n = 5
X = [95, 85, 80, 70, 60]
Y = [85, 95, 70, 65, 70]

mean_X = sum(X)/len(X)
mean_Y = sum(Y)/len(Y)


# determine the equation parameters for y = a + b*x 

b = ((n * sum(x*y for x, y in zip(X,Y))) - (sum(X) * sum(Y))) / (n * sum(x**2 for x in X) - (sum(X)**2))

a = mean_Y - (b * mean_X)

# calculate the predicted y for x = 80

y_predicted = a + (b * 80)

# should come out to # 78.288
print(round(y_predicted, 3))

#python
sxy, sx, sy, sx2=0, 0, 0, 0
for _ in range(5):
    x, y=list(map(int, input().split()))
    sx+=x
    sy+=y
    sxy+=x*y
    sx2+=x**2
b=(5*sxy-sx*sy)/(5*sx2-sx**2)
a=(sy-b*sx)/5
print(round(a+b*80, 3))

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

double dot_product(vector<double>x, vector<double> y)
{
    double sum=0;
    for(int i=0; i<x.size(); ++i)
    {
        sum+=x[i]*y[i];
    }
    return sum;
}

double sum(vector<double> x, int p=1)
{   double sum=0;
    for(int i=0; i<x.size(); i++)
        sum+=pow(x[i], p);
    return sum;
}
double mean(vector<double> x)
{   double total=sum(x);
    return total/x.size();
}

double linear_regression(vector<double> x, vector<double>y, double t)
{   double n=double(x.size());
    double sumX=sum(x,1);
    double sumX2=sum(x,2);
    double sumY=sum(y,1);
    double meanX=mean(x);
    double meanY=mean(y);
    
    double b=(n*dot_product(x, y)-sumX*sumY)/(n*sumX2-sumX*sumX);
    double a=meanY-b*meanX;
    
    return a+b*t;
    
}

int main() {
    /* Enter your code here. Read input from STDIN. Print output to STDOUT */   
    int a=5;
    vector<double> math(a);
    vector<double> stat(a);
    double m,s;    
    for(int i=0; i<a; ++i)
    {
        cin>>m>>s;
        math.push_back(m);
        stat.push_back(s);
    }
    double math_grade=80;
    double stat_grade=linear_regression(math,stat,math_grade);
    
    cout<<fixed<<setprecision(3);
    cout<<stat_grade<<endl;
    return 0;
}

}

x = [95, 85, 80, 70, 60]
y = [85, 95, 70, 65, 70]

sum_x = sum(x)
sum_y = sum(y)
n = len(x) # or len(y)

b = (n * sum(x[i] * y[i] for i in range(n))) - (sum_x * sum_y)
b /= n * sum(list(map(lambda i: i*i, x))) - sum_x ** 2
# or b /= n * sum(i ** 2 for i in x) - sum_x ** 2

mean_x = sum_x / n
mean_y = sum_y / n

a = mean_y - b * mean_x

print(a + b * 80)

import statistics
import math

X = [95, 85, 80, 70, 60]
Y = [85, 95, 70, 65, 70]

mean_x = statistics.mean(X)
mean_y = statistics.mean(Y)

diff_x = 0
diff_y = 0
for i in range(len(X)):
    diff_x += pow(X[i] - mean_x, 2)
    diff_y += pow(Y[i] - mean_y, 2)
    
stand_dev_x = math.sqrt(1 / len(X) * diff_x)
stand_dev_y = math.sqrt(1 / len(Y) * diff_x)

sum = 0
for i in range(len(X)):
    sum += ((X[i] - mean_x) / stand_dev_x ) * ((Y[i] - mean_y) / stand_dev_y)
    
r = 1 / len(X) * sum

b = r * stand_dev_y / stand_dev_x
a = mean_y - b * mean_x

answer = a + b * 80

print(round(answer, 3))