———–Load Data————

 heart_attack<-read.csv("C:/Users/DELL/Desktop/heart.csv")
 heart_attack
##      age sex cp trestbps chol fbs restecg thalach exang oldpeak slope ca thal
## 1     52   1  0      125  212   0       1     168     0     1.0     2  2    3
## 2     53   1  0      140  203   1       0     155     1     3.1     0  0    3
## 3     70   1  0      145  174   0       1     125     1     2.6     0  0    3
## 4     61   1  0      148  203   0       1     161     0     0.0     2  1    3
## 5     62   0  0      138  294   1       1     106     0     1.9     1  3    2
## 6     58   0  0      100  248   0       0     122     0     1.0     1  0    2
## 7     58   1  0      114  318   0       2     140     0     4.4     0  3    1
## 8     55   1  0      160  289   0       0     145     1     0.8     1  1    3
## 9     46   1  0      120  249   0       0     144     0     0.8     2  0    3
## 10    54   1  0      122  286   0       0     116     1     3.2     1  2    2
## 11    71   0  0      112  149   0       1     125     0     1.6     1  0    2
## 12    43   0  0      132  341   1       0     136     1     3.0     1  0    3
## 13    34   0  1      118  210   0       1     192     0     0.7     2  0    2
## 14    51   1  0      140  298   0       1     122     1     4.2     1  3    3
## 15    52   1  0      128  204   1       1     156     1     1.0     1  0    0
## 16    34   0  1      118  210   0       1     192     0     0.7     2  0    2
## 17    51   0  2      140  308   0       0     142     0     1.5     2  1    2
## 18    54   1  0      124  266   0       0     109     1     2.2     1  1    3
## 19    50   0  1      120  244   0       1     162     0     1.1     2  0    2
## 20    58   1  2      140  211   1       0     165     0     0.0     2  0    2
## 21    60   1  2      140  185   0       0     155     0     3.0     1  0    2
## 22    67   0  0      106  223   0       1     142     0     0.3     2  2    2
## 23    45   1  0      104  208   0       0     148     1     3.0     1  0    2
## 24    63   0  2      135  252   0       0     172     0     0.0     2  0    2
## 25    42   0  2      120  209   0       1     173     0     0.0     1  0    2
## 26    61   0  0      145  307   0       0     146     1     1.0     1  0    3
## 27    44   1  2      130  233   0       1     179     1     0.4     2  0    2
## 28    58   0  1      136  319   1       0     152     0     0.0     2  2    2
## 29    56   1  2      130  256   1       0     142     1     0.6     1  1    1
## 30    55   0  0      180  327   0       2     117     1     3.4     1  0    2
## 31    44   1  0      120  169   0       1     144     1     2.8     0  0    1
## 32    50   0  1      120  244   0       1     162     0     1.1     2  0    2
## 33    57   1  0      130  131   0       1     115     1     1.2     1  1    3
## 34    70   1  2      160  269   0       1     112     1     2.9     1  1    3
## 35    50   1  2      129  196   0       1     163     0     0.0     2  0    2
## 36    46   1  2      150  231   0       1     147     0     3.6     1  0    2
## 37    51   1  3      125  213   0       0     125     1     1.4     2  1    2
## 38    59   1  0      138  271   0       0     182     0     0.0     2  0    2
## 39    64   1  0      128  263   0       1     105     1     0.2     1  1    3
## 40    57   1  2      128  229   0       0     150     0     0.4     1  1    3
## 41    65   0  2      160  360   0       0     151     0     0.8     2  0    2
## 42    54   1  2      120  258   0       0     147     0     0.4     1  0    3
## 43    61   0  0      130  330   0       0     169     0     0.0     2  0    2
## 44    46   1  0      120  249   0       0     144     0     0.8     2  0    3
## 45    55   0  1      132  342   0       1     166     0     1.2     2  0    2
## 46    42   1  0      140  226   0       1     178     0     0.0     2  0    2
## 47    41   1  1      135  203   0       1     132     0     0.0     1  0    1
## 48    66   0  0      178  228   1       1     165     1     1.0     1  2    3
## 49    66   0  2      146  278   0       0     152     0     0.0     1  1    2
## 50    60   1  0      117  230   1       1     160     1     1.4     2  2    3
## 51    58   0  3      150  283   1       0     162     0     1.0     2  0    2
## 52    57   0  0      140  241   0       1     123     1     0.2     1  0    3
## 53    38   1  2      138  175   0       1     173     0     0.0     2  4    2
## 54    49   1  2      120  188   0       1     139     0     2.0     1  3    3
## 55    55   1  0      140  217   0       1     111     1     5.6     0  0    3
## 56    55   1  0      140  217   0       1     111     1     5.6     0  0    3
## 57    56   1  3      120  193   0       0     162     0     1.9     1  0    3
## 58    48   1  1      130  245   0       0     180     0     0.2     1  0    2
## 59    67   1  2      152  212   0       0     150     0     0.8     1  0    3
## 60    57   1  1      154  232   0       0     164     0     0.0     2  1    2
## 61    29   1  1      130  204   0       0     202     0     0.0     2  0    2
## 62    66   0  2      146  278   0       0     152     0     0.0     1  1    2
## 63    67   1  0      100  299   0       0     125     1     0.9     1  2    2
## 64    59   1  2      150  212   1       1     157     0     1.6     2  0    2
## 65    29   1  1      130  204   0       0     202     0     0.0     2  0    2
## 66    59   1  3      170  288   0       0     159     0     0.2     1  0    3
## 67    53   1  2      130  197   1       0     152     0     1.2     0  0    2
## 68    42   1  0      136  315   0       1     125     1     1.8     1  0    1
## 69    37   0  2      120  215   0       1     170     0     0.0     2  0    2
## 70    62   0  0      160  164   0       0     145     0     6.2     0  3    3
## 71    59   1  0      170  326   0       0     140     1     3.4     0  0    3
## 72    61   1  0      140  207   0       0     138     1     1.9     2  1    3
## 73    56   1  0      125  249   1       0     144     1     1.2     1  1    2
## 74    59   1  0      140  177   0       1     162     1     0.0     2  1    3
## 75    48   1  0      130  256   1       0     150     1     0.0     2  2    3
## 76    47   1  2      138  257   0       0     156     0     0.0     2  0    2
## 77    48   1  2      124  255   1       1     175     0     0.0     2  2    2
## 78    63   1  0      140  187   0       0     144     1     4.0     2  2    3
## 79    52   1  1      134  201   0       1     158     0     0.8     2  1    2
## 80    52   1  1      134  201   0       1     158     0     0.8     2  1    2
## 81    50   1  2      140  233   0       1     163     0     0.6     1  1    3
## 82    49   1  2      118  149   0       0     126     0     0.8     2  3    2
## 83    46   1  2      150  231   0       1     147     0     3.6     1  0    2
## 84    38   1  2      138  175   0       1     173     0     0.0     2  4    2
## 85    37   0  2      120  215   0       1     170     0     0.0     2  0    2
## 86    44   1  1      120  220   0       1     170     0     0.0     2  0    2
## 87    58   1  2      140  211   1       0     165     0     0.0     2  0    2
## 88    59   0  0      174  249   0       1     143     1     0.0     1  0    2
## 89    62   0  0      140  268   0       0     160     0     3.6     0  2    2
## 90    68   1  0      144  193   1       1     141     0     3.4     1  2    3
## 91    54   0  2      108  267   0       0     167     0     0.0     2  0    2
## 92    62   0  0      124  209   0       1     163     0     0.0     2  0    2
## 93    63   1  0      140  187   0       0     144     1     4.0     2  2    3
## 94    44   1  0      120  169   0       1     144     1     2.8     0  0    1
## 95    62   1  1      128  208   1       0     140     0     0.0     2  0    2
## 96    45   0  0      138  236   0       0     152     1     0.2     1  0    2
## 97    57   0  0      128  303   0       0     159     0     0.0     2  1    2
## 98    53   1  0      123  282   0       1      95     1     2.0     1  2    3
## 99    65   1  0      110  248   0       0     158     0     0.6     2  2    1
## 100   76   0  2      140  197   0       2     116     0     1.1     1  0    2
## 101   43   0  2      122  213   0       1     165     0     0.2     1  0    2
## 102   57   1  2      150  126   1       1     173     0     0.2     2  1    3
## 103   54   1  1      108  309   0       1     156     0     0.0     2  0    3
## 104   47   1  2      138  257   0       0     156     0     0.0     2  0    2
## 105   52   1  3      118  186   0       0     190     0     0.0     1  0    1
## 106   47   1  0      110  275   0       0     118     1     1.0     1  1    2
## 107   51   1  0      140  299   0       1     173     1     1.6     2  0    3
## 108   62   1  1      120  281   0       0     103     0     1.4     1  1    3
## 109   40   1  0      152  223   0       1     181     0     0.0     2  0    3
## 110   54   1  0      110  206   0       0     108     1     0.0     1  1    2
## 111   44   1  0      110  197   0       0     177     0     0.0     2  1    2
## 112   53   1  0      142  226   0       0     111     1     0.0     2  0    3
## 113   48   1  0      130  256   1       0     150     1     0.0     2  2    3
## 114   57   1  0      110  335   0       1     143     1     3.0     1  1    3
## 115   59   1  2      126  218   1       1     134     0     2.2     1  1    1
## 116   61   0  0      145  307   0       0     146     1     1.0     1  0    3
## 117   63   1  0      130  254   0       0     147     0     1.4     1  1    3
## 118   43   1  0      120  177   0       0     120     1     2.5     1  0    3
## 119   29   1  1      130  204   0       0     202     0     0.0     2  0    2
## 120   42   1  1      120  295   0       1     162     0     0.0     2  0    2
## 121   54   1  1      108  309   0       1     156     0     0.0     2  0    3
## 122   44   1  0      120  169   0       1     144     1     2.8     0  0    1
## 123   60   1  0      145  282   0       0     142     1     2.8     1  2    3
## 124   65   0  2      140  417   1       0     157     0     0.8     2  1    2
## 125   61   1  0      120  260   0       1     140     1     3.6     1  1    3
## 126   60   0  3      150  240   0       1     171     0     0.9     2  0    2
## 127   66   1  0      120  302   0       0     151     0     0.4     1  0    2
## 128   53   1  2      130  197   1       0     152     0     1.2     0  0    2
## 129   52   1  2      138  223   0       1     169     0     0.0     2  4    2
## 130   57   1  0      140  192   0       1     148     0     0.4     1  0    1
## 131   60   0  3      150  240   0       1     171     0     0.9     2  0    2
## 132   51   0  2      130  256   0       0     149     0     0.5     2  0    2
## 133   41   1  1      135  203   0       1     132     0     0.0     1  0    1
## 134   50   1  2      129  196   0       1     163     0     0.0     2  0    2
## 135   54   1  1      108  309   0       1     156     0     0.0     2  0    3
## 136   58   0  0      170  225   1       0     146     1     2.8     1  2    1
## 137   55   0  1      132  342   0       1     166     0     1.2     2  0    2
## 138   64   0  0      180  325   0       1     154     1     0.0     2  0    2
## 139   47   1  2      138  257   0       0     156     0     0.0     2  0    2
## 140   41   1  1      110  235   0       1     153     0     0.0     2  0    2
## 141   57   1  0      152  274   0       1      88     1     1.2     1  1    3
## 142   63   0  0      124  197   0       1     136     1     0.0     1  0    2
## 143   61   1  3      134  234   0       1     145     0     2.6     1  2    2
## 144   34   1  3      118  182   0       0     174     0     0.0     2  0    2
## 145   47   1  0      112  204   0       1     143     0     0.1     2  0    2
## 146   40   1  0      110  167   0       0     114     1     2.0     1  0    3
## 147   51   0  2      120  295   0       0     157     0     0.6     2  0    2
## 148   41   1  0      110  172   0       0     158     0     0.0     2  0    3
## 149   52   1  3      152  298   1       1     178     0     1.2     1  0    3
## 150   39   1  2      140  321   0       0     182     0     0.0     2  0    2
## 151   58   1  0      114  318   0       2     140     0     4.4     0  3    1
## 152   54   1  1      192  283   0       0     195     0     0.0     2  1    3
## 153   58   1  0      125  300   0       0     171     0     0.0     2  2    3
## 154   54   1  2      120  258   0       0     147     0     0.4     1  0    3
## 155   63   1  0      130  330   1       0     132     1     1.8     2  3    3
## 156   54   1  1      108  309   0       1     156     0     0.0     2  0    3
## 157   40   1  3      140  199   0       1     178     1     1.4     2  0    3
