.013985   1.872180       1   \n",
      "cholesteral                     0.391407          0.002224   0.294157       1   \n",
      "sugarlow                        0.397905          0.018518   2.490549       1   \n",
      "electrosttAbnormality           0.392399          0.004745   0.629361       1   \n",
      "electroventricHypertrophy       0.393649          0.007906   1.051882       1   \n",
      "maxHeartRate                    0.402640          0.030059   4.090787       1   \n",
      "ExerciseAnginayes               0.396512          0.015070   2.019730       1   \n",
      "oldpeak                         0.404147          0.033676   4.600093       1   \n",
      "slopeflat                       0.393696          0.008026   1.067946       1   \n",
      "slopeupsloping                  0.390980          0.001135   0.149973       1   \n",
      "vesselsColored                  0.449061          0.130325  19.780910       1   \n",
      "thalnormal                      0.392377          0.004689   0.621919       1   \n",
      "thalreversableEffect            0.393405          0.007290   0.969355       1   \n",
      "\n",
      "                           Den DF      Pr>F  \n",
      "sexmale                       132  0.022591  \n",
      "chestpainatypicalAngina       132  0.010445  \n",
      "chestpainnonAnginal           132  0.017147  \n",
      "chestpaintypicalAngina        132  0.000157  \n",
      "restbpress                    132  0.173550  \n",
      "cholesteral                   132  0.588483  \n",
      "sugarlow                      132  0.116925  \n",
      "electrosttAbnormality         132  0.429013  \n",
      "electroventricHypertrophy     132  0.306950  \n",
      "maxHeartRate                  132  0.045138  \n",
      "ExerciseAnginayes             132  0.157625  \n",
      "oldpeak                       132  0.033802  \n",
      "slopeflat                     132  0.303300  \n",
      "slopeupsloping                132  0.699185  \n",
      "vesselsColored                132  0.000018  \n",
      "thalnormal                    132  0.431749  \n",
      "thalreversableEffect          132  0.326642  \n",
      "\n",
      "Variable slopeupsloping will be removed\n",
      "\n",
      "\n",
      "====================== Step 3 backward selection results =======================\n",
      "                           Wilks' Lambda  Partial R-Square    F Value  Num DF  \\\n",
      "sexmale                         0.407255          0.039961   5.536054       1   \n",
      "chestpainatypicalAngina         0.410717          0.048053   6.713645       1   \n",
      "chestpainnonAnginal             0.408154          0.042077   5.842021       1   \n",
      "chestpaintypicalAngina          0.436303          0.103879  15.417452       1   \n",
      "restbpress                      0.396268          0.013342   1.798522       1   \n",
      "cholesteral                     0.391857          0.002236   0.298057       1   \n",
      "sugarlow                        0.399178          0.020536   2.788604       1   \n",
      "electrosttAbnormality           0.393135          0.005481   0.732954       1   \n",
      "electroventricHypertrophy       0.393932          0.007493   1.004102       1   \n",
      "maxHeartRate                    0.402704          0.029113   3.988168       1   \n",
      "ExerciseAnginayes               0.396680          0.014368   1.938852       1   \n",
      "oldpeak                         0.405450          0.035689   4.922248       1   \n",
      "slopeflat                       0.396077          0.012867   1.733586       1   \n",
      "vesselsColored                  0.456018          0.142620  22.123724       1   \n",
      "thalnormal                      0.392612          0.004157   0.555181       1   \n",
      "thalreversableEffect            0.394134          0.008001   1.072658       1   \n",
      "\n",
      "                           Den DF      Pr>F  \n",
      "sexmale                       133  0.020095  \n",
      "chestpainatypicalAngina       133  0.010636  \n",
      "chestpainnonAnginal           133  0.017004  \n",
      "chestpaintypicalAngina        133  0.000138  \n",
      "restbpress                    133  0.182177  \n",
      "cholesteral                   133  0.586018  \n",
      "sugarlow                      133  0.097289  \n",
      "electrosttAbnormality         133  0.393467  \n",
      "electroventricHypertrophy     133  0.318140  \n",
      "maxHeartRate                  133  0.047862  \n",
      "ExerciseAnginayes             133  0.166117  \n",
      "oldpeak                       133  0.028209  \n",
      "slopeflat                     133  0.190218  \n",
      "vesselsColored                133  0.000006  \n",
      "thalnormal                    133  0.457523  \n",
      "thalreversableEffect          133  0.302225  \n",
      "\n",
      "Variable cholesteral will be removed\n",
      "\n",
      "\n",
      "====================== Step 4 backward selection results =======================\n",
      "                           Wilks' Lambda  Partial R-Square    F Value  Num DF  \\\n",
      "sexmale                         0.409528          0.043151   6.043007       1   \n",
      "chestpainatypicalAngina         0.411805          0.048441   6.821489       1   \n",
      "chestpainnonAnginal             0.408653          0.041101   5.743665       1   \n",
      "chestpaintypicalAngina          0.436743          0.102776  15.349524       1   \n",
      "restbpress                      0.396703          0.012217   1.657322       1   \n",
      "sugarlow                        0.400138          0.020696   2.831918       1   \n",
      "electrosttAbnormality           0.393716          0.004723   0.635860       1   \n",
