Merge pull request #208 from posi2/master

#issue 154

Author: prateekiiest

EXPONENTIAL REGRESSION

@@ -0,0 +1,39 @@
+#include<bits/stdc++.h>
+#include<iomanip>
+using namespace std;
+#define f float
+void exponential(f x[], f y[], int n){
+    f Y[n],sumx=0,sumy=0,sumxy=0,sumx2=0;
+    double a,b,A;
+    for(int i=0;i<=n-1;i++)
+    {
+        Y[i]=log(y[i]);
+    }
+    for(int i=0;i<=n-1;i++)
+    {
+        sumx=sumx +x[i];
+        sumx2=sumx2 +x[i]*x[i];
+        sumy=sumy +Y[i];
+        sumxy=sumxy +x[i]*Y[i];
+
+    }
+    A=((sumx2*sumy -sumx*sumxy)*1.0/(n*sumx2-sumx*sumx)*1.0);
+    b=((n*sumxy-sumx*sumy)*1.0/(n*sumx2-sumx*sumx)*1.0);
+    a=exp(A);
+    printf("\n The curve is Y= %4.3fe^%4.3fX",a,b);
+}
+
+int main()
+{
+int i,n;
+cout<<"welcome to linear regression\n";
+cout<<"enter number of data you want to enter\n";
+cin>>n;
+f x[n],y[n];
+cout<<"enter x variables\n";
+for(i=0;i<n;++i) cin>>x[i];
+cout<<"enter y variables\n";
+for(i=0;i<n;++i) cin>>y[i];
+ exponential(x,y,n);
+return 0;
+}

LINEAR REGRESSION

@@ -0,0 +1,34 @@
+#include<bits/stdc++.h>
+#include<iomanip>
+using namespace std;
+#define f float
+void linear(f x[],f y[],int n)
+{
+    f cx=0,cy=0,sumxy=0,sumx2=0;
+    double a,b;
+    for(int i=0;i<=n-1;i++)
+    {
+        cx=cx+x[i];
+        sumx2=sumx2 +x[i]*x[i];
+        cy=cy+y[i];
+        sumxy=sumxy +x[i]*y[i];
+
+    }
+    a=((sumx2*cy -cx*sumxy)*1.0/(n*sumx2-cx*cx)*1.0);
+    b=((n*sumxy-cx*cy)*1.0/(n*sumx2-cx*cx)*1.0);
+    printf("\n\nThe line is Y=%3.3f +%3.3f X",a,b);
+}
+int main()
+{
+int i,n;
+cout<<"welcome to linear regression\n";
+cout<<"enter number of data you want to enter\n";
+cin>>n;
+f x[n],y[n];
+cout<<"enter x variables\n";
+for(i=0;i<n;++i) cin>>x[i];
+cout<<"enter y variables\n";
+for(i=0;i<n;++i) cin>>y[i];
+ linear(x,y,n);
+return 0;
+}

polynomial regression

@@ -0,0 +1,78 @@
+#include<bits/stdc++.h>
+#include<iomanip>
+using namespace std;
+#define f float
+void poly(float x[], float y[], int N){
+    int n;
+    cout << "\nPlease enter the degress:\n";
+    cin >> n;
+
+    double X[2*n+1];                        //Array that will store the values of sigma(xi),sigma(xi^2),sigma(xi^3)....sigma(xi^2n)
+    for (int i=0;i<2*n+1;i++)
+    {
+        X[i]=0;
+        for (int j=0;j<N;j++)
+            X[i]=X[i]+pow(x[j],i);        //consecutive positions of the array will store N,sigma(xi),sigma(xi^2),sigma(xi^3)....sigma(xi^2n)
+    }
+    double B[n+1][n+2],a[n+1];            //B is the Normal matrix(augmented) that will store the equations, 'a' is for value of the final coefficients
+    for (int i=0;i<=n;i++)
+        for (int j=0;j<=n;j++)
+            B[i][j]=X[i+j];            //Build the Normal matrix by storing the corresponding coefficients at the right positions except the last column of the matrix
+    double Y[n+1];                    //Array to store the values of sigma(yi),sigma(xi*yi),sigma(xi^2*yi)...sigma(xi^n*yi)
+    for (int i=0;i<n+1;i++)
+    {
+        Y[i]=0;
+        for (int j=0;j<N;j++)
+            Y[i]=Y[i]+pow(x[j],i)*y[j];        //consecutive positions will store sigma(yi),sigma(xi*yi),sigma(xi^2*yi)...sigma(xi^n*yi)
+    }
+    for (int i=0;i<=n;i++)
+        B[i][n+1]=Y[i];                //load the values of Y as the last column of B(Normal Matrix but augmented)
+    n=n+1;                //n is made n+1 because the Gaussian Elimination part below was for n equations, but here n is the degree of polynomial and for n degree we get n+1 equations
+
+    for (int i=0;i<n;i++)                    //From now Gaussian Elimination starts(can be ignored) to solve the set of linear equations (Pivotisation)
+        for (int k=i+1;k<n;k++)
+            if (B[i][i]<B[k][i])
+                for (int j=0;j<=n;j++)
+                {
+                    double temp=B[i][j];
+                    B[i][j]=B[k][j];
+                    B[k][j]=temp;
+                }
+
+    for (int i=0;i<n-1;i++)            //loop to perform the gauss elimination
+        for (int k=i+1;k<n;k++)
+        {
+            double t=B[k][i]/B[i][i];
+            for (int j=0;j<=n;j++)
+                B[k][j]=B[k][j]-t*B[i][j];    //make the elements below the pivot elements equal to zero or elimnate the variables
+        }
+    for (int i=n-1;i>=0;i--)                //back-substitution
+    {                        //x is an array whose values correspond to the values of x,y,z..
+        a[i]=B[i][n];                //make the variable to be calculated equal to the rhs of the last equation
+        for (int j=0;j<n;j++)
+            if (j!=i)            //then subtract all the lhs values except the coefficient of the variable whose value                                   is being calculated
+                a[i]=a[i]-B[i][j]*a[j];
+        a[i]=a[i]/B[i][i];            //now finally divide the rhs by the coefficient of the variable to be calculated
+    }
+
+    cout<<"\nThe curve is:Y=";
+    for (int i=0;i<n;i++)
+        cout<<" + ("<<a[i]<<")"<<"x^"<<i;
+    cout<<"\n";
+
+}
+
+int main()
+{
+int i,n;
+cout<<"welcome to linear regression\n";
+cout<<"enter number of data you want to enter\n";
+cin>>n;
+f x[n],y[n];
+cout<<"enter x variables\n";
+for(i=0;i<n;++i) cin>>x[i];
+cout<<"enter y variables\n";
+for(i=0;i<n;++i) cin>>y[i];
+ poly(x,y,n);
+return 0;
+}