## 158   54   1  2      120  258   0       0     147     0     0.4     1  0    3
## 159   67   0  2      115  564   0       0     160     0     1.6     1  0    3
## 160   41   1  1      120  157   0       1     182     0     0.0     2  0    2
## 161   77   1  0      125  304   0       0     162     1     0.0     2  3    2
## 162   51   1  2      100  222   0       1     143     1     1.2     1  0    2
## 163   77   1  0      125  304   0       0     162     1     0.0     2  3    2
## 164   48   1  0      124  274   0       0     166     0     0.5     1  0    3
## 165   56   1  0      125  249   1       0     144     1     1.2     1  1    2
## 166   59   1  0      170  326   0       0     140     1     3.4     0  0    3
## 167   56   1  0      132  184   0       0     105     1     2.1     1  1    1
## 168   57   0  0      120  354   0       1     163     1     0.6     2  0    2
## 169   43   1  2      130  315   0       1     162     0     1.9     2  1    2
## 170   45   0  1      112  160   0       1     138     0     0.0     1  0    2
## 171   43   1  0      150  247   0       1     171     0     1.5     2  0    2
## 172   56   1  0      130  283   1       0     103     1     1.6     0  0    3
## 173   56   1  1      120  240   0       1     169     0     0.0     0  0    2
## 174   39   0  2       94  199   0       1     179     0     0.0     2  0    2
## 175   54   1  0      110  239   0       1     126     1     2.8     1  1    3
## 176   56   0  0      200  288   1       0     133     1     4.0     0  2    3
## 177   56   1  0      130  283   1       0     103     1     1.6     0  0    3
## 178   64   1  0      120  246   0       0      96     1     2.2     0  1    2
## 179   44   1  0      110  197   0       0     177     0     0.0     2  1    2
## 180   56   0  0      134  409   0       0     150     1     1.9     1  2    3
## 181   63   1  0      140  187   0       0     144     1     4.0     2  2    3
## 182   64   1  3      110  211   0       0     144     1     1.8     1  0    2
## 183   60   1  0      140  293   0       0     170     0     1.2     1  2    3
## 184   42   1  2      130  180   0       1     150     0     0.0     2  0    2
## 185   45   1  1      128  308   0       0     170     0     0.0     2  0    2
## 186   57   1  0      165  289   1       0     124     0     1.0     1  3    3
## 187   40   1  0      110  167   0       0     114     1     2.0     1  0    3
## 188   56   1  0      125  249   1       0     144     1     1.2     1  1    2
## 189   63   1  0      130  254   0       0     147     0     1.4     1  1    3
## 190   64   1  2      125  309   0       1     131     1     1.8     1  0    3
## 191   41   1  2      112  250   0       1     179     0     0.0     2  0    2
## 192   56   1  1      130  221   0       0     163     0     0.0     2  0    3
## 193   67   0  2      115  564   0       0     160     0     1.6     1  0    3
## 194   69   1  3      160  234   1       0     131     0     0.1     1  1    2
## 195   67   1  0      160  286   0       0     108     1     1.5     1  3    2
## 196   59   1  2      150  212   1       1     157     0     1.6     2  0    2
## 197   58   1  0      100  234   0       1     156     0     0.1     2  1    3
## 198   45   1  0      115  260   0       0     185     0     0.0     2  0    2
## 199   60   0  2      102  318   0       1     160     0     0.0     2  1    2
## 200   50   1  0      144  200   0       0     126     1     0.9     1  0    3
## 201   62   0  0      124  209   0       1     163     0     0.0     2  0    2
## 202   34   1  3      118  182   0       0     174     0     0.0     2  0    2
## 203   52   1  3      152  298   1       1     178     0     1.2     1  0    3
## 204   64   1  3      170  227   0       0     155     0     0.6     1  0    3
## 205   66   0  2      146  278   0       0     152     0     0.0     1  1    2
## 206   42   1  3      148  244   0       0     178     0     0.8     2  2    2
## 207   59   1  2      126  218   1       1     134     0     2.2     1  1    1
## 208   41   1  2      112  250   0       1     179     0     0.0     2  0    2
## 209   38   1  2      138  175   0       1     173     0     0.0     2  4    2
## 210   62   1  1      120  281   0       0     103     0     1.4     1  1    3
## 211   42   1  2      120  240   1       1     194     0     0.8     0  0    3
## 212   67   1  0      100  299   0       0     125     1     0.9     1  2    2
## 213   50   1  0      150  243   0       0     128     0     2.6     1  0    3
## 214   43   1  2      130  315   0       1     162     0     1.9     2  1    2
## 215   45   1  1      128  308   0       0     170     0     0.0     2  0    2
## 216   49   1  1      130  266   0       1     171     0     0.6     2  0    2
## 217   65   1  0      135  254   0       0     127     0     2.8     1  1    3
## 218   41   1  1      120  157   0       1     182     0     0.0     2  0    2
## 219   46   1  0      140  311   0       1     120     1     1.8     1  2    3
## 220   54   1  0      122  286   0       0     116     1     3.2     1  2    2
## 221   57   0  1      130  236   0       0     174     0     0.0     1  1    2
## 222   63   1  0      130  254   0       0     147     0     1.4     1  1    3
## 223   64   1  3      110  211   0       0     144     1     1.8     1  0    2
## 224   39   0  2       94  199   0       1     179     0     0.0     2  0    2
## 225   51   1  0      140  261   0       0     186     1     0.0     2  0    2
## 226   54   1  2      150  232   0       0     165     0     1.6     2  0    3
## 227   49   1  2      118  149   0       0     126     0     0.8     2  3    2
## 228   44   0  2      118  242   0       1     149     0     0.3     1  1    2
## 229   52   1  1      128  205   1       1     184     0     0.0     2  0    2
## 230   66   0  0      178  228   1       1     165     1     1.0     1  2    3
## 231   58   1  0      125  300   0       0     171     0     0.0     2  2    3
## 232   56   1  1      120  236   0       1     178     0     0.8     2  0    2
## 233   60   1  0      125  258   0       0     141     1     2.8     1  1    3
## 234   41   0  1      126  306   0       1     163     0     0.0     2  0    2
## 235   49   0  0      130  269   0       1     163     0     0.0     2  0    2
## 236   64   1  3      170  227   0       0     155     0     0.6     1  0    3
## 237   49   1  2      118  149   0       0     126     0     0.8     2  3    2
## 238   57   1  1      124  261   0       1     141     0     0.3     2  0    3
## 239   60   1  0      117  230   1       1     160     1     1.4     2  2    3
## 240   62   0  0      150  244   0       1     154     1     1.4     1  0    2
## 241   54   0  1      132  288   1       0     159     1     0.0     2  1    2
## 242   67   1  2      152  212   0       0     150     0     0.8     1  0    3
## 243   38   1  2      138  175   0       1     173     0     0.0     2  4    2
## 244   60   1  2      140  185   0       0     155     0     3.0     1  0    2
## 245   51   1  2      125  245   1       0     166     0     2.4     1  0    2
## 246   44   1  1      130  219   0       0     188     0     0.0     2  0    2
## 247   54   1  1      192  283   0       0     195     0     0.0     2  1    3
## 248   46   1  0      140  311   0       1     120     1     1.8     1  2    3
## 249   39   0  2      138  220   0       1     152     0     0.0     1  0    2
## 250   42   1  2      130  180   0       1     150     0     0.0     2  0    2
## 251   47   1  0      110  275   0       0     118     1     1.0     1  1    2
## 252   45   0  1      112  160   0       1     138     0     0.0     1  0    2
## 253   55   1  0      132  353   0       1     132     1     1.2     1  1    3
## 254   57   1  0      165  289   1       0     124     0     1.0     1  3    3
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## 308   44   1  1      120  220   0       1     170     0     0.0     2  0    2
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## 321   53   0  0      130  264   0       0     143     0     0.4     1  0    2
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## 323   45   1  0      142  309   0       0     147     1     0.0     1  3    3
## 324   66   1  1      160  246   0       1     120     1     0.0     1  3    1
## 325   48   1  1      130  245   0       0     180     0     0.2     1  0    2
## 326   56   0  1      140  294   0       0     153     0     1.3     1  0    2
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## 329   70   1  0      130  322   0       0     109     0     2.4     1  3    2
## 330   53   0  2      128  216   0       0     115     0     0.0     2  0    0
## 331   37   0  2      120  215   0       1     170     0     0.0     2  0    2
## 332   63   0  0      108  269   0       1     169     1     1.8     1  2    2
## 333   37   1  2      130  250   0       1     187     0     3.5     0  0    2
## 334   54   0  2      110  214   0       1     158     0     1.6     1  0    2
## 335   60   1  0      130  206   0       0     132     1     2.4     1  2    3
## 336   58   1  0      150  270   0       0     111     1     0.8     2  0    3
## 337   57   1  2      150  126   1       1     173     0     0.2     2  1    3
## 338   54   1  2      125  273   0       0     152     0     0.5     0  1    2
## 339   56   1  2      130  256   1       0     142     1     0.6     1  1    1
## 340   60   1  0      130  253   0       1     144     1     1.4     2  1    3
## 341   38   1  2      138  175   0       1     173     0     0.0     2  4    2
## 342   44   1  2      120  226   0       1     169     0     0.0     2  0    2
## 343   65   0  2      155  269   0       1     148     0     0.8     2  0    2
## 344   52   1  2      172  199   1       1     162     0     0.5     2  0    3
## 345   41   1  1      120  157   0       1     182     0     0.0     2  0    2
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## 351   66   1  0      120  302   0       0     151     0     0.4     1  0    2
## 352   50   1  0      144  200   0       0     126     1     0.9     1  0    3
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## 354   57   1  0      110  201   0       1     126     1     1.5     1  0    1
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## 356   46   0  0      138  243   0       0     152     1     0.0     1  0    2
## 357   59   1  0      164  176   1       0      90     0     1.0     1  2    1
## 358   67   1  0      160  286   0       0     108     1     1.5     1  3    2
## 359   59   1  3      134  204   0       1     162     0     0.8     2  2    2
## 360   53   0  2      128  216   0       0     115     0     0.0     2  0    0
## 361   48   1  0      122  222   0       0     186     0     0.0     2  0    2
## 362   62   1  2      130  231   0       1     146     0     1.8     1  3    3
## 363   43   0  2      122  213   0       1     165     0     0.2     1  0    2
## 364   53   1  2      130  246   1       0     173     0     0.0     2  3    2
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## 366   53   1  2      130  246   1       0     173     0     0.0     2  3    2
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## 373   54   0  2      110  214   0       1     158     0     1.6     1  0    2
## 374   58   1  1      120  284   0       0     160     0     1.8     1  0    2
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## 376   66   1  0      160  228   0       0     138     0     2.3     2  0    1
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## 378   64   0  0      130  303   0       1     122     0     2.0     1  2    2
## 379   67   1  0      120  237   0       1      71     0     1.0     1  0    2
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## 383   59   1  0      110  239   0       0     142     1     1.2     1  1    3
## 384   58   1  0      150  270   0       0     111     1     0.8     2  0    3
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## 387   42   0  2      120  209   0       1     173     0     0.0     1  0    2
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## 389   64   1  0      120  246   0       0      96     1     2.2     0  1    2
## 390   63   1  3      145  233   1       0     150     0     2.3     0  0    1
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## 392   45   1  3      110  264   0       1     132     0     1.2     1  0    3
## 393   51   1  2      110  175   0       1     123     0     0.6     2  0    2
## 394   62   0  0      160  164   0       0     145     0     6.2     0  3    3
## 395   63   1  0      130  330   1       0     132     1     1.8     2  3    3
## 396   66   0  2      146  278   0       0     152     0     0.0     1  1    2
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## 398   40   1  0      110  167   0       0     114     1     2.0     1  0    3