      "electroventricHypertrophy       0.394296          0.006188   0.834316       1   \n",
      "maxHeartRate                    0.403514          0.028891   3.986532       1   \n",
      "ExerciseAnginayes               0.397982          0.015392   2.094745       1   \n",
      "oldpeak                         0.406739          0.036590   5.089300       1   \n",
      "slopeflat                       0.396831          0.012535   1.701067       1   \n",
      "vesselsColored                  0.456268          0.141170  22.026289       1   \n",
      "thalnormal                      0.393948          0.005309   0.715220       1   \n",
      "thalreversableEffect            0.394533          0.006784   0.915272       1   \n",
      "\n",
      "                           Den DF      Pr>F  \n",
      "sexmale                       134  0.015238  \n",
      "chestpainatypicalAngina       134  0.010034  \n",
      "chestpainnonAnginal           134  0.017929  \n",
      "chestpaintypicalAngina        134  0.000142  \n",
      "restbpress                    134  0.200184  \n",
      "sugarlow                      134  0.094737  \n",
      "electrosttAbnormality         134  0.426625  \n",
      "electroventricHypertrophy     134  0.362668  \n",
      "maxHeartRate                  134  0.047892  \n",
      "ExerciseAnginayes             134  0.150142  \n",
      "oldpeak                       134  0.025694  \n",
      "slopeflat                     134  0.194384  \n",
      "vesselsColored                134  0.000007  \n",
      "thalnormal                    134  0.399224  \n",
      "thalreversableEffect          134  0.340442  \n",
      "\n",
      "Variable electrosttAbnormality will be removed\n",
      "\n",
      "\n",
      "====================== Step 5 backward selection results =======================\n",
      "                           Wilks' Lambda  Partial R-Square    F Value  Num DF  \\\n",
      "sexmale                         0.410873          0.041757   5.882798       1   \n",
      "chestpainatypicalAngina         0.414253          0.049575   7.041772       1   \n",
      "chestpainnonAnginal             0.411211          0.042545   5.998803       1   \n",
      "chestpaintypicalAngina          0.440501          0.106208  16.041826       1   \n",
      "restbpress                      0.400086          0.015922   2.184188       1   \n",
      "sugarlow                        0.402213          0.021126   2.913628       1   \n",
      "electroventricHypertrophy       0.395665          0.004925   0.668218       1   \n",
      "maxHeartRate                    0.405997          0.030248   4.210902       1   \n",
      "ExerciseAnginayes               0.400247          0.016317   2.239323       1   \n",
      "oldpeak                         0.409876          0.039425   5.540870       1   \n",
      "slopeflat                       0.399037          0.013335   1.824583       1   \n",
      "vesselsColored                  0.456813          0.138125  21.635246       1   \n",
      "thalnormal                      0.395655          0.004900   0.664812       1   \n",
      "thalreversableEffect            0.396233          0.006351   0.862875       1   \n",
      "\n",
      "                           Den DF      Pr>F  \n",
      "sexmale                       135  0.016611  \n",
      "chestpainatypicalAngina       135  0.008919  \n",
      "chestpainnonAnginal           135  0.015597  \n",
      "chestpaintypicalAngina        135  0.000102  \n",
      "restbpress                    135  0.141764  \n",
      "sugarlow                      135  0.090133  \n",
      "electroventricHypertrophy     135  0.415114  \n",
      "maxHeartRate                  135  0.042098  \n",
      "ExerciseAnginayes             135  0.136874  \n",
      "oldpeak                       135  0.020020  \n",
      "slopeflat                     135  0.179028  \n",
      "vesselsColored                135  0.000008  \n",
      "thalnormal                    135  0.416302  \n",
      "thalreversableEffect          135  0.354593  \n",
      "\n",
      "Variable thalnormal will be removed\n",
      "\n",
      "\n",
      "====================== Step 6 backward selection results =======================\n",
      "                           Wilks' Lambda  Partial R-Square    F Value  Num DF  \\\n",
      "sexmale                         0.417444          0.052196   7.489525       1   \n",
      "chestpainatypicalAngina         0.415723          0.048272   6.897966       1   \n",
      "chestpainnonAnginal             0.413922          0.044132   6.279052       1   \n",
      "chestpaintypicalAngina          0.440939          0.102699  15.565699       1   \n",
      "restbpress                      0.403027          0.018292   2.534024       1   \n",
      "sugarlow                        0.403748          0.020045   2.781833       1   \n",
      "electroventricHypertrophy       0.397602          0.004898   0.669371       1   \n",
      "maxHeartRate                    0.408842          0.032255   4.532833       1   \n",
      "ExerciseAnginayes               0.401628          0.014873   2.053222       1   \n",
      "oldpeak                         0.411139          0.037661   5.322282       1   \n",
      "slopeflat                       0.402652          0.017377   2.405049       1   \n",
      "vesselsColored                  0.460870          0.141503  22.416487       1   \n",
      "thalreversableEffect            0.423809          0.066430   9.677416       1   \n",
      "\n",
      "                           Den DF      Pr>F  \n",
      "sexmale                       136  0.007035  \n",
      "chestpainatypicalAngina       136  0.009619  \n",
