so far we have used void functions....not we will be using functions that return

Question

so far we have used void functions....not we will be using functions that return values. Using the list of numbers provided,,,,,,find the best fit of a streight line through it (regression analysis): to generate the equation y = mx + b.

data linear regression:

0 0
1 6.88
1.5 15.48
2 27.52
2.5 43
3 61.92
3.27 73.56
3.496 84.08
3.5 84.28
3.524 85.44
3.732 95.82
4 110.1
4.5 139.3
5 172

So this was the question....I answered Like below:

/*
Dweep Dey Program 5
02/20/17
This program will return values, y=mx+b, regression coefficient
*/

using namespace std;
#include <iostream>
#include <fstream>

// global variable declerations
float x[50], y[50];
int NumOfDataPoints,n,i;
float m, b;

// function declerations
float sumX();
float sumY();
float sumXY();
float sumXsq();
void getData();

int main()

{
   getData();//this function gets data and puts it in arrays x and y
   NumOfDataPoints = n; // number of data points is the n
// computing m and b using function calls
   m = ((n*sumXY()) - (sumX()*sumY())) / ((n*sumXsq()) - (sumX()*sumX()));
   b = ((sumY() - (m*sumX())) / (n));
cout<<"y = "<<m<<"x"<<"+ "<<b<<endl;

system("pause"); //so we can see the equation printed on the screen above

return 0;
}

void getData() //get Data begins
   { int   i=0;
   ifstream datfile; //the data buffer
   datfile.open("thedata.txt"); //opens the data file on the disk
   while (!datfile.eof())//while the file is not empty keep reading
   {
       datfile>>x[i]; datfile>>y[i]; //put the X and Y points in arrays
       cout<<x[i]<<" "<<y[i]<<endl;//show data on screen
       i++; //get ready for next data point
   }
datfile.close();//all done with disk file
n = i-1; //store the number of data pairs in a place called "n"
   }
  
  
   float sumX()
{
float ans = 0.0;
for(int i = 0;i<=n-1;i++)// sum of all x
ans = ans + x[i];
return ans;   
}
  
float sumY()
{
float ans = 0.0;
for(int i = 0;i<=n-1;i++) // sum of all y
ans = ans +y[i];
return ans;   
}
  
float sumXY()
{
float ans = 0.0;
for(int i = 0;i<=n-1 ;i++) // sum of all (xy)
ans = ans + x[i]*y[i];
return ans;   
}
  
float sumXsq()
{
float ans = 0.0;
for(int i = 0;i<=n-1;i++) // sum of all x^2
ans = ans +x[i]*x[i];
return ans;
}

** Professor said, this program is good. This program give the right value of m and b....He gave me 45 out of 50...as he want me to calculate r....the program above is good, can i just get help to calculate r....let me know what you add ....please do not say need more information :( FYI: The values of m= 34.5349, b= -29.808, ( My program output this values) , need to calculate r which value will be 0.91789***

*** Do not change any format or add any new header please ( professor instruct)

Thank you so much!

Explanation / Answer

// C++ code
using namespace std;
#include <iostream>
#include <fstream>
#include <math.h>
// global variable declerations
float x[50], y[50];
int NumOfDataPoints,n,i;
float m, b;
// function declerations
float sumX();
float sumY();
float sumXY();
float sumXsq();
void getData();
int main()
{
getData();//this function gets data and puts it in arrays x and y
NumOfDataPoints = n; // number of data points is the n
// computing m and b using function calls
m = ((n*sumXY()) - (sumX()*sumY())) / ((n*sumXsq()) - (sumX()*sumX()));
b = ((sumY() - (m*sumX())) / (n));
cout<<"y = "<<m<<"x"<<"+ "<<b<<endl;

float averageY = sumY()/NumOfDataPoints;
float sum_Y_residue = 0, sum_residue = 0, resiue = 0, y_residue;
for (int i = 0; i < NumOfDataPoints; i++)
{
y_residue = pow((y[i] - b - (m * x[i])), 2);

sum_Y_residue += y_residue;

//current residue squared (y[i] - averageY)^2
resiue = pow(y[i] - averageY, 2);

sum_residue += resiue;
}

printf("r = %0.6lf ", (sum_residue - sum_Y_residue)/sum_residue);

return 0;
}

void getData() //get Data begins
{ int i=0;
ifstream datfile; //the data buffer
datfile.open("thedata.txt"); //opens the data file on the disk
while (!datfile.eof())//while the file is not empty keep reading
{
datfile>>x[i]; datfile>>y[i]; //put the X and Y points in arrays
cout<<x[i]<<" "<<y[i]<<endl;//show data on screen
i++; //get ready for next data point
}
datfile.close();//all done with disk file
n = i-1; //store the number of data pairs in a place called "n"
}
  
  
float sumX()
{
float ans = 0.0;
for(int i = 0;i<=n-1;i++)// sum of all x
ans = ans + x[i];
return ans;   
}
  
float sumY()
{
float ans = 0.0;
for(int i = 0;i<=n-1;i++) // sum of all y
ans = ans +y[i];
return ans;   
}
  
float sumXY()
{
float ans = 0.0;
for(int i = 0;i<=n-1 ;i++) // sum of all (xy)
ans = ans + x[i]*y[i];
return ans;   
}
  
float sumXsq()
{
float ans