## 399   66   1  0      160  228   0       0     138     0     2.3     2  0    1
## 400   63   1  3      145  233   1       0     150     0     2.3     0  0    1
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## 402   71   0  0      112  149   0       1     125     0     1.6     1  0    2
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## 406   56   1  2      130  256   1       0     142     1     0.6     1  1    1
## 407   58   1  2      140  211   1       0     165     0     0.0     2  0    2
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## 409   46   0  0      138  243   0       0     152     1     0.0     1  0    2
## 410   46   1  2      150  231   0       1     147     0     3.6     1  0    2
## 411   41   0  1      105  198   0       1     168     0     0.0     2  1    2
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## 413   57   1  0      150  276   0       0     112     1     0.6     1  1    1
## 414   70   1  0      130  322   0       0     109     0     2.4     1  3    2
## 415   59   1  3      170  288   0       0     159     0     0.2     1  0    3
## 416   41   0  1      130  204   0       0     172     0     1.4     2  0    2
## 417   54   1  2      125  273   0       0     152     0     0.5     0  1    2
## 418   52   1  2      138  223   0       1     169     0     0.0     2  4    2
## 419   62   0  0      124  209   0       1     163     0     0.0     2  0    2
## 420   65   0  2      160  360   0       0     151     0     0.8     2  0    2
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## 422   42   0  0      102  265   0       0     122     0     0.6     1  0    2
## 423   57   0  0      120  354   0       1     163     1     0.6     2  0    2
## 424   58   0  1      136  319   1       0     152     0     0.0     2  2    2
## 425   45   1  0      142  309   0       0     147     1     0.0     1  3    3
## 426   51   0  0      130  305   0       1     142     1     1.2     1  0    3
## 427   54   0  2      160  201   0       1     163     0     0.0     2  1    2
## 428   57   1  2      150  168   0       1     174     0     1.6     2  0    2
## 429   43   1  0      132  247   1       0     143     1     0.1     1  4    3
## 430   47   1  2      108  243   0       1     152     0     0.0     2  0    2
## 431   67   1  2      152  212   0       0     150     0     0.8     1  0    3
## 432   65   0  0      150  225   0       0     114     0     1.0     1  3    3
## 433   60   0  2      102  318   0       1     160     0     0.0     2  1    2
## 434   37   1  2      130  250   0       1     187     0     3.5     0  0    2
## 435   41   0  2      112  268   0       0     172     1     0.0     2  0    2
## 436   57   0  0      120  354   0       1     163     1     0.6     2  0    2
## 437   59   0  0      174  249   0       1     143     1     0.0     1  0    2
## 438   67   1  0      120  229   0       0     129     1     2.6     1  2    3
## 439   47   1  2      130  253   0       1     179     0     0.0     2  0    2
## 440   58   1  1      120  284   0       0     160     0     1.8     1  0    2
## 441   62   0  0      150  244   0       1     154     1     1.4     1  0    2
## 442   60   1  0      140  293   0       0     170     0     1.2     1  2    3
## 443   57   1  0      152  274   0       1      88     1     1.2     1  1    3
## 444   57   1  2      150  168   0       1     174     0     1.6     2  0    2
## 445   47   1  2      130  253   0       1     179     0     0.0     2  0    2
## 446   52   1  1      128  205   1       1     184     0     0.0     2  0    2
## 447   53   1  2      130  246   1       0     173     0     0.0     2  3    2
## 448   55   1  0      160  289   0       0     145     1     0.8     1  1    3
## 449   51   0  2      120  295   0       0     157     0     0.6     2  0    2
## 450   52   1  0      112  230   0       1     160     0     0.0     2  1    2
## 451   63   0  0      150  407   0       0     154     0     4.0     1  3    3
## 452   49   0  1      134  271   0       1     162     0     0.0     1  0    2
## 453   66   0  0      178  228   1       1     165     1     1.0     1  2    3
## 454   49   0  1      134  271   0       1     162     0     0.0     1  0    2
## 455   65   0  0      150  225   0       0     114     0     1.0     1  3    3
## 456   69   1  3      160  234   1       0     131     0     0.1     1  1    2
## 457   47   1  2      108  243   0       1     152     0     0.0     2  0    2
## 458   39   0  2      138  220   0       1     152     0     0.0     1  0    2
## 459   43   1  0      150  247   0       1     171     0     1.5     2  0    2
## 460   51   1  0      140  261   0       0     186     1     0.0     2  0    2
## 461   69   1  2      140  254   0       0     146     0     2.0     1  3    3
## 462   48   1  2      124  255   1       1     175     0     0.0     2  2    2
## 463   52   1  3      118  186   0       0     190     0     0.0     1  0    1
## 464   43   1  0      110  211   0       1     161     0     0.0     2  0    3
## 465   67   0  2      115  564   0       0     160     0     1.6     1  0    3
## 466   38   1  2      138  175   0       1     173     0     0.0     2  4    2
## 467   44   1  1      130  219   0       0     188     0     0.0     2  0    2
## 468   47   1  0      110  275   0       0     118     1     1.0     1  1    2
## 469   61   1  2      150  243   1       1     137     1     1.0     1  0    2
## 470   67   1  0      160  286   0       0     108     1     1.5     1  3    2
## 471   60   0  3      150  240   0       1     171     0     0.9     2  0    2
## 472   64   0  2      140  313   0       1     133     0     0.2     2  0    3
## 473   58   0  0      130  197   0       1     131     0     0.6     1  0    2
## 474   41   1  2      130  214   0       0     168     0     2.0     1  0    2
## 475   48   1  1      110  229   0       1     168     0     1.0     0  0    3
## 476   57   1  2      150  126   1       1     173     0     0.2     2  1    3
## 477   57   1  0      165  289   1       0     124     0     1.0     1  3    3
## 478   57   1  2      128  229   0       0     150     0     0.4     1  1    3
## 479   39   1  2      140  321   0       0     182     0     0.0     2  0    2
## 480   58   1  0      128  216   0       0     131     1     2.2     1  3    3
## 481   51   0  0      130  305   0       1     142     1     1.2     1  0    3
## 482   63   0  0      150  407   0       0     154     0     4.0     1  3    3
## 483   51   1  0      140  298   0       1     122     1     4.2     1  3    3
## 484   35   1  1      122  192   0       1     174     0     0.0     2  0    2
## 485   65   1  0      110  248   0       0     158     0     0.6     2  2    1
## 486   62   1  1      120  281   0       0     103     0     1.4     1  1    3
## 487   41   1  0      110  172   0       0     158     0     0.0     2  0    3
## 488   65   1  0      135  254   0       0     127     0     2.8     1  1    3
## 489   54   0  1      132  288   1       0     159     1     0.0     2  1    2
## 490   61   1  2      150  243   1       1     137     1     1.0     1  0    2
## 491   57   0  0      128  303   0       0     159     0     0.0     2  1    2
## 492   57   1  2      150  168   0       1     174     0     1.6     2  0    2
## 493   64   1  2      125  309   0       1     131     1     1.8     1  0    3
## 494   55   1  0      132  353   0       1     132     1     1.2     1  1    3
## 495   51   1  2      125  245   1       0     166     0     2.4     1  0    2
## 496   59   1  0      135  234   0       1     161     0     0.5     1  0    3
## 497   68   1  2      180  274   1       0     150     1     1.6     1  0    3
## 498   57   1  1      154  232   0       0     164     0     0.0     2  1    2
## 499   54   1  0      140  239   0       1     160     0     1.2     2  0    2
## 500   46   0  2      142  177   0       0     160     1     1.4     0  0    2
## 501   71   0  0      112  149   0       1     125     0     1.6     1  0    2
## 502   35   0  0      138  183   0       1     182     0     1.4     2  0    2
## 503   46   0  2      142  177   0       0     160     1     1.4     0  0    2
## 504   45   0  1      130  234   0       0     175     0     0.6     1  0    2
## 505   47   1  2      108  243   0       1     152     0     0.0     2  0    2
## 506   44   0  2      118  242   0       1     149     0     0.3     1  1    2
## 507   61   1  0      120  260   0       1     140     1     3.6     1  1    3
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## 509   56   0  0      200  288   1       0     133     1     4.0     0  2    3
## 510   55   0  0      180  327   0       2     117     1     3.4     1  0    2
## 511   54   0  1      132  288   1       0     159     1     0.0     2  1    2
## 512   43   1  0      120  177   0       0     120     1     2.5     1  0    3
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## 515   44   1  1      120  220   0       1     170     0     0.0     2  0    2
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## 517   60   1  0      130  206   0       0     132     1     2.4     1  2    3
## 518   41   0  1      105  198   0       1     168     0     0.0     2  1    2
## 519   49   1  2      120  188   0       1     139     0     2.0     1  3    3
## 520   61   1  0      148  203   0       1     161     0     0.0     2  1    3
## 521   59   1  0      140  177   0       1     162     1     0.0     2  1    3
## 522   58   1  1      125  220   0       1     144     0     0.4     1  4    3
## 523   67   0  2      152  277   0       1     172     0     0.0     2  1    2
## 524   61   1  0      148  203   0       1     161     0     0.0     2  1    3
## 525   58   1  2      112  230   0       0     165     0     2.5     1  1    3
## 526   51   0  2      130  256   0       0     149     0     0.5     2  0    2
## 527   62   0  0      160  164   0       0     145     0     6.2     0  3    3
## 528   62   0  0      124  209   0       1     163     0     0.0     2  0    2
## 529   59   1  3      178  270   0       0     145     0     4.2     0  0    3
## 530   69   1  3      160  234   1       0     131     0     0.1     1  1    2
## 531   60   0  0      150  258   0       0     157     0     2.6     1  2    3
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## 536   76   0  2      140  197   0       2     116     0     1.1     1  0    2
## 537   50   0  2      120  219   0       1     158     0     1.6     1  0    2
## 538   52   1  1      120  325   0       1     172     0     0.2     2  0    2
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## 540   64   1  3      170  227   0       0     155     0     0.6     1  0    3
## 541   58   1  0      128  259   0       0     130     1     3.0     1  2    3
## 542   44   1  2      140  235   0       0     180     0     0.0     2  0    2
## 543   62   0  0      140  394   0       0     157     0     1.2     1  0    2
## 544   59   1  3      134  204   0       1     162     0     0.8     2  2    2
## 545   54   1  2      125  273   0       0     152     0     0.5     0  1    2
## 546   48   1  1      110  229   0       1     168     0     1.0     0  0    3
## 547   70   1  0      130  322   0       0     109     0     2.4     1  3    2
## 548   67   0  0      106  223   0       1     142     0     0.3     2  2    2
## 549   51   0  2      120  295   0       0     157     0     0.6     2  0    2
## 550   68   1  2      118  277   0       1     151     0     1.0     2  1    3
## 551   69   1  2      140  254   0       0     146     0     2.0     1  3    3
## 552   54   1  0      122  286   0       0     116     1     3.2     1  2    2
## 553   43   0  0      132  341   1       0     136     1     3.0     1  0    3
## 554   53   1  2      130  197   1       0     152     0     1.2     0  0    2
## 555   58   1  0      100  234   0       1     156     0     0.1     2  1    3
## 556   67   1  0      125  254   1       1     163     0     0.2     1  2    3
## 557   59   1  0      140  177   0       1     162     1     0.0     2  1    3
## 558   48   1  0      122  222   0       0     186     0     0.0     2  0    2
## 559   39   0  2       94  199   0       1     179     0     0.0     2  0    2
## 560   67   1  0      120  237   0       1      71     0     1.0     1  0    2
## 561   58   0  0      130  197   0       1     131     0     0.6     1  0    2
## 562   65   0  2      155  269   0       1     148     0     0.8     2  0    2
## 563   42   0  2      120  209   0       1     173     0     0.0     1  0    2
## 564   44   1  0      112  290   0       0     153     0     0.0     2  1    2
## 565   56   1  0      132  184   0       0     105     1     2.1     1  1    1
## 566   53   0  0      138  234   0       0     160     0     0.0     2  0    2
## 567   50   0  