      "chestpainnonAnginal           136  0.013397  \n",
      "chestpaintypicalAngina        136  0.000127  \n",
      "restbpress                    136  0.113737  \n",
      "sugarlow                      136  0.097640  \n",
      "electroventricHypertrophy     136  0.414702  \n",
      "maxHeartRate                  136  0.035053  \n",
      "ExerciseAnginayes             136  0.154179  \n",
      "oldpeak                       136  0.022565  \n",
      "slopeflat                     136  0.123268  \n",
      "vesselsColored                136  0.000005  \n",
      "thalreversableEffect          136  0.002273  \n",
      "\n",
      "Variable electroventricHypertrophy will be removed\n",
      "\n",
      "\n",
      "====================== Step 7 backward selection results =======================\n",
      "                         Wilks' Lambda  Partial R-Square    F Value  Num DF  \\\n",
      "sexmale                       0.420956          0.055478   8.046977       1   \n",
      "chestpainatypicalAngina       0.418392          0.049691   7.163594       1   \n",
      "chestpainnonAnginal           0.416175          0.044627   6.399484       1   \n",
      "chestpaintypicalAngina        0.444648          0.105805  16.210398       1   \n",
      "restbpress                    0.405184          0.018713   2.612513       1   \n",
      "sugarlow                      0.405372          0.019166   2.677050       1   \n",
      "maxHeartRate                  0.410360          0.031089   4.395911       1   \n",
      "ExerciseAnginayes             0.404261          0.016471   2.294300       1   \n",
      "oldpeak                       0.415631          0.043377   6.212088       1   \n",
      "slopeflat                     0.404662          0.017446   2.432584       1   \n",
      "vesselsColored                0.467272          0.149099  24.005791       1   \n",
      "thalreversableEffect          0.424401          0.063146   9.234051       1   \n",
      "\n",
      "                         Den DF      Pr>F  \n",
      "sexmale                     137  0.005250  \n",
      "chestpainatypicalAngina     137  0.008348  \n",
      "chestpainnonAnginal         137  0.012547  \n",
      "chestpaintypicalAngina      137  0.000093  \n",
      "restbpress                  137  0.108324  \n",
      "sugarlow                    137  0.104099  \n",
      "maxHeartRate                137  0.037864  \n",
      "ExerciseAnginayes           137  0.132153  \n",
      "oldpeak                     137  0.013880  \n",
      "slopeflat                   137  0.121144  \n",
      "vesselsColored              137  0.000003  \n",
      "thalreversableEffect        137  0.002846  \n",
      "\n",
      "Variable ExerciseAnginayes will be removed\n",
      "\n",
      "\n",
      "====================== Step 8 backward selection results =======================\n",
      "                         Wilks' Lambda  Partial R-Square    F Value  Num DF  \\\n",
      "sexmale                       0.430245          0.060394   8.870105       1   \n",
      "chestpainatypicalAngina       0.430059          0.059988   8.806591       1   \n",
      "chestpainnonAnginal           0.429872          0.059579   8.742837       1   \n",
      "chestpaintypicalAngina        0.457101          0.115598  18.037639       1   \n",
      "restbpress                    0.414100          0.023760   3.358669       1   \n",
      "sugarlow                      0.412059          0.018926   2.662180       1   \n",
      "maxHeartRate                  0.421814          0.041614   5.992152       1   \n",
      "oldpeak                       0.425421          0.049739   7.223204       1   \n",
      "slopeflat                     0.412181          0.019215   2.703597       1   \n",
      "vesselsColored                0.470765          0.141268  22.701974       1   \n",
      "thalreversableEffect          0.432783          0.065904   9.736476       1   \n",
      "\n",
      "                         Den DF      Pr>F  \n",
      "sexmale                     138  0.003425  \n",
      "chestpainatypicalAngina     138  0.003539  \n",
      "chestpainnonAnginal         138  0.003657  \n",
      "chestpaintypicalAngina      138  0.000040  \n",
      "restbpress                  138  0.069008  \n",
      "sugarlow                    138  0.105040  \n",
      "maxHeartRate                138  0.015625  \n",
      "oldpeak                     138  0.008082  \n",
      "slopeflat                   138  0.102398  \n",
      "vesselsColored              138  0.000005  \n",
      "thalreversableEffect        138  0.002200  \n",
      "\n",
      "Variable sugarlow will be removed\n",
      "\n",
      "\n",
      "====================== Step 9 backward selection results =======================\n",
      "                         Wilks' Lambda  Partial R-Square    F Value  Num DF  \\\n",
      "sexmale                       0.437069          0.057221   8.436494       1   \n",
      "chestpainatypicalAngina       0.437514          0.058180   8.586570       1   \n",
      "chestpainnonAnginal           0.445484          0.075031  11.275258       1   \n",
      "chestpaintypicalAngina        0.471064          0.125259  19.904149       1   \n",
      "restbpress                    0.419220          0.017080   2.415438       1   \n",
      "maxHeartRate                  0.427785          0.036761   5.304726       1   \n",
      "oldpeak                       0.435439          0.053692   7.886679       1   \n",
      "slopeflat                     0.420956          0.021135   3.001165       1   \n",
      "vesselsColored                0.472897          0.128649  20.522313       1   \n",
      "thalreversableEffect          0.437975          0.059171   8.742009       1   \n",
