How do I write a code in C++ for fitting a quadratic polynomial to a dataset?

Question

I'm not brilliant at coding, I'm just starting off and the code I created runs with that many errors I feel like I should just start again, but I have no clue what to do differently.

Below is the code I'm running that's coming back with all the errors, I just can't put my finger on what I'm doing wrong and it's so overwhelming.

Please help if you can, thank you x

Edit: sorry I forgot to add the errors! I've got 23 errors, most are 'array type is not assignable' and 'expression did not evaluate to a constant'

#include<iomanip>
#include<cmath>
using namespace std;
int main()
{
    int i, j, k, n, N;
    cout.precision(4);                        //set precision
    cout.setf(ios::fixed);
    cout << "\nEnter the no. of data pairs to be entered:\n";        //To find the size of arrays that will store x,y, and z values
    cin >> N;
    double x[N], y[N];
    cout << "\nEnter the x-axis values:\n";                //Input x-values
    for (i = 0; i < N; i++)
        cin >> x[i];
    cout << "\nEnter the y-axis values:\n";                //Input y-values
    for (i = 0; i < N; i++)
        cin >> y[i];
    cout << "\nWhat degree of Polynomial do you want to use for the fit?\n";
    cin >> n;                                // n is the degree of Polynomial 
    double X[2 * n + 1];                        //Array that will store the values of sigma(xi),sigma(xi^2),sigma(xi^3)....sigma(xi^2n)
    for (i = 0; i < 2 * n + 1; i++)
    {
        X[i] = 0;
        for (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 (i = 0; i <= n; i++)
        for (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 (i = 0; i < n + 1; i++)
    {
        Y[i] = 0;
        for (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 (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
    cout << "\nThe Normal(Augmented Matrix) is as follows:\n";
    for (i = 0; i < n; i++)            //print the Normal-augmented matrix
    {
        for (j = 0; j <= n; j++)
            cout << B[i][j] << setw(16);
        cout << "\n";
    }
    for (i = 0; i < n; i++)                    //From now Gaussian Elimination starts(can be ignored) to solve the set of linear equations (Pivotisation)
        for (k = i + 1; k < n; k++)
            if (B[i][i] < B[k][i])
                for (j = 0; j <= n; j++)
                {
                    double temp = B[i][j];
                    B[i][j] = B[k][j];
                    B[k][j] = temp;
                }

    for (i = 0; i < n - 1; i++)            //loop to perform the gauss elimination
        for (k = i + 1; k < n; k++)
        {
            double t = B[k][i] / B[i][i];
            for (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 (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 (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 values of the coefficients are as follows:\n";
    for (i = 0; i < n; i++)
        cout << "x^" << i << "=" << a[i] << endl;            // Print the values of x^0,x^1,x^2,x^3,....    
    cout << "\nHence the fitted Polynomial is given by:\ny=";
    for (i = 0; i < n; i++)
        cout << " + (" << a[i] << ")" << "x^" << i;
    cout << "\n";
    return 0;
    }

Answer 1

You have in your code several variables which are declared as double x[N], where N is a variable that is known only at run-time. This is not guaranteed to be supported. Instead, you should use a std::vector, initialized like this: std::vector<double> x(N). This creates a vector of doubles of size N, zero-initialized. Look up how to use vectors here: https://en.cppreference.com/w/cpp/container/vector . Also, you should use descriptive variable names, which will help you read and understand your own code (and others you're asking for help). Don't be afraid of 23 error messages, I routinely get 100+ on first compilation of a fresh batch of code. Often they can cascade where one causes a lot of others down the line, so work starting from the one that's earliest in the code, recompiling after every bugfix. The 100+ effectively become 30 or so, sometimes.

Also, it would be helpful to split your function into several functions, and test each one individually, then bring them all together.