0      110  254   0       0     159     0     0.0     2  0    2
## 568   41   1  2      130  214   0       0     168     0     2.0     1  0    2
## 569   54   0  2      160  201   0       1     163     0     0.0     2  1    2
## 570   42   1  2      120  240   1       1     194     0     0.8     0  0    3
## 571   54   0  2      135  304   1       1     170     0     0.0     2  0    2
## 572   60   1  0      145  282   0       0     142     1     2.8     1  2    3
## 573   34   1  3      118  182   0       0     174     0     0.0     2  0    2
## 574   44   1  0      112  290   0       0     153     0     0.0     2  1    2
## 575   60   1  0      125  258   0       0     141     1     2.8     1  1    3
## 576   43   1  0      150  247   0       1     171     0     1.5     2  0    2
## 577   52   1  3      152  298   1       1     178     0     1.2     1  0    3
## 578   70   1  0      130  322   0       0     109     0     2.4     1  3    2
## 579   62   0  0      140  394   0       0     157     0     1.2     1  0    2
## 580   58   1  0      146  218   0       1     105     0     2.0     1  1    3
## 581   46   1  1      101  197   1       1     156     0     0.0     2  0    3
## 582   44   1  2      140  235   0       0     180     0     0.0     2  0    2
## 583   55   1  1      130  262   0       1     155     0     0.0     2  0    2
## 584   43   1  0      120  177   0       0     120     1     2.5     1  0    3
## 585   55   1  0      132  353   0       1     132     1     1.2     1  1    3
## 586   40   1  3      140  199   0       1     178     1     1.4     2  0    3
## 587   64   1  2      125  309   0       1     131     1     1.8     1  0    3
## 588   59   1  0      164  176   1       0      90     0     1.0     1  2    1
## 589   61   0  0      145  307   0       0     146     1     1.0     1  0    3
## 590   54   1  0      122  286   0       0     116     1     3.2     1  2    2
## 591   74   0  1      120  269   0       0     121     1     0.2     2  1    2
## 592   63   0  0      108  269   0       1     169     1     1.8     1  2    2
## 593   70   1  2      160  269   0       1     112     1     2.9     1  1    3
## 594   63   0  0      108  269   0       1     169     1     1.8     1  2    2
## 595   64   1  0      145  212   0       0     132     0     2.0     1  2    1
## 596   61   1  0      148  203   0       1     161     0     0.0     2  1    3
## 597   59   1  1      140  221   0       1     164     1     0.0     2  0    2
## 598   38   1  2      138  175   0       1     173     0     0.0     2  4    2
## 599   58   1  1      120  284   0       0     160     0     1.8     1  0    2
## 600   63   0  1      140  195   0       1     179     0     0.0     2  2    2
## 601   62   0  2      130  263   0       1      97     0     1.2     1  1    3
## 602   46   1  0      140  311   0       1     120     1     1.8     1  2    3
## 603   58   0  2      120  340   0       1     172     0     0.0     2  0    2
## 604   63   0  1      140  195   0       1     179     0     0.0     2  2    2
## 605   47   1  2      130  253   0       1     179     0     0.0     2  0    2
## 606   71   0  2      110  265   1       0     130     0     0.0     2  1    2
## 607   66   1  0      112  212   0       0     132     1     0.1     2  1    2
## 608   42   1  0      136  315   0       1     125     1     1.8     1  0    1
## 609   64   1  0      145  212   0       0     132     0     2.0     1  2    1
## 610   55   0  0      180  327   0       2     117     1     3.4     1  0    2
## 611   43   0  0      132  341   1       0     136     1     3.0     1  0    3
## 612   55   0  0      128  205   0       2     130     1     2.0     1  1    3
## 613   58   0  0      170  225   1       0     146     1     2.8     1  2    1
## 614   55   1  0      140  217   0       1     111     1     5.6     0  0    3
## 615   51   0  0      130  305   0       1     142     1     1.2     1  0    3
## 616   50   0  2      120  219   0       1     158     0     1.6     1  0    2
## 617   43   1  0      115  303   0       1     181     0     1.2     1  0    2
## 618   41   0  1      126  306   0       1     163     0     0.0     2  0    2
## 619   49   1  1      130  266   0       1     171     0     0.6     2  0    2
## 620   65   1  0      110  248   0       0     158     0     0.6     2  2    1
## 621   57   1  0      152  274   0       1      88     1     1.2     1  1    3
## 622   48   1  0      130  256   1       0     150     1     0.0     2  2    3
## 623   62   0  0      138  294   1       1     106     0     1.9     1  3    2
## 624   61   1  3      134  234   0       1     145     0     2.6     1  2    2
## 625   59   1  3      178  270   0       0     145     0     4.2     0  0    3
## 626   69   1  2      140  254   0       0     146     0     2.0     1  3    3
## 627   58   1  2      132  224   0       0     173     0     3.2     2  2    3
## 628   38   1  3      120  231   0       1     182     1     3.8     1  0    3
## 629   69   0  3      140  239   0       1     151     0     1.8     2  2    2
## 630   65   1  3      138  282   1       0     174     0     1.4     1  1    2
## 631   45   1  3      110  264   0       1     132     0     1.2     1  0    3
## 632   49   1  1      130  266   0       1     171     0     0.6     2  0    2
## 633   45   0  1      130  234   0       0     175     0     0.6     1  0    2
## 634   61   1  0      138  166   0       0     125     1     3.6     1  1    2
## 635   52   1  0      125  212   0       1     168     0     1.0     2  2    3
## 636   53   0  0      130  264   0       0     143     0     0.4     1  0    2
## 637   59   0  0      174  249   0       1     143     1     0.0     1  0    2
## 638   58   0  2      120  340   0       1     172     0     0.0     2  0    2
## 639   65   1  3      138  282   1       0     174     0     1.4     1  1    2
## 640   58   0  0      130  197   0       1     131     0     0.6     1  0    2
## 641   46   0  0      138  243   0       0     152     1     0.0     1  0    2
## 642   56   0  0      134  409   0       0     150     1     1.9     1  2    3
## 643   64   1  0      128  263   0       1     105     1     0.2     1  1    3
## 644   65   1  0      120  177   0       1     140     0     0.4     2  0    3
## 645   44   1  2      120  226   0       1     169     0     0.0     2  0    2
## 646   50   1  0      150  243   0       0     128     0     2.6     1  0    3
## 647   47   1  2      108  243   0       1     152     0     0.0     2  0    2
## 648   64   0  0      130  303   0       1     122     0     2.0     1  2    2
## 649   71   0  0      112  149   0       1     125     0     1.6     1  0    2
## 650   45   0  1      130  234   0       0     175     0     0.6     1  0    2
## 651   62   1  0      120  267   0       1      99     1     1.8     1  2    3
## 652   41   1  1      120  157   0       1     182     0     0.0     2  0    2
## 653   66   0  3      150  226   0       1     114     0     2.6     0  0    2
## 654   56   1  0      130  283   1       0     103     1     1.6     0  0    3
## 655   41   0  1      126  306   0       1     163     0     0.0     2  0    2
## 656   41   1  1      110  235   0       1     153     0     0.0     2  0    2
## 657   57   0  1      130  236   0       0     174     0     0.0     1  1    2
## 658   39   0  2      138  220   0       1     152     0     0.0     1  0    2
## 659   64   1  2      125  309   0       1     131     1     1.8     1  0    3
## 660   59   1  0      138  271   0       0     182     0     0.0     2  0    2
## 661   61   1  0      138  166   0       0     125     1     3.6     1  1    2
## 662   58   1  0      114  318   0       2     140     0     4.4     0  3    1
## 663   47   1  0      112  204   0       1     143     0     0.1     2  0    2
## 664   58   0  0      100  248   0       0     122     0     1.0     1  0    2
## 665   66   0  3      150  226   0       1     114     0     2.6     0  0    2
## 666   65   0  2      140  417   1       0     157     0     0.8     2  1    2
## 667   35   1  1      122  192   0       1     174     0     0.0     2  0    2
## 668   57   1  1      124  261   0       1     141     0     0.3     2  0    3
## 669   29   1  1      130  204   0       0     202     0     0.0     2  0    2
## 670   66   1  1      160  246   0       1     120     1     0.0     1  3    1
## 671   61   0  0      130  330   0       0     169     0     0.0     2  0    2
## 672   52   1  0      125  212   0       1     168     0     1.0     2  2    3
## 673   68   1  2      118  277   0       1     151     0     1.0     2  1    3
## 674   54   1  2      120  258   0       0     147     0     0.4     1  0    3
## 675   63   1  0      130  330   1       0     132     1     1.8     2  3    3
## 676   58   1  0      100  234   0       1     156     0     0.1     2  1    3
## 677   60   1  0      130  253   0       1     144     1     1.4     2  1    3
## 678   63   1  0      130  254   0       0     147     0     1.4     1  1    3
## 679   41   0  2      112  268   0       0     172     1     0.0     2  0    2
## 680   68   1  2      180  274   1       0     150     1     1.6     1  0    3
## 681   42   1  1      120  295   0       1     162     0     0.0     2  0    2
## 682   59   1  0      170  326   0       0     140     1     3.4     0  0    3
## 683   59   1  0      164  176   1       0      90     0     1.0     1  2    1
## 684   43   1  0      120  177   0       0     120     1     2.5     1  0    3
## 685   60   1  2      140  185   0       0     155     0     3.0     1  0    2
## 686   63   0  0      150  407   0       0     154     0     4.0     1  3    3
## 687   52   1  0      128  204   1       1     156     1     1.0     1  0    0
## 688   58   1  0      125  300   0       0     171     0     0.0     2  2    3
## 689   56   0  0      200  288   1       0     133     1     4.0     0  2    3
## 690   54   0  2      135  304   1       1     170     0     0.0     2  0    2
## 691   58   1  2      105  240   0       0     154     1     0.6     1  0    3
## 692   55   0  1      135  250   0       0     161     0     1.4     1  0    2
## 693   53   1  0      140  203   1       0     155     1     3.1     0  0    3
## 694   63   0  1      140  195   0       1     179     0     0.0     2  2    2
## 695   39   1  0      118  219   0       1     140     0     1.2     1  0    3
## 696   35   1  0      126  282   0       0     156     1     0.0     2  0    3
## 697   50   0  2      120  219   0       1     158     0     1.6     1  0    2
## 698   67   1  2      152  212   0       0     150     0     0.8     1  0    3
## 699   66   1  0      112  212   0       0     132     1     0.1     2  1    2
## 700   35   1  0      126  282   0       0     156     1     0.0     2  0    3
## 701   41   1  2      130  214   0       0     168     0     2.0     1  0    2
## 702   35   1  0      120  198   0       1     130     1     1.6     1  0    3
## 703   71   0  1      160  302   0       1     162     0     0.4     2  2    2
## 704   57   1  0      110  201   0       1     126     1     1.5     1  0    1
## 705   51   1  2       94  227   0       1     154     1     0.0     2  1    3
## 706   58   1  0      128  216   0       0     131     1     2.2     1  3    3
## 707   57   1  2      128  229   0       0     150     0     0.4     1  1    3
## 708   56   0  1      140  294   0       0     153     0     1.3     1  0    2
## 709   60   0  2      120  178   1       1      96     0     0.0     2  0    2
## 710   45   1  3      110  264   0       1     132     0     1.2     1  0    3
## 711   56   1  1      130  221   0       0     163     0     0.0     2  0    3
## 712   35   1  0      120  198   0       1     130     1     1.6     1  0    3
## 713   45   0  1      112  160   0       1     138     0     0.0     1  0    2
## 714   66   0  3      150  226   0       1     114     0     2.6     0  0    2
## 715   51   1  3      125  213   0       0     125     1     1.4     2  1    2
## 716   70   1  1      156  245   0       0     143     0     0.0     2  0    2
## 717   55   0  0      128  205   0       2     130     1     2.0     1  1    3
## 718   56   1  2      130  256   1       0     142     1     0.6     1  1    1
## 719   55   0  1      135  250   0       0     161     0     1.4     1  0    2
## 720   52   1  0      108  233   1       1     147     0     0.1     2  3    3
## 721   64   1  2      140  335   0       1     158     0     0.0     2  0    2
## 722   45   1  0      115  260   0       0     185     0     0.0     2  0    2
## 723   67   0  2      152  277   0       1     172     0     0.0     2  1    2
## 724   68   0  2      120  211   0       0     115     0     1.5     1  0    2
## 725   74   0  1      120  269   0       0     121     1     0.2     2  1    2
## 726   60   0  0      150  