      "\n",
      "                         Den DF      Pr>F  \n",
      "sexmale                     139  0.004280  \n",
      "chestpainatypicalAngina     139  0.003960  \n",
      "chestpainnonAnginal         139  0.001014  \n",
      "chestpaintypicalAngina      139  0.000017  \n",
      "restbpress                  139  0.122418  \n",
      "maxHeartRate                139  0.022752  \n",
      "oldpeak                     139  0.005697  \n",
      "slopeflat                   139  0.085423  \n",
      "vesselsColored              139  0.000013  \n",
      "thalreversableEffect        139  0.003655  \n",
      "\n",
      "Variable restbpress will be removed\n",
      "\n",
      "\n",
      "====================== Step 10 backward selection results =======================\n",
      "                         Wilks' Lambda  Partial R-Square    F Value  Num DF  \\\n",
      "sexmale                       0.439368          0.045856   6.728378       1   \n",
      "chestpainatypicalAngina       0.442844          0.053346   7.889247       1   \n",
      "chestpainnonAnginal           0.452659          0.073873  11.167170       1   \n",
      "chestpaintypicalAngina        0.473989          0.115549  18.290368       1   \n",
      "maxHeartRate                  0.433855          0.033732   4.887314       1   \n",
      "oldpeak                       0.450985          0.070436  10.608222       1   \n",
      "slopeflat                     0.427790          0.020034   2.862142       1   \n",
      "vesselsColored                0.483113          0.132252  21.337160       1   \n",
      "thalreversableEffect          0.453183          0.074943  11.342002       1   \n",
      "\n",
      "                         Den DF      Pr>F  \n",
      "sexmale                     140  0.010498  \n",
      "chestpainatypicalAngina     140  0.005684  \n",
      "chestpainnonAnginal         140  0.001068  \n",
      "chestpaintypicalAngina      140  0.000035  \n",
      "maxHeartRate                140  0.028678  \n",
      "oldpeak                     140  0.001413  \n",
      "slopeflat                   140  0.092911  \n",
      "vesselsColored              140  0.000009  \n",
      "thalreversableEffect        140  0.000979  \n",
      "\n",
      "Variable slopeflat will be removed\n",
      "\n",
      "\n",
      "====================== Step 11 backward selection results =======================\n",
      "                         Wilks' Lambda  Partial R-Square    F Value  Num DF  \\\n",
      "sexmale                       0.447931          0.044965   6.638500       1   \n",
      "chestpainatypicalAngina       0.452985          0.055620   8.304242       1   \n",
      "chestpainnonAnginal           0.463630          0.077302  11.812728       1   \n",
      "chestpaintypicalAngina        0.484038          0.116205  18.539203       1   \n",
      "maxHeartRate                  0.447156          0.043307   6.382762       1   \n",
      "oldpeak                       0.465282          0.080579  12.357399       1   \n",
      "vesselsColored                0.490839          0.128451  20.780993       1   \n",
      "thalreversableEffect          0.462909          0.075864  11.575027       1   \n",
      "\n",
      "                         Den DF      Pr>F  \n",
      "sexmale                     141  0.011008  \n",
      "chestpainatypicalAngina     141  0.004574  \n",
      "chestpainnonAnginal         141  0.000773  \n",
      "chestpaintypicalAngina      141  0.000031  \n",
      "maxHeartRate                141  0.012628  \n",
      "oldpeak                     141  0.000591  \n",
      "vesselsColored              141  0.000011  \n",
      "thalreversableEffect        141  0.000870  \n",
      "\n",
      "Variable maxHeartRate will be removed\n",
      "\n",
      "\n",
      "====================== Step 12 backward selection results =======================\n",
      "                         Wilks' Lambda  Partial R-Square    F Value  Num DF  \\\n",
      "sexmale                       0.471424          0.051478   7.706666       1   \n",
      "chestpainatypicalAngina       0.481815          0.071935  11.006537       1   \n",
      "chestpainnonAnginal           0.496517          0.099416  15.675469       1   \n",
      "chestpaintypicalAngina        0.517758          0.136362  22.420771       1   \n",
      "oldpeak                       0.508254          0.120212  19.402486       1   \n",
      "vesselsColored                0.517777          0.136394  22.426798       1   \n",
      "thalreversableEffect          0.479144          0.066762  10.158350       1   \n",
      "\n",
      "                         Den DF      Pr>F  \n",
      "sexmale                     142  0.006244  \n",
      "chestpainatypicalAngina     142  0.001153  \n",
      "chestpainnonAnginal         142  0.000118  \n",
      "chestpaintypicalAngina      142  0.000005  \n",
      "oldpeak                     142  0.000021  \n",
      "vesselsColored              142  0.000005  \n",
      "thalreversableEffect        142  0.001767  \n",
      "\n",
      "No variable can be removed\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-1 {\n",
       "  /* Definition of color scheme common for light and dark mode */\n",
       "  --sklearn-color-text: #000;\n",
       "  --sklearn-color-text-muted: #666;\n",
       "  --sklearn-color-line: gray;\n",
       "  /* Definition of color scheme for unfitted estimators */\n",
       "  --sklearn-color-unfitted-level-0: #fff5e6;\n",
       "  --sklearn-color-unfitted-level-1: #f6e4d2;\n",
       "  --sklearn-color-unfitted-level-2: #ffe0b3;\n",
       "  --sklearn-color-unfitted-level-3: chocolate;\n",
