Exponential regression

#include <iostream>
#include <vector>
#include <utility>
#include <math.h>

using namespace std;

pair <double, double> exponential_regression(vector <double> & x, vector <double> & y){
    int N = x.size();

    double S_x, S_lny, S_x_lny, S_x2;

    for(int i = 0; i < N; ++i){
        S_x += x[i];
        S_lny += log(y[i]);
        S_x_lny += x[i] * log(y[i]);
        S_x2 += x[i] * x[i];
    }

    double a = (N * S_x_lny - S_x * S_lny) / (N * S_x2 - S_x * S_x);
    double b = (S_x2 * S_lny - S_x * S_x_lny) / (N * S_x2 - S_x * S_x);

    return make_pair(a, b);
}

int main(){
    cout << "Enter the number of points:\n";
    int N;
    cin >> N;

    vector <double> x(N);
    vector <double> y(N);

    cout << "Enter " << N << " pairs of coordinates (x, y):\n";
    for(int i = 0; i < N; ++i){
        cin >> x[i] >> y[i];
    }

    pair <double, double> line = exponential_regression(x, y);
    cout << "a = " << line.first << ", b = " << line.second << "\n";

    system("PAUSE");
    return 0;
}