258   0       0     157     0     2.6     1  2    3
## 727   48   1  0      124  274   0       0     166     0     0.5     1  0    3
## 728   56   1  1      130  221   0       0     163     0     0.0     2  0    3
## 729   46   1  0      140  311   0       1     120     1     1.8     1  2    3
## 730   55   0  1      135  250   0       0     161     0     1.4     1  0    2
## 731   44   1  1      120  220   0       1     170     0     0.0     2  0    2
## 732   52   1  0      112  230   0       1     160     0     0.0     2  1    2
## 733   51   1  2       94  227   0       1     154     1     0.0     2  1    3
## 734   44   0  2      108  141   0       1     175     0     0.6     1  0    2
## 735   52   1  0      128  204   1       1     156     1     1.0     1  0    0
## 736   50   1  2      129  196   0       1     163     0     0.0     2  0    2
## 737   59   1  0      110  239   0       0     142     1     1.2     1  1    3
## 738   67   1  0      120  229   0       0     129     1     2.6     1  2    3
## 739   58   1  0      125  300   0       0     171     0     0.0     2  2    3
## 740   52   1  0      128  255   0       1     161     1     0.0     2  1    3
## 741   44   1  2      140  235   0       0     180     0     0.0     2  0    2
## 742   41   0  2      112  268   0       0     172     1     0.0     2  0    2
## 743   63   1  0      130  330   1       0     132     1     1.8     2  3    3
## 744   58   1  1      125  220   0       1     144     0     0.4     1  4    3
## 745   60   0  2      102  318   0       1     160     0     0.0     2  1    2
## 746   51   1  2      100  222   0       1     143     1     1.2     1  0    2
## 747   64   1  2      140  335   0       1     158     0     0.0     2  0    2
## 748   60   1  0      117  230   1       1     160     1     1.4     2  2    3
## 749   44   1  2      120  226   0       1     169     0     0.0     2  0    2
## 750   58   1  1      125  220   0       1     144     0     0.4     1  4    3
## 751   55   1  1      130  262   0       1     155     0     0.0     2  0    2
## 752   65   0  2      160  360   0       0     151     0     0.8     2  0    2
## 753   48   1  1      130  245   0       0     180     0     0.2     1  0    2
## 754   65   1  0      120  177   0       1     140     0     0.4     2  0    3
## 755   51   0  2      130  256   0       0     149     0     0.5     2  0    2
## 756   48   1  2      124  255   1       1     175     0     0.0     2  2    2
## 757   64   1  0      120  246   0       0      96     1     2.2     0  1    2
## 758   66   1  0      160  228   0       0     138     0     2.3     2  0    1
## 759   46   0  1      105  204   0       1     172     0     0.0     2  0    2
## 760   61   0  0      130  330   0       0     169     0     0.0     2  0    2
## 761   57   1  0      150  276   0       0     112     1     0.6     1  1    1
## 762   49   0  0      130  269   0       1     163     0     0.0     2  0    2
## 763   56   1  1      130  221   0       0     163     0     0.0     2  0    3
## 764   58   0  3      150  283   1       0     162     0     1.0     2  0    2
## 765   63   1  0      140  187   0       0     144     1     4.0     2  2    3
## 766   57   1  0      110  335   0       1     143     1     3.0     1  1    3
## 767   57   1  0      110  335   0       1     143     1     3.0     1  1    3
## 768   68   1  0      144  193   1       1     141     0     3.4     1  2    3
## 769   46   1  1      101  197   1       1     156     0     0.0     2  0    3
## 770   71   0  2      110  265   1       0     130     0     0.0     2  1    2
## 771   41   1  1      135  203   0       1     132     0     0.0     1  0    1
## 772   45   0  0      138  236   0       0     152     1     0.2     1  0    2
## 773   62   0  0      150  244   0       1     154     1     1.4     1  0    2
## 774   65   0  0      150  225   0       0     114     0     1.0     1  3    3
## 775   48   0  2      130  275   0       1     139     0     0.2     2  0    2
## 776   51   1  2      100  222   0       1     143     1     1.2     1  0    2
## 777   61   0  0      145  307   0       0     146     1     1.0     1  0    3
## 778   53   1  0      123  282   0       1      95     1     2.0     1  2    3
## 779   59   1  3      134  204   0       1     162     0     0.8     2  2    2
## 780   34   0  1      118  210   0       1     192     0     0.7     2  0    2
## 781   44   1  0      120  169   0       1     144     1     2.8     0  0    1
## 782   58   1  0      146  218   0       1     105     0     2.0     1  1    3
## 783   64   0  0      130  303   0       1     122     0     2.0     1  2    2
## 784   56   1  1      120  240   0       1     169     0     0.0     0  0    2
## 785   54   1  2      150  232   0       0     165     0     1.6     2  0    3
## 786   55   1  0      160  289   0       0     145     1     0.8     1  1    3
## 787   67   1  0      125  254   1       1     163     0     0.2     1  2    3
## 788   51   1  0      140  298   0       1     122     1     4.2     1  3    3
## 789   62   0  0      138  294   1       1     106     0     1.9     1  3    2
## 790   62   1  1      120  281   0       0     103     0     1.4     1  1    3
## 791   54   1  0      110  239   0       1     126     1     2.8     1  1    3
## 792   54   1  0      110  239   0       1     126     1     2.8     1  1    3
## 793   68   1  0      144  193   1       1     141     0     3.4     1  2    3
## 794   60   0  2      120  178   1       1      96     0     0.0     2  0    2
## 795   61   1  3      134  234   0       1     145     0     2.6     1  2    2
## 796   62   1  1      128  208   1       0     140     0     0.0     2  0    2
## 797   41   1  1      135  203   0       1     132     0     0.0     1  0    1
## 798   65   0  0      150  225   0       0     114     0     1.0     1  3    3
## 799   59   1  3      170  288   0       0     159     0     0.2     1  0    3
## 800   43   1  0      115  303   0       1     181     0     1.2     1  0    2
## 801   67   1  0      120  229   0       0     129     1     2.6     1  2    3
## 802   63   1  3      145  233   1       0     150     0     2.3     0  0    1
## 803   63   0  0      124  197   0       1     136     1     0.0     1  0    2
## 804   52   1  0      112  230   0       1     160     0     0.0     2  1    2
## 805   58   0  0      130  197   0       1     131     0     0.6     1  0    2
## 806   53   1  0      142  226   0       0     111     1     0.0     2  0    3
## 807   57   1  0      150  276   0       0     112     1     0.6     1  1    1
## 808   44   1  2      130  233   0       1     179     1     0.4     2  0    2
## 809   51   1  2       94  227   0       1     154     1     0.0     2  1    3
## 810   54   0  2      110  214   0       1     158     0     1.6     1  0    2
## 811   40   1  0      110  167   0       0     114     1     2.0     1  0    3
## 812   57   1  1      124  261   0       1     141     0     0.3     2  0    3
## 813   62   0  0      140  268   0       0     160     0     3.6     0  2    2
## 814   53   1  0      140  203   1       0     155     1     3.1     0  0    3
## 815   62   1  1      128  208   1       0     140     0     0.0     2  0    2
## 816   58   1  2      105  240   0       0     154     1     0.6     1  0    3
## 817   70   1  1      156  245   0       0     143     0     0.0     2  0    2
## 818   45   1  0      115  260   0       0     185     0     0.0     2  0    2
## 819   42   1  3      148  244   0       0     178     0     0.8     2  2    2
## 820   58   0  0      170  225   1       0     146     1     2.8     1  2    1
## 821   61   1  0      140  207   0       0     138     1     1.9     2  1    3
## 822   62   0  0      140  268   0       0     160     0     3.6     0  2    2
## 823   60   1  0      130  253   0       1     144     1     1.4     2  1    3
## 824   54   1  0      140  239   0       1     160     0     1.2     2  0    2
## 825   61   1  0      138  166   0       0     125     1     3.6     1  1    2
## 826   63   0  2      135  252   0       0     172     0     0.0     2  0    2
## 827   42   1  2      130  180   0       1     150     0     0.0     2  0    2
## 828   57   1  2      128  229   0       0     150     0     0.4     1  1    3
## 829   44   1  2      130  233   0       1     179     1     0.4     2  0    2
## 830   54   1  0      124  266   0       0     109     1     2.2     1  1    3
## 831   51   1  2      100  222   0       1     143     1     1.2     1  0    2
## 832   58   1  1      125  220   0       1     144     0     0.4     1  4    3
## 833   68   1  2      118  277   0       1     151     0     1.0     2  1    3
## 834   55   1  0      140  217   0       1     111     1     5.6     0  0    3
## 835   42   1  0      136  315   0       1     125     1     1.8     1  0    1
## 836   49   1  2      118  149   0       0     126     0     0.8     2  3    2
## 837   53   0  0      138  234   0       0     160     0     0.0     2  0    2
## 838   52   1  2      172  199   1       1     162     0     0.5     2  0    3
## 839   51   1  3      125  213   0       0     125     1     1.4     2  1    2
## 840   51   1  0      140  261   0       0     186     1     0.0     2  0    2
## 841   70   1  0      145  174   0       1     125     1     2.6     0  0    3
## 842   35   0  0      138  183   0       1     182     0     1.4     2  0    2
## 843   58   1  2      112  230   0       0     165     0     2.5     1  1    3
## 844   59   1  3      160  273   0       0     125     0     0.0     2  0    2
## 845   60   1  0      140  293   0       0     170     0     1.2     1  2    3
## 846   56   1  0      132  184   0       0     105     1     2.1     1  1    1
## 847   35   0  0      138  183   0       1     182     0     1.4     2  0    2
## 848   61   1  0      138  166   0       0     125     1     3.6     1  1    2
## 849   58   0  3      150  283   1       0     162     0     1.0     2  0    2
## 850   52   1  0      128  255   0       1     161     1     0.0     2  1    3
## 851   58   1  1      120  284   0       0     160     0     1.8     1  0    2
## 852   37   1  2      130  250   0       1     187     0     3.5     0  0    2
## 853   52   1  0      128  255   0       1     161     1     0.0     2  1    3
## 854   67   1  0      120  229   0       0     129     1     2.6     1  2    3
## 855   65   1  3      138  282   1       0     174     0     1.4     1  1    2
## 856   46   1  1      101  197   1       1     156     0     0.0     2  0    3
## 857   68   0  2      120  211   0       0     115     0     1.5     1  0    2
## 858   43   1  0      115  303   0       1     181     0     1.2     1  0    2
## 859   68   0  2      120  211   0       0     115     0     1.5     1  0    2
## 860   51   1  0      140  299   0       1     173     1     1.6     2  0    3
## 861   52   1  0      112  230   0       1     160     0     0.0     2  1    2
## 862   64   1  2      140  335   0       1     158     0     0.0     2  0    2
## 863   59   1  3      170  288   0       0     159     0     0.2     1  0    3
## 864   52   1  0      125  212   0       1     168     0     1.0     2  2    3
## 865   59   1  3      160  273   0       0     125     0     0.0     2  0    2
## 866   60   0  3      150  240   0       1     171     0     0.9     2  0    2
## 867   41   1  2      112  250   0       1     179     0     0.0     2  0    2
## 868   41   1  1      110  235   0       1     153     0     0.0     2  0    2
## 869   56   1  1      120  240   0       1     169     0     0.0     0  0    2
## 870   56   1  1      120  236   0       1     178     0     0.8     2  0    2
## 871   48   0  2      130  275   0       1     139     0     0.2     2  0    2
## 872   39   1  2      140  321   0       0     182     0     0.0     2  0    2
## 873   64   1  3      170  227   0       0     155     0     0.6     1  0    3
## 874   57   1  0      140  192   0       1     148     0     0.4     1  0    1
## 875   59   1  3      160  273   0       0     125     0     0.0     2  0    2
## 876   60   1  0      130  206   0       0     132     1     2.4     1  2    3
## 877   61   1  0      140  207   0       0     138     1     1.9     2  1    3
## 878   43   0  2      122  213   0       1     165     0     0.2     1  0    2
## 879   54   1  0      120  188   0       1     113     0     1.4     1  1    3
## 880   59   1  0      138  271   0       0     182     0     0.0     2  0    2
## 881   57   1  0      132  207   0       1     168     1     0.0     2  0    3
## 882   57   1  1      154  232   0       0     164     0     0.0     2  1    2
## 883   57   1  0      130  131   0       1     115     1     1.2     1  1    3
## 884   48   1  0      124  274   0       0     166     0     0.5     1  0    3
## 885   70   1  0      145  174   0       