       "  /* Definition of color scheme for fitted estimators */\n",
       "  --sklearn-color-fitted-level-0: #f0f8ff;\n",
       "  --sklearn-color-fitted-level-1: #d4ebff;\n",
       "  --sklearn-color-fitted-level-2: #b3dbfd;\n",
       "  --sklearn-color-fitted-level-3: cornflowerblue;\n",
       "}\n",
       "\n",
       "#sk-container-id-1.light {\n",
       "  /* Specific color for light theme */\n",
       "  --sklearn-color-text-on-default-background: black;\n",
       "  --sklearn-color-background: white;\n",
       "  --sklearn-color-border-box: black;\n",
       "  --sklearn-color-icon: #696969;\n",
       "}\n",
       "\n",
       "#sk-container-id-1.dark {\n",
       "  --sklearn-color-text-on-default-background: white;\n",
       "  --sklearn-color-background: #111;\n",
       "  --sklearn-color-border-box: white;\n",
       "  --sklearn-color-icon: #878787;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 pre {\n",
       "  padding: 0;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 input.sk-hidden--visually {\n",
       "  border: 0;\n",
       "  clip: rect(1px 1px 1px 1px);\n",
       "  clip: rect(1px, 1px, 1px, 1px);\n",
       "  height: 1px;\n",
       "  margin: -1px;\n",
       "  overflow: hidden;\n",
       "  padding: 0;\n",
       "  position: absolute;\n",
       "  width: 1px;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-dashed-wrapped {\n",
       "  border: 1px dashed var(--sklearn-color-line);\n",
       "  margin: 0 0.4em 0.5em 0.4em;\n",
       "  box-sizing: border-box;\n",
       "  padding-bottom: 0.4em;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-container {\n",
       "  /* jupyter's `normalize.less` sets `[hidden] { display: none; }`\n",
       "     but bootstrap.min.css set `[hidden] { display: none !important; }`\n",
       "     so we also need the `!important` here to be able to override the\n",
       "     default hidden behavior on the sphinx rendered scikit-learn.org.\n",
       "     See: https://github.com/scikit-learn/scikit-learn/issues/21755 */\n",
       "  display: inline-block !important;\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-text-repr-fallback {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       "div.sk-parallel-item,\n",
       "div.sk-serial,\n",
       "div.sk-item {\n",
       "  /* draw centered vertical line to link estimators */\n",
       "  background-image: linear-gradient(var(--sklearn-color-text-on-default-background), var(--sklearn-color-text-on-default-background));\n",
       "  background-size: 2px 100%;\n",
       "  background-repeat: no-repeat;\n",
       "  background-position: center center;\n",
       "}\n",
       "\n",
       "/* Parallel-specific style estimator block */\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item::after {\n",
       "  content: \"\";\n",
       "  width: 100%;\n",
       "  border-bottom: 2px solid var(--sklearn-color-text-on-default-background);\n",
       "  flex-grow: 1;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel {\n",
       "  display: flex;\n",
       "  align-items: stretch;\n",
       "  justify-content: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item:first-child::after {\n",
       "  align-self: flex-end;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item:last-child::after {\n",
       "  align-self: flex-start;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item:only-child::after {\n",
       "  width: 0;\n",
       "}\n",
       "\n",
       "/* Serial-specific style estimator block */\n",
       "\n",
       "#sk-container-id-1 div.sk-serial {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "  align-items: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  padding-right: 1em;\n",
       "  padding-left: 1em;\n",
       "}\n",
       "\n",
       "\n",
       "/* Toggleable style: style used for estimator/Pipeline/ColumnTransformer box that is\n",
       "clickable and can be expanded/collapsed.\n",
       "- Pipeline and ColumnTransformer use this feature and define the default style\n",
       "- Estimators will overwrite some part of the style using the `sk-estimator` class\n",
       "*/\n",
       "\n",
       "/* Pipeline and ColumnTransformer style (default) */\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable {\n",
       "  /* Default theme specific background. It is overwritten whether we have a\n",
       "  specific estimator or a Pipeline/ColumnTransformer */\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "/* Toggleable label */\n",
       "#sk-container-id-1 label.sk-toggleable__label {\n",
       "  cursor: pointer;\n",
       "  display: flex;\n",
       "  width: 100%;\n",
       "  margin-bottom: 0;\n",
       "  padding: 0.5em;\n",
       "  box-sizing: border-box;\n",
       "  text-align: center;\n",
       "  align-items: center;\n",
       "  justify-content: center;\n",
       "  gap: 0.5em;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 label.sk-toggleable__label .caption {\n",
       "  font-size: 0.6rem;\n",
       "  font-weight: lighter;\n",
       "  color: var(--sklearn-color-text-muted);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 label.sk-toggleable__label-arrow:before {\n",
       "  /* Arrow on the left of the label */\n",
       "  content: \"▸\";\n",
       "  float: left;\n",
       "  margin-right: 0.25em;\n",
       "  color: var(--sklearn-color-icon);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 label.sk-toggleable__label-arrow:hover:before {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "/* Toggleable content - dropdown */\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content {\n",
       "  display: none;\n",
       "  text-align: left;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content pre {\n",
