day8_1

//In this challenge, we practice using linear regression techniques.//

#include <cmath>
#include <cstdio>
#include <vector>
#include <iostream>
#include <algorithm>
#include <iomanip>
using namespace std;

/* If our data shows a linear relationship between X and Y , then the straight line which best describes the relationship is the regression line. The regression line is given by yHat = a + bX. */

float getValueB(vector<std::pair<int,int>> v){
    long unsigned n = v.size();
    float xiyiProductSum, xSum, ySum, xSquaredSum = 0.0f;
    //v.first -> x, v.second -> y§
    for(int i = 0; i < n; i++){
        xiyiProductSum += (v[i].first * v[i].second);
        xSum += v[i].first;
        ySum += v[i].second;
        xSquaredSum += pow(v[i].first, 2);
    }
    float B = ((n*(xiyiProductSum)-((xSum)*(ySum)))/((n*xSquaredSum)-pow(xSum, 2)));
    return B;
}

float getValueA(vector<std::pair<int,int>> v, float B){
    long unsigned n = v.size();
    float xMean, yMean = 0.0f;
    int xSum, ySum = 0;
    for(int i = 0; i < n; i++){
        xSum += v[i].first;
        ySum += v[i].second;
    }
    xMean = xSum / n;
    yMean = ySum / n;
    float A = yMean - (xMean * B);
    return A;
}


int main() {
    /* Enter your code here. Read input from STDIN. Print output to STDOUT */
    std::vector<std::pair<int,int>> xyGrades;
    int x,y = 0;
    while(cin >> x >> y){
        xyGrades.push_back(make_pair(x,y));
    }   
    float B = getValueB(xyGrades);
    float A = getValueA(xyGrades, B);
    float expectedGrade = B * 80.0f + A;
    cout << fixed << setprecision(3) << expectedGrade;    
    return 0;
}