1     125     1     2.6     0  0    3
## 886   57   1  0      165  289   1       0     124     0     1.0     1  3    3
## 887   61   1  0      120  260   0       1     140     1     3.6     1  1    3
## 888   57   1  0      110  201   0       1     126     1     1.5     1  0    1
## 889   60   0  0      150  258   0       0     157     0     2.6     1  2    3
## 890   63   0  0      150  407   0       0     154     0     4.0     1  3    3
## 891   55   0  0      128  205   0       2     130     1     2.0     1  1    3
## 892   64   0  0      180  325   0       1     154     1     0.0     2  0    2
## 893   54   1  0      110  239   0       1     126     1     2.8     1  1    3
## 894   52   1  0      128  204   1       1     156     1     1.0     1  0    0
## 895   51   1  0      140  299   0       1     173     1     1.6     2  0    3
## 896   62   0  2      130  263   0       1      97     0     1.2     1  1    3
## 897   59   1  3      178  270   0       0     145     0     4.2     0  0    3
## 898   52   1  1      134  201   0       1     158     0     0.8     2  1    2
## 899   42   0  0      102  265   0       0     122     0     0.6     1  0    2
## 900   59   1  0      135  234   0       1     161     0     0.5     1  0    3
## 901   61   1  3      134  234   0       1     145     0     2.6     1  2    2
## 902   42   0  0      102  265   0       0     122     0     0.6     1  0    2
## 903   62   0  0      140  268   0       0     160     0     3.6     0  2    2
## 904   59   1  2      126  218   1       1     134     0     2.2     1  1    1
## 905   55   1  1      130  262   0       1     155     0     0.0     2  0    2
## 906   64   1  0      120  246   0       0      96     1     2.2     0  1    2
## 907   42   1  0      140  226   0       1     178     0     0.0     2  0    2
## 908   50   0  1      120  244   0       1     162     0     1.1     2  0    2
## 909   62   1  0      120  267   0       1      99     1     1.8     1  2    3
## 910   50   1  0      144  200   0       0     126     1     0.9     1  0    3
## 911   50   1  2      140  233   0       1     163     0     0.6     1  1    3
## 912   58   0  1      136  319   1       0     152     0     0.0     2  2    2
## 913   35   1  0      120  198   0       1     130     1     1.6     1  0    3
## 914   45   1  0      104  208   0       0     148     1     3.0     1  0    2
## 915   66   1  0      112  212   0       0     132     1     0.1     2  1    2
## 916   46   1  0      120  249   0       0     144     0     0.8     2  0    3
## 917   65   1  0      135  254   0       0     127     0     2.8     1  1    3
## 918   47   1  2      130  253   0       1     179     0     0.0     2  0    2
## 919   59   1  3      134  204   0       1     162     0     0.8     2  2    2
## 920   38   1  3      120  231   0       1     182     1     3.8     1  0    3
## 921   39   1  0      118  219   0       1     140     0     1.2     1  0    3
## 922   58   1  0      146  218   0       1     105     0     2.0     1  1    3
## 923   44   1  1      120  263   0       1     173     0     0.0     2  0    3
## 924   54   1  0      140  239   0       1     160     0     1.2     2  0    2
## 925   61   0  0      130  330   0       0     169     0     0.0     2  0    2
## 926   57   1  0      130  131   0       1     115     1     1.2     1  1    3
## 927   54   1  0      110  206   0       0     108     1     0.0     1  1    2
## 928   42   1  2      120  240   1       1     194     0     0.8     0  0    3
## 929   54   1  0      124  266   0       0     109     1     2.2     1  1    3
## 930   60   1  0      130  206   0       0     132     1     2.4     1  2    3
## 931   65   1  0      135  254   0       0     127     0     2.8     1  1    3
## 932   40   1  0      152  223   0       1     181     0     0.0     2  0    3
## 933   51   0  2      140  308   0       0     142     0     1.5     2  1    2
## 934   38   1  3      120  231   0       1     182     1     3.8     1  0    3
## 935   42   1  2      130  180   0       1     150     0     0.0     2  0    2
## 936   56   1  1      120  240   0       1     169     0     0.0     0  0    2
## 937   43   1  2      130  315   0       1     162     0     1.9     2  1    2
## 938   64   1  2      140  335   0       1     158     0     0.0     2  0    2
## 939   53   1  0      142  226   0       0     111     1     0.0     2  0    3
## 940   49   0  1      134  271   0       1     162     0     0.0     1  0    2
## 941   57   0  0      140  241   0       1     123     1     0.2     1  0    3
## 942   52   0  2      136  196   0       0     169     0     0.1     1  0    2
## 943   69   0  3      140  239   0       1     151     0     1.8     2  2    2
## 944   65   1  0      120  177   0       1     140     0     0.4     2  0    3
## 945   66   0  0      178  228   1       1     165     1     1.0     1  2    3
## 946   56   1  3      120  193   0       0     162     0     1.9     1  0    3
## 947   67   0  2      152  277   0       1     172     0     0.0     2  1    2
## 948   54   0  2      160  201   0       1     163     0     0.0     2  1    2
## 949   70   1  0      145  174   0       1     125     1     2.6     0  0    3
## 950   57   1  0      132  207   0       1     168     1     0.0     2  0    3
## 951   67   1  0      160  286   0       0     108     1     1.5     1  3    2
## 952   62   0  2      130  263   0       1      97     0     1.2     1  1    3
## 953   54   0  2      135  304   1       1     170     0     0.0     2  0    2
## 954   45   0  0      138  236   0       0     152     1     0.2     1  0    2
## 955   53   0  0      130  264   0       0     143     0     0.4     1  0    2
## 956   62   1  2      130  231   0       1     146     0     1.8     1  3    3
## 957   49   0  0      130  269   0       1     163     0     0.0     2  0    2
## 958   50   1  2      140  233   0       1     163     0     0.6     1  1    3
## 959   65   0  2      140  417   1       0     157     0     0.8     2  1    2
## 960   69   0  3      140  239   0       1     151     0     1.8     2  2    2
## 961   52   0  2      136  196   0       0     169     0     0.1     1  0    2
## 962   58   0  0      100  248   0       0     122     0     1.0     1  0    2
## 963   52   1  0      108  233   1       1     147     0     0.1     2  3    3
## 964   57   0  0      140  241   0       1     123     1     0.2     1  0    3
## 965   44   0  2      108  141   0       1     175     0     0.6     1  0    2
## 966   76   0  2      140  197   0       2     116     0     1.1     1  0    2
## 967   58   1  0      128  259   0       0     130     1     3.0     1  2    3
## 968   60   0  2      120  178   1       1      96     0     0.0     2  0    2
## 969   53   1  0      140  203   1       0     155     1     3.1     0  0    3
## 970   52   1  1      120  325   0       1     172     0     0.2     2  0    2
## 971   38   1  2      138  175   0       1     173     0     0.0     2  4    2
## 972   52   1  2      172  199   1       1     162     0     0.5     2  0    3
## 973   52   1  3      118  186   0       0     190     0     0.0     1  0    1
## 974   51   1  2      125  245   1       0     166     0     2.4     1  0    2
## 975   43   1  0      110  211   0       1     161     0     0.0     2  0    3
## 976   39   1  0      118  219   0       1     140     0     1.2     1  0    3
## 977   63   0  0      108  269   0       1     169     1     1.8     1  2    2
## 978   52   1  1      128  205   1       1     184     0     0.0     2  0    2
## 979   44   1  0      110  197   0       0     177     0     0.0     2  1    2
## 980   45   1  0      142  309   0       0     147     1     0.0     1  3    3
## 981   57   1  0      140  192   0       1     148     0     0.4     1  0    1
## 982   39   1  0      118  219   0       1     140     0     1.2     1  0    3
## 983   67   0  0      106  223   0       1     142     0     0.3     2  2    2
## 984   64   1  0      128  263   0       1     105     1     0.2     1  1    3
## 985   59   1  0      135  234   0       1     161     0     0.5     1  0    3
## 986   62   1  2      130  231   0       1     146     0     1.8     1  3    3
## 987   55   0  0      180  327   0       2     117     1     3.4     1  0    2
## 988   57   1  1      154  232   0       0     164     0     0.0     2  1    2
## 989   60   1  0      140  293   0       0     170     0     1.2     1  2    3
## 990   71   0  1      160  302   0       1     162     0     0.4     2  2    2
## 991   56   1  1      120  236   0       1     178     0     0.8     2  0    2
## 992   60   1  0      117  230   1       1     160     1     1.4     2  2    3
## 993   50   0  0      110  254   0       0     159     0     0.0     2  0    2
## 994   43   1  0      132  247   1       0     143     1     0.1     1  4    3
## 995   59   1  0      110  239   0       0     142     1     1.2     1  1    3
## 996   44   1  1      120  263   0       1     173     0     0.0     2  0    3
## 997   56   0  0      134  409   0       0     150     1     1.9     1  2    3
## 998   54   1  0      120  188   0       1     113     0     1.4     1  1    3
## 999   42   1  0      136  315   0       1     125     1     1.8     1  0    1
## 1000  67   1  0      125  254   1       1     163     0     0.2     1  2    3
## 1001  64   1  0      145  212   0       0     132     0     2.0     1  2    1
## 1002  42   1  0      140  226   0       1     178     0     0.0     2  0    2
## 1003  66   1  0      112  212   0       0     132     1     0.1     2  1    2
## 1004  52   1  0      108  233   1       1     147     0     0.1     2  3    3
## 1005  51   0  2      140  308   0       0     142     0     1.5     2  1    2
## 1006  55   0  0      128  205   0       2     130     1     2.0     1  1    3
## 1007  58   1  2      140  211   1       0     165     0     0.0     2  0    2
## 1008  56   1  3      120  193   0       0     162     0     1.9     1  0    3
## 1009  42   1  1      120  295   0       1     162     0     0.0     2  0    2
## 1010  40   1  0      152  223   0       1     181     0     0.0     2  0    3
## 1011  51   1  0      140  299   0       1     173     1     1.6     2  0    3
## 1012  45   1  1      128  308   0       0     170     0     0.0     2  0    2
## 1013  48   1  1      110  229   0       1     168     0     1.0     0  0    3
## 1014  58   1  0      114  318   0       2     140     0     4.4     0  3    1
## 1015  44   0  2      108  141   0       1     175     0     0.6     1  0    2
## 1016  58   1  0      128  216   0       0     131     1     2.2     1  3    3
## 1017  65   1  3      138  282   1       0     174     0     1.4     1  1    2
## 1018  53   1  0      123  282   0       1      95     1     2.0     1  2    3
## 1019  41   1  0      110  172   0       0     158     0     0.0     2  0    3
## 1020  47   1  0      112  204   0       1     143     0     0.1     2  0    2
## 1021  59   1  1      140  221   0       1     164     1     0.0     2  0    2
## 1022  60   1  0      125  258   0       0     141     1     2.8     1  1    3
## 1023  47   1  0      110  275   0       0     118     1     1.0     1  1    2
## 1024  50   0  0      110  254   0       0     159     0     0.0     2  0    2
## 1025  54   1  0      120  188   0       1     113     0     1.4     1  1    3
##      target
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## 888       1
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## 892       1
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## 897       1
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## 914       1
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## 921       0
## 922       0
## 923       1
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## 965       1
## 966       1
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## 968       1
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## 970       1
## 971       1
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## 973       1
## 974       1
## 975       1
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## 977       0
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## 981       1
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## 983       1
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## 990       1
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## 995       0
## 996       1
## 997       0
## 998       0
## 999       0
## 1000      0
## 1001      0
## 1002      1
## 1003      0
## 1004      1
## 1005      1
## 1006      0
## 1007      1
## 1008      1
## 1009      1
## 1010      0
## 1011      0
## 1012      1
## 1013      0
## 1014      0
## 1015      1
## 1016      0
## 1017      0
## 1018      0
## 1019      0
## 1020      1
## 1021      1
## 1022      0
## 1023      0
## 1024      1
## 1025      0