       "  margin: 0.2em;\n",
       "  border-radius: 0.25em;\n",
       "  color: var(--sklearn-color-text);\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content.fitted pre {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 input.sk-toggleable__control:checked~div.sk-toggleable__content {\n",
       "  /* Expand drop-down */\n",
       "  display: block;\n",
       "  width: 100%;\n",
       "  overflow: visible;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {\n",
       "  content: \"▾\";\n",
       "}\n",
       "\n",
       "/* Pipeline/ColumnTransformer-specific style */\n",
       "\n",
       "#sk-container-id-1 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator-specific style */\n",
       "\n",
       "/* Colorize estimator box */\n",
       "#sk-container-id-1 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-label label.sk-toggleable__label,\n",
       "#sk-container-id-1 div.sk-label label {\n",
       "  /* The background is the default theme color */\n",
       "  color: var(--sklearn-color-text-on-default-background);\n",
       "}\n",
       "\n",
       "/* On hover, darken the color of the background */\n",
       "#sk-container-id-1 div.sk-label:hover label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "/* Label box, darken color on hover, fitted */\n",
       "#sk-container-id-1 div.sk-label.fitted:hover label.sk-toggleable__label.fitted {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator label */\n",
       "\n",
       "#sk-container-id-1 div.sk-label label {\n",
       "  font-family: monospace;\n",
       "  font-weight: bold;\n",
       "  line-height: 1.2em;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-label-container {\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "/* Estimator-specific */\n",
       "#sk-container-id-1 div.sk-estimator {\n",
       "  font-family: monospace;\n",
       "  border: 1px dotted var(--sklearn-color-border-box);\n",
       "  border-radius: 0.25em;\n",
       "  box-sizing: border-box;\n",
       "  margin-bottom: 0.5em;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-estimator.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "/* on hover */\n",
       "#sk-container-id-1 div.sk-estimator:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-estimator.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Specification for estimator info (e.g. \"i\" and \"?\") */\n",
       "\n",
       "/* Common style for \"i\" and \"?\" */\n",
       "\n",
       ".sk-estimator-doc-link,\n",
       "a:link.sk-estimator-doc-link,\n",
       "a:visited.sk-estimator-doc-link {\n",
       "  float: right;\n",
       "  font-size: smaller;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "  border-radius: 1em;\n",
       "  height: 1em;\n",
       "  width: 1em;\n",
       "  text-decoration: none !important;\n",
       "  margin-left: 0.5em;\n",
       "  text-align: center;\n",
       "  /* unfitted */\n",
       "  border: var(--sklearn-color-unfitted-level-3) 1pt solid;\n",
       "  color: var(--sklearn-color-unfitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted,\n",
       "a:link.sk-estimator-doc-link.fitted,\n",
       "a:visited.sk-estimator-doc-link.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "  border: var(--sklearn-color-fitted-level-3) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "div.sk-estimator:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  border: var(--sklearn-color-fitted-level-0) 1pt solid;\n",
       "  color: var(--sklearn-color-unfitted-level-0);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "div.sk-estimator.fitted:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "  border: var(--sklearn-color-fitted-level-0) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-0);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "/* Span, style for the box shown on hovering the info icon */\n",
       ".sk-estimator-doc-link span {\n",
       "  display: none;\n",
       "  z-index: 9999;\n",
       "  position: relative;\n",
       "  font-weight: normal;\n",
       "  right: .2ex;\n",
       "  padding: .5ex;\n",
       "  margin: .5ex;\n",
       "  width: min-content;\n",
       "  min-width: 20ex;\n",
       "  max-width: 50ex;\n",
       "  color: var(--sklearn-color-text);\n",
       "  box-shadow: 2pt 2pt 4pt #999;\n",
       "  /* unfitted */\n",
       "  background: var(--sklearn-color-unfitted-level-0);\n",
       "  border: .5pt solid var(--sklearn-color-unfitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted span {\n",
       "  /* fitted */\n",
       "  background: var(--sklearn-color-fitted-level-0);\n",
       "  border: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link:hover span {\n",
       "  display: block;\n",
       "}\n",
       "\n",
       "/* \"?\"-specific style due to the `<a>` HTML tag */\n",
       "\n",
       "#sk-container-id-1 a.estimator_doc_link {\n",
       "  float: right;\n",
       "  font-size: 1rem;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "  border-radius: 1rem;\n",
       "  height: 1rem;\n",
       "  width: 1rem;\n",
       "  text-decoration: none;\n",
       "  /* unfitted */\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 a.estimator_doc_link.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "#sk-container-id-1 a.estimator_doc_link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 a.estimator_doc_link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "\n",
       ".estimator-table {\n",
       "    font-family: monospace;\n",
       "}\n",
       "\n",
       ".estimator-table summary {\n",
       "    padding: .5rem;\n",
       "    cursor: pointer;\n",
       "}\n",
       "\n",
       ".estimator-table summary::marker {\n",
