import java.io.BufferedReader;
import java.io.FileReader;
import java.util.ArrayList;
import java.util.List;

/**
* Linear Regression class
*/
public class LinearRegression {

/**
* A class to hold predictor variables matrix
* And response variable matrix.
* And name of each coefficient.
*/
class Data {
   double[][] X;
   double[][] y;
   String[] names;
}

/**
* This method take two 2D matrices and
* multiplies them and return the resulted matrix.
* @param a
* @param b
* @return
*/
public static double[][] multiply(double[][] a, double[][] b) {
   int rowA = a.length;
   int colA = a[0].length;
   int rowB = b.length;
   int colB = b[0].length;
   double[][] result = new double[rowA][colB];
   if(colA == rowB) {
         for (int i = 0; i < rowA; i++) {
            for (int j = 0; j < colB; j++) {
               for (int k = 0; k < rowB; k++) {
                     result[i][j] += a[i][k] * b[k][j];
               }
            }
         }
   }
   return result;
}

/**
* Utility method to print the matrix.
* @param c
*/
public static void printMatrix(double[][] c){
   int row = c.length;
   int col = c[0].length;

   for (int i=0; i<row; i++) {
         for (int j=0; j<col; j++) {
            System.out.print(c[i][j] + "    ");
         }
         System.out.println();
   }
}

/**
* Utility method to print the predictor name and
* its coefficient.
* @param c
* @param name
*/
public static void printCoefficient(double[][] c, String[] name){
   int row = c.length;
   int col = c[0].length;

   for (int i=0; i<row; i++) {
         for (int j=0; j<col; j++) {
            System.out.print(name[i] + " : " + c[i][j] + "    ");
         }
         System.out.println();
   }
}

/**
* This method finds the cofactor of a given matrix.
* @param mat
* @param factor
* @param p
* @param q
* @param n
*/
public static void coFactor(double[][] mat, double factor[][], int p, int q, int n){
   int i = 0;
   int j = 0;

   for(int r=0; r <n; r++) {
         for(int c=0; c<n;c++) {
            if(r != p && c != q) {
               factor[i][j] = mat[r][c];
               j++;
               if(j == n-1){
                     j = 0;
                     i++;
               }
            }
         }
   }
}

/**
* This method find determinant of the matrix.
* @param mat
* @param n
* @return
*/
public static double determinant(double[][] mat, int n) {
   int N

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