take a quick view of the data

View(heart_attack)

NOW, we’ll follow the steps for pre-processing for this we’ll check for missing values there are no missing values in this data set but to make sure we’ll use the function of sum()

is.na(heart_attack)
##           age   sex    cp trestbps  chol   fbs restecg thalach exang oldpeak
##    [1,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##    [2,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##    [3,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##    [4,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##    [5,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##    [6,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##    [7,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##    [8,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##    [9,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##   [10,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##   [11,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##   [12,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##   [13,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##   [14,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##   [15,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##   [16,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##   [17,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##   [18,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##   [19,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##   [20,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##   [21,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##   [22,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##   [23,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##   [24,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##   [25,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##   [26,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##   [27,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##   [28,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##   [29,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##   [30,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##   [31,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##   [32,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##   [33,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
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##  [770,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
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##  [772,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [773,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [774,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [775,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [776,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [777,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [778,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [779,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [780,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [781,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [782,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [783,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [784,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [785,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [786,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [787,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [788,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [789,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [790,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [791,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [792,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [793,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [794,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [795,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [796,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [797,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [798,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [799,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [800,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [801,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [802,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [803,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [804,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [805,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [806,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [807,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [808,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [809,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [810,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [811,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [812,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [813,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [814,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [815,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [816,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [817,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [818,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [819,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [820,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [821,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [822,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [823,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [824,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [825,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [826,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [827,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [828,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [829,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [830,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [831,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [832,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [833,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [834,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [835,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [836,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [837,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [838,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [839,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [840,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [841,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [842,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [843,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [844,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [845,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [846,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [847,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [848,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [849,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [850,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [851,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [852,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
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##  [855,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [856,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [857,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [858,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
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##  [860,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [861,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [862,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [863,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [864,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
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##  [866,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
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##  [871,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
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##  [883,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
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##  [886,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
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##  [889,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [890,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [891,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
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##  [894,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
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##  [897,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [898,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
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##  [900,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
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##  [930,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [931,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
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##  [933,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [934,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
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##  [937,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [938,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
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##  [940,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
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##  [960,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
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##  [963,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
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##  [965,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
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##  [967,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [968,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [969,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [970,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [971,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [972,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
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##  [976,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
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##  [978,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
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##  [980,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [981,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [982,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [983,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [984,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [985,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [986,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [987,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [988,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [989,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [990,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [991,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [992,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [993,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [994,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [995,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [996,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [997,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##  [998,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
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## [1000,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
## [1001,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
## [1002,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
## [1003,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
## [1004,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
## [1005,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
## [1006,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
## [1007,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
## [1008,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
## [1009,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
## [1010,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
## [1011,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
## [1012,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
## [1013,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
## [1014,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
## [1015,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
## [1016,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
## [1017,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
## [1018,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
## [1019,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
## [1020,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
## [1021,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
## [1022,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
## [1023,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
## [1024,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
## [1025,] FALSE FALSE FALSE    FALSE FALSE FALSE   FALSE   FALSE FALSE   FALSE
##         slope    ca  thal target
##    [1,] FALSE FALSE FALSE  FALSE
##    [2,] FALSE FALSE FALSE  FALSE
##    [3,] FALSE FALSE FALSE  FALSE
##    [4,] FALSE FALSE FALSE  FALSE
##    [5,] FALSE FALSE FALSE  FALSE
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##   [90,] FALSE FALSE FALSE  FALSE
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##  [100,] FALSE FALSE FALSE  FALSE
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##  [148,] FALSE FALSE FALSE  FALSE
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##  [150,] FALSE FALSE FALSE  FALSE
##  [151,] FALSE FALSE FALSE  FALSE
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sum(is.na(heart_attack))
## [1] 0
table(heart_attack$target)
## 
##   0   1 
## 499 526
prop.table(table(heart_attack$target))
## 
##         0         1 
## 0.4868293 0.5131707
pie(table(heart_attack$target), main="Class Distribution")

class(heart_attack$target)
## [1] "integer"
if (class(heart_attack$target) == "factor") {
  heart_attack$target <- as.numeric(as.character(heart_attack$target))
}
model1 <- lm(target ~ ., data = heart_attack)

model1
## 
## Call:
## lm(formula = target ~ ., data = heart_attack)
## 
## Coefficients:
## (Intercept)          age          sex           cp     trestbps         chol  
##    0.879266    -0.001430    -0.210721     0.111820    -0.001818    -0.000458  
##         fbs      restecg      thalach        exang      oldpeak        slope  
##    0.004225     0.044308     0.002878    -0.144644    -0.061020     0.076220  
##          ca         thal  
##   -0.095612    -0.115237
summary(model1)
## 
## Call:
## lm(formula = target ~ ., data = heart_attack)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.92108 -0.21388  0.04493  0.26507  0.95158 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.8792656  0.1578856   5.569 3.28e-08 ***
## age         -0.0014296  0.0014432  -0.991 0.322151    
## sex         -0.2107215  0.0255809  -8.237 5.40e-16 ***
## cp           0.1118197  0.0120981   9.243  < 2e-16 ***
## trestbps    -0.0018183  0.0006758  -2.691 0.007247 ** 
## chol        -0.0004580  0.0002273  -2.015 0.044173 *  
## fbs          0.0042250  0.0320768   0.132 0.895237    
## restecg      0.0443080  0.0214084   2.070 0.038739 *  
## thalach      0.0028781  0.0006051   4.756 2.26e-06 ***
## exang       -0.1446437  0.0275997  -5.241 1.95e-07 ***
## oldpeak     -0.0610202  0.0121847  -5.008 6.49e-07 ***
## slope        0.0762203  0.0227286   3.354 0.000828 ***
## ca          -0.0956120  0.0116263  -8.224 6.02e-16 ***
## thal        -0.1152366  0.0188241  -6.122 1.32e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3505 on 1011 degrees of freedom
## Multiple R-squared:  0.5149, Adjusted R-squared:  0.5087 
## F-statistic: 82.56 on 13 and 1011 DF,  p-value: < 2.2e-16

Interpretation: Positive coefficients (e.g., cp, slope, thalach) indicate that an increase in the corresponding independent variable is associated with an increase in the estimated value of the dependent variable. Negative coefficients (e.g., age, sex, exang) indicate that an increase in the corresponding independent variable is associated with a decrease in the estimated value of the dependent variable. The magnitude of the coefficient represents the strength of the relationship between the independent and dependent variables. For example, larger absolute values indicate stronger effects.

Interpretation: This logistic regression model suggests that the predictor variables age, sex, cp (chest pain type), trestbps (resting blood pressure), chol (serum cholesterol), fbs (fasting blood sugar), restecg (resting electrocardiographic results), thalach (maximum heart rate achieved), exang (exercise-induced angina), oldpeak (ST depression induced by exercise relative to rest), slope (slope of the peak exercise ST segment), ca (number of major vessels colored by fluoroscopy), and thal (thalassemia type) are associated with the target variable, each with varying degrees of impact, as indicated by their coefficients. apply regrssion

model2<-glm(model_glm <- glm(target ~ ., data = heart_attack, family = binomial))
model2
## 
## Call:  glm(formula = model_glm <- glm(target ~ ., data = heart_attack, 
##     family = binomial))
## 
## Coefficients:
## (Intercept)          age          sex           cp     trestbps         chol  
##    0.879266    -0.001430    -0.210721     0.111820    -0.001818    -0.000458  
##         fbs      restecg      thalach        exang      oldpeak        slope  
##    0.004225     0.044308     0.002878    -0.144644    -0.061020     0.076220  
##          ca         thal  
##   -0.095612    -0.115237  
## 
## Degrees of Freedom: 1024 Total (i.e. Null);  1011 Residual
## Null Deviance:       256.1 
## Residual Deviance: 124.2     AIC: 775.6

—————-apply KNN—————-

1-fold cross validation

set.seed(123)


index <- sample(1:nrow(heart_attack), nrow(heart_attack))

# Split the data into training and testing sets (1-fold cross-validation)
train_data <- heart_attack[index <= nrow(heart_attack) * 0.8, ]  # 80% for training
test_data <- heart_attack[index > nrow(heart_attack) * 0.8, ]    # 20% for testing

# Here you would typically fit your model using the training data,
# but since you don't want to fit a model, we'll proceed to evaluation

# For example, let's calculate the mean of the target variable in the training set
mean_target_training <- mean(heart_attack$target)

This line calculates the mean of the target variable (target) in the training set (heart_attack$target). However, it’s worth noting that this line doesn’t fit any model to the training data; it simply calculates a summary statistic (mean) as an example. Typically, after splitting the data, you would fit a model using the training data and then evaluate its performance on the testing data. In this case, model fitting and evaluation are not included in the provided code snippet.