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       "</style><body><div id=\"sk-container-id-1\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>STEPDISC(method=&#x27;backward&#x27;)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-1\" type=\"checkbox\" checked><label for=\"sk-estimator-id-1\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow\"><div><div>STEPDISC</div></div><div><span class=\"sk-estimator-doc-link fitted\">i<span>Fitted</span></span></div></label><div class=\"sk-toggleable__content fitted\" data-param-prefix=\"\">\n",
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       "            <td class=\"param\">verbose</td>\n",
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       "    \n",
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      ],
      "text/plain": [
       "STEPDISC(method='backward')"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from discrimintools import DISCRIM, STEPDISC\n",
    "#split into X and y\n",
    "y, X = D[\"disease\"], D.drop(columns=[\"disease\"])\n",
    "clf = DISCRIM().fit(X,y)\n",
    "clf2 = STEPDISC(method=\"backward\",alpha=0.01,verbose=True)\n",
    "clf2.fit(clf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Selected variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['sexmale', 'chestpainatypicalAngina', 'chestpainnonAnginal', 'chestpaintypicalAngina', 'oldpeak', 'vesselsColored', 'thalreversableEffect']\n"
     ]
    }
   ],
   "source": [
    "#selected variables\n",
    "print(clf2.summary_.selected)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### summary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                     Stepwise Discriminant Analysis - Results                     \n",
      "\n",
      "====================== Before backward selection  =======================\n",
      "\n",
      "                     Discriminant Analysis - Results                     \n",
      "\n",
      "Summary Information:\n",
      "               Infos  Value                  DF  DF value\n",
      "0  Total Sample Size    150            DF Total       149\n",
      "1          Variables     18   DF Within Classes       148\n",
      "2            Classes      2  DF Between Classes         1\n",
      "\n",
      "Class Level Information:\n",
      "          Frequency  Proportion  Prior Probability\n",
      "absence          82      0.5467             0.5467\n",
      "presence         68      0.4533             0.4533\n",
      "\n",
      "Pooled Covariance Matrix Information:\n",
      "        Rank  Natural Log of the Determinant\n",
      "Pooled    18                         -5.6739\n",
      "\n",
      "Linear Discriminant Function for disease:\n",
      "                            absence  presence\n",
      "Constant                  -124.3546 -127.3863\n",
      "age                          1.1836    1.1914\n",
      "sexmale                     14.2659   15.9123\n",
      "chestpainatypicalAngina      0.5668   -1.8839\n",
      "chestpainnonAnginal          3.4872    1.6652\n",
      "chestpaintypicalAngina      -2.8081   -7.4223\n",
      "restbpress                   0.3460    0.3690\n",
      "cholesteral                  0.0407    0.0373\n",
      "sugarlow                    10.4057   11.7146\n",
      "electrosttAbnormality      -15.8118  -12.8213\n",
      "electroventricHypertrophy   -1.8553   -1.2411\n",
      "maxHeartRate                 0.4856    0.4579\n",
      "ExerciseAnginayes            4.9170    5.9612\n",
      "oldpeak                      3.0652    3.7751\n",
      "slopeflat                   18.6429   19.8215\n",
      "slopeupsloping              14.7467   15.2526\n",
      "vesselsColored              -2.5087   -1.0308\n",
      "thalnormal                  21.1525   20.1211\n",
      "thalreversableEffect        14.8540   16.1636\n",
      "\n",
      "Classification Summary for Calibration Data:\n",
      "\n",
      "Observation Profile:\n",
      "                        Read  Used\n",
      "Number of Observations   150   150\n",
      "\n",
      "Number of Observations Classified into disease:\n",
      "prediction  absence  presence  Total\n",
      "disease                             \n",
      "absence          75         7     82\n",
      "presence         12        56     68\n",
      "Total            87        63    150\n",
      "\n",
      "Percent Classified into disease:\n",
      "prediction  absence  presence  Total\n",
      "disease                             \n",
      "absence     91.4634    8.5366  100.0\n",
      "presence    17.6471   82.3529  100.0\n",
      "Total       58.0000   42.0000  100.0\n",
      "Priors       0.5467    0.4533    NaN\n",
      "\n",
      "Error Count Estimates for disease:\n",
      "        absence  presence   Total\n",
      "Rate     0.0854    0.1765  0.1267\n",
      "Priors   0.5467    0.4533     NaN\n",
      "\n",
      "Classification Report for disease:\n",
      "              precision  recall  f1-score   support\n",
      "absence          0.8621  0.9146    0.8876   82.0000\n",
      "presence         0.8889  0.8235    0.8550   68.0000\n",
      "accuracy         0.8733  0.8733    0.8733    0.8733\n",
      "macro avg        0.8755  0.8691    0.8713  150.0000\n",
      "weighted avg     0.8742  0.8733    0.8728  150.0000\n",
      "\n",
      "====================== After backward selection  =======================\n",
      "\n",
      "                     Discriminant Analysis - Results                     \n",
      "\n",
      "Summary Information:\n",
      "               Infos  Value                  DF  DF value\n",
      "0  Total Sample Size    150            DF Total       149\n",
      "1          Variables      7   DF Within Classes       148\n",
      "2            Classes      2  DF Between Classes         1\n",
      "\n",
      "Class Level Information:\n",
      "          Frequency  Proportion  Prior Probability\n",
      "absence          82      0.5467             0.5467\n",
      "presence         68      0.4533             0.4533\n",
      "\n",
      "Pooled Covariance Matrix Information:\n",
      "        Rank  Natural Log of the Determinant\n",
      "Pooled     7                        -10.5735\n",
      "\n",
      "Linear Discriminant Function for disease:\n",
      "                         absence  presence\n",
      "Constant                 -3.5002   -6.2648\n",
      "sexmale                   3.0078    4.6211\n",
      "chestpainatypicalAngina   4.6553    1.9352\n",
      "chestpainnonAnginal       4.6453    2.1583\n",
      "chestpaintypicalAngina    2.6881   -2.0794\n",
      "oldpeak                   0.7868    1.8112\n",
      "vesselsColored            0.7138    2.0291\n",
      "thalreversableEffect      0.6085    2.4439\n",
      "\n",
      "Classification Summary for Calibration Data:\n",
      "\n",
      "Observation Profile:\n",
      "                        Read  Used\n",
      "Number of Observations   150   150\n",
      "\n",
      "Number of Observations Classified into disease:\n",
      "prediction  absence  presence  Total\n",
      "disease                             \n",
      "absence          72        10     82\n",
      "presence         12        56     68\n",
      "Total            84        66    150\n",
      "\n",
      "Percent Classified into disease:\n",
      "prediction  absence  presence  Total\n",
      "disease                             \n",
      "absence     87.8049   12.1951  100.0\n",
      "presence    17.6471   82.3529  100.0\n",
      "Total       56.0000   44.0000  100.0\n",
      "Priors       0.5467    0.4533    NaN\n",
      "\n",
      "Error Count Estimates for disease:\n",
      "        absence  presence   Total\n",
      "Rate     0.1220    0.1765  0.1467\n",
      "Priors   0.5467    0.4533     NaN\n",
      "\n",
      "Classification Report for disease:\n",
      "              precision  recall  f1-score   support\n",
      "absence          0.8571  0.8780    0.8675   82.0000\n",
      "presence         0.8485  0.8235    0.8358   68.0000\n",
      "accuracy         0.8533  0.8533    0.8533    0.8533\n",
      "macro avg        0.8528  0.8508    0.8516  150.0000\n",
      "weighted avg     0.8532  0.8533    0.8531  150.0000\n"
     ]
    }
   ],
   "source": [
    "from discrimintools import summarySTEPDISC\n",
    "summarySTEPDISC(clf2,detailed=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Evaluation of prediction on testing dataset\n",
    "\n",
    "#### Testing data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "Index: 120 entries, 150 to 269\n",
      "Data columns (total 14 columns):\n",
      " #   Column          Non-Null Count  Dtype  \n",
      "---  ------          --------------  -----  \n",
      " 0   disease         120 non-null    object \n",
      " 1   age             120 non-null    int64  \n",
      " 2   sex             120 non-null    object \n",
      " 3   chestpain       120 non-null    object \n",
      " 4   restbpress      120 non-null    int64  \n",
      " 5   cholesteral     120 non-null    int64  \n",
      " 6   sugar           120 non-null    object \n",
      " 7   electro         120 non-null    object \n",
      " 8   maxHeartRate    120 non-null    int64  \n",
      " 9   ExerciseAngina  120 non-null    object \n",
      " 10  oldpeak         120 non-null    float64\n",
      " 11  slope           120 non-null    object \n",
      " 12  vesselsColored  120 non-null    int64  \n",
      " 13  thal            120 non-null    object \n",
      "dtypes: float64(1), int64(5), object(8)\n",
      "memory usage: 14.1+ KB\n"
     ]
    }
   ],
   "source": [
    "#testining data\n",
    "DTest = load_heart(\"test\")\n",
    "DTest.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Observation Profile:\n",
      "                        Read  Used\n",
      "Number of Observations   120   120\n",
      "\n",
      "Number of Observations Classified into disease:\n",
      "prediction  absence  presence  Total\n",
      "disease                             \n",
      "absence          59         9     68\n",
      "presence         11        41     52\n",
      "Total            70        50    120\n",
      "\n",
      "Percent Classified into disease:\n",
      "prediction    absence   presence  Total\n",
      "disease                                \n",
      "absence     86.764706  13.235294  100.0\n",
      "presence    21.153846  78.846154  100.0\n",
      "Total       58.333333  41.666667  100.0\n",
      "Priors       0.546667   0.453333    NaN\n",
      "\n",
      "Error Count Estimates for disease:\n",
      "         absence  presence    Total\n",
      "Rate    0.132353  0.211538  0.16825\n",
      "Priors  0.546667  0.453333      NaN\n",
      "\n",
      "Classification Report for disease:\n",
      "              precision    recall  f1-score     support\n",
      "absence        0.842857  0.867647  0.855072   68.000000\n",
      "presence       0.820000  0.788462  0.803922   52.000000\n",
      "accuracy       0.833333  0.833333  0.833333    0.833333\n",
      "macro avg      0.831429  0.828054  0.829497  120.000000\n",
      "weighted avg   0.832952  0.833333  0.832907  120.000000\n"
     ]
    }
   ],
   "source": [
    "#split into X and y\n",
    "yTest, XTest = DTest[\"disease\"], DTest.drop(columns=[\"disease\"])\n",
    "eval_test = clf2.eval_predict(XTest,yTest,verbose=True)"
   ]
  }
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