Overall, this code sets up a data splitting procedure using a 1-fold cross-validation approach and randomly divides the dataset into training and testing sets for further analysis or model building. 2-fold cross validation

# Set a seed for reproducibility
set.seed(123)

# Create an index for splitting the data into two folds
index <- sample(1:nrow(heart_attack))

# Split the data into two folds
fold1 <- heart_attack[index %% 2 == 0, ]  # Fold 1
fold2 <- heart_attack[index %% 2 != 0, ]  # Fold 2

# Perform 2-fold cross-validation

# Fold 1 as training, Fold 2 as testing
train_data_fold1 <- fold1
test_data_fold1 <- fold2

# Fit your model (or use a prediction method) using train_data_fold1

# For example, let's calculate the mean of the target variable in train_data_fold1
mean_target_fold1 <- mean(train_data_fold1$target)
# Use the mean as a baseline prediction for test_data_fold1
predicted_mean_fold1 <- rep(mean_target_fold1, nrow(test_data_fold1))

# Calculate some metric (e.g., mean squared error) for evaluation
MSE_fold1 <- mean((predicted_mean_fold1 - test_data_fold1$target)^2)

# Print the mean squared error for Fold 1
print(paste("Mean Squared Error for Fold 1:", MSE_fold1))
## [1] "Mean Squared Error for Fold 1: 0.249908633167051"
# Fold 2 as training, Fold 1 as testing
train_data_fold2 <- fold2
test_data_fold2 <- fold1

# Fit your model (or use a prediction method) using train_data_fold2

# For example, let's calculate the mean of the target variable in train_data_fold2
mean_target_fold2 <- mean(train_data_fold2$target)

# Use the mean as a baseline prediction for test_data_fold2
predicted_mean_fold2 <- rep(mean_target_fold2, nrow(test_data_fold2))

# Calculate some metric (e.g., mean squared error) for evaluation
MSE_fold2 <- mean((predicted_mean_fold2 - test_data_fold2$target)^2)

# Print the mean squared error for Fold 2
print(paste("Mean Squared Error for Fold 2:", MSE_fold2))
## [1] "Mean Squared Error for Fold 2: 0.250498543414593"
# Define the control parameters for 3-fold cross-validation
library(caret)
## Warning: package 'caret' was built under R version 4.3.3
## Loading required package: ggplot2
## Loading required package: lattice
heart_attack$target <- factor(heart_attack$target)


ctrl <- trainControl(method = "cv", number = 3)

# Train your model using 3-fold cross-validation with linear regression (lm)
model_3fold <- train(target ~ ., data = heart_attack, method = "glm", trControl = ctrl)

# Print the results
print(model_3fold)
## Generalized Linear Model 
## 
## 1025 samples
##   13 predictor
##    2 classes: '0', '1' 
## 
## No pre-processing
## Resampling: Cross-Validated (3 fold) 
## Summary of sample sizes: 682, 684, 684 
## Resampling results:
## 
##   Accuracy   Kappa    
##   0.8429275  0.6846486

Interpretation: The code demonstrates two different approaches to cross-validation: manual implementation of 2-fold cross-validation and utilizing the train() function from the caret package for 3-fold cross-validation. Cross-validation helps evaluate the performance of a model and assess its generalization ability by partitioning the dataset into multiple subsets for training and testing iteratively. 3-fold cross validation

# Define the control parameters for 3-fold cross-validation
library(caret)
heart_attack$target <- factor(heart_attack$target)


ctrl <- trainControl(method = "cv", number = 3)

# Train your model using 3-fold cross-validation with linear regression (lm)
model_3fold <- train(target ~ ., data = heart_attack, method = "glm", trControl = ctrl)

# Print the results
print(model_3fold)
## Generalized Linear Model 
## 
## 1025 samples
##   13 predictor
##    2 classes: '0', '1' 
## 
## No pre-processing
## Resampling: Cross-Validated (3 fold) 
## Summary of sample sizes: 684, 684, 682 
## Resampling results:
## 
##   Accuracy   Kappa  
##   0.8292366  0.65739

Interpretation: The code performs model training and evaluation using 3-fold cross-validation with linear regression. Cross-validation helps assess the performance and generalization ability of the model by partitioning the dataset into multiple subsets for training and testing iteratively. The results printed provide insights into the model’s performance metrics obtained from cross-validation. These metrics help evaluate how well the model generalizes to unseen data.

Interpretation: The first part of the code calculates the optimal cutoff value based on the binary prediction (predicted) and the true binary labels (test$sex). The second part trains a KNN model using cross-validation and evaluates it using a confusion matrix to assess its performance. Overall, the code performs cutoff optimization and evaluates a KNN model using a confusion matrix to understand its classification performance.

library(caret)
set.seed(1234)

# Train the KNN model
model_knn <- train(target ~ ., 
                   data = heart_attack, 
                   method = "knn", 
                   trControl=trainControl(method = "cv", number = 5))
    
head(model_knn)
## $method
## [1] "knn"
## 
## $modelInfo
## $modelInfo$label
## [1] "k-Nearest Neighbors"
## 
## $modelInfo$library
## NULL
## 
## $modelInfo$loop
## NULL
## 
## $modelInfo$type
## [1] "Classification" "Regression"    
## 
## $modelInfo$parameters
##   parameter   class      label
## 1         k numeric #Neighbors
## 
## $modelInfo$grid
## function (x, y, len = NULL, search = "grid") 
## {
##     if (search == "grid") {
##         out <- data.frame(k = (5:((2 * len) + 4))[(5:((2 * len) + 
##             4))%%2 > 0])
##     }
##     else {
##         by_val <- if (is.factor(y)) 
##             length(levels(y))
##         else 1
##         out <- data.frame(k = sample(seq(1, floor(nrow(x)/3), 
##             by = by_val), size = len, replace = TRUE))
##     }
## }
## 
## $modelInfo$fit
## function (x, y, wts, param, lev, last, classProbs, ...) 
## {
##     if (is.factor(y)) {
##         knn3(as.matrix(x), y, k = param$k, ...)
##     }
##     else {
##         knnreg(as.matrix(x), y, k = param$k, ...)
##     }
## }
## <bytecode: 0x000002806e3daf10>
## 
## $modelInfo$predict
## function (modelFit, newdata, submodels = NULL) 
## {
##     if (modelFit$problemType == "Classification") {
##         out <- predict(modelFit, newdata, type = "class")
##     }
##     else {
##         out <- predict(modelFit, newdata)
##     }
##     out
## }
## <bytecode: 0x000002806e5544a8>
## 
## $modelInfo$predictors
## function (x, ...) 
## colnames(x$learn$X)
## 
## $modelInfo$tags
## [1] "Prototype Models"
## 
## $modelInfo$prob
## function (modelFit, newdata, submodels = NULL) 
## predict(modelFit, newdata, type = "prob")
## 
## $modelInfo$levels
## function (x) 
## levels(x$learn$y)
## 
## $modelInfo$sort
## function (x) 
## x[order(-x[, 1]), ]
## 
## 
## $modelType
## [1] "Classification"
## 
## $results
##   k  Accuracy     Kappa AccuracySD    KappaSD
## 1 5 0.6809916 0.3617139 0.01059727 0.02212386
## 2 7 0.7287732 0.4575272 0.01722177 0.03389509
## 3 9 0.7307435 0.4614475 0.03020486 0.06045208
## 
## $pred
## NULL
## 
## $bestTune
##   k
## 3 9
# Make predictions
predictions <- predict(model_knn, data = heart_attack)
predictions
##    [1] 1 0 0 1 0 1 0 0 0 0 0 0 1 0 1 1 0 0 1 1 0 1 1 1 1 1 1 0 0 0 1 1 0 0 1 1 0
##   [38] 1 0 0 0 0 1 0 1 1 0 0 1 0 1 0 1 0 0 0 1 1 0 1 1 1 0 0 1 0 1 0 1 0 0 0 0 0
##   [75] 1 1 1 0 0 0 1 1 1 1 1 1 1 1 0 0 1 1 0 1 0 1 1 0 1 1 1 1 1 1 1 0 0 0 1 1 1
##  [112] 0 1 0 0 1 0 0 1 1 1 1 0 0 0 1 1 1 1 0 1 0 0 1 1 1 1 1 1 1 0 0 0 1 1 0 1 0
##  [149] 0 1 0 0 1 0 0 1 1 0 1 1 1 1 1 1 0 0 0 1 1 0 1 0 1 1 0 0 0 0 1 0 0 1 0 1 1
##  [186] 0 0 0 0 1 1 1 1 1 0 0 1 1 1 1 1 1 0 0 1 1 0 1 1 0 1 0 0 1 1 1 0 1 0 0 1 0
##  [223] 1 1 1 0 1 0 1 0 1 1 0 1 1 0 1 0 0 1 1 0 1 0 1 1 0 0 1 1 0 0 0 0 0 0 1 1 1
##  [260] 1 1 0 1 1 1 1 0 0 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 0 0 1 1 1 0 1 0 0 0
##  [297] 0 0 1 1 1 1 1 0 1 0 0 1 0 1 0 1 0 1 1 1 0 1 0 1 0 1 0 1 1 1 0 0 0 1 1 0 1
##  [334] 1 0 0 1 1 0 0 1 1 1 1 1 1 0 1 0 0 1 1 0 0 0 1 0 0 1 1 1 0 1 1 1 1 0 0 0 0
##  [371] 0 0 1 1 1 1 1 0 0 1 0 1 1 0 0 0 1 1 0 1 0 0 0 0 0 1 0 0 1 1 0 0 1 1 0 0 1
##  [408] 1 1 1 1 0 0 0 0 1 1 1 1 0 1 0 1 0 0 0 1 1 0 1 0 0 1 1 1 1 1 0 1 1 1 0 0 1
##  [445] 1 1 1 0 1 0 1 1 0 1 0 1 1 1 1 1 0 1 1 1 1 1 1 0 1 0 1 0 0 1 0 1 0 0 1 0 0
##  [482] 1 0 1 1 0 0 0 1 1 1 1 1 0 1 1 0 1 1 1 0 1 1 1 1 0 0 1 0 0 1 0 1 1 1 0 0 1
##  [519] 0 1 0 0 1 1 0 0 0 1 0 1 0 1 0 1 1 1 1 1 0 0 0 1 0 1 1 0 0 1 1 1 0 0 0 1 1
##  [556] 0 0 1 1 0 0 1 1 1 0 1 1 1 1 1 0 0 1 1 0 1 0 0 0 0 1 1 1 0 0 1 1 0 1 0 1 0
##  [593] 0 0 0 1 1 1 1 1 0 0 1 1 1 1 1 0 0 0 0 0 1 0 0 1 1 1 1 1 0 1 0 0 0 0 1 1 1
##  [630] 0 0 1 1 0 1 0 1 1 0 0 1 0 0 0 1 0 1 0 0 1 0 1 0 0 1 1 1 1 1 1 0 0 1 1 0 0
##  [667] 1 0 1 1 1 1 1 0 0 1 0 0 1 0 1 0 0 0 0 1 1 1 0 0 0 1 0 1 1 0 1 0 1 0 1 0 0
##  [704] 0 1 0 0 1 0 0 1 0 0 0 0 1 0 0 1 1 0 1 1 1 1 0 1 1 0 1 1 0 1 1 1 1 1 0 1 1
##  [741] 1 1 0 0 1 1 0 0 1 0 1 0 1 0 0 1 0 1 1 1 0 1 1 1 0 0 0 0 1 1 0 1 1 0 1 1 1
##  [778] 0 1 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 1 1 0 0 0 0
##  [815] 0 0 1 1 1 1 0 0 0 1 0 1 1 0 1 0 1 0 1 0 0 1 1 1 0 1 0 1 0 0 0 0 1 0 1 1 1
##  [852] 1 1 0 0 1 1 1 1 0 0 0 0 1 0 1 1 1 1 1 1 1 0 0 0 0 0 1 0 1 1 1 0 1 0 0 0 0
##  [889] 0 1 0 1 0 1 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 0 0 1 1 0 0 1 1 1 1 0 1 1 1
##  [926] 0 1 1 0 0 0 1 0 1 1 1 1 0 0 1 0 1 1 0 0 1 1 1 0 1 0 0 0 1 0 0 1 1 0 1 1 1
##  [963] 1 0 1 1 0 0 0 1 1 1 1 1 1 1 0 1 1 0 0 1 1 0 1 0 0 1 0 0 1 0 1 0 1 1 0 0 0
## [1000] 0 0 1 1 1 0 0 1 1 1 1 0 1 0 0 1 0 0 0 0 1 1 0 0 1 0
## Levels: 0 1
# Convert predictions and target to factors with the same levels
predictions <- factor(predictions, levels = levels(heart_attack$target))

# Create the confusion matrix
#conf_matrix <- confusionMatrix(predictions, heart_attack$target)
#conf_matrix

# Print confusion matrix
#print(conf_matrix)

Interpretation: The code first checks the lengths and missing values of the true and predicted labels to ensure data consistency and integrity. It then converts the true and predicted labels to factors with appropriate levels for creating the confusion matrix. Finally, it attempts to create a confusion matrix, but there seems to be a mistake in using test\(age instead of test\)sex for the true labels, which might result in an error or incorrect evaluation. To correct the code, ensure that the correct variables are used for comparison in the confusion matrix creation. If the intention is to compare the true and predicted binary sex labels, replace test\(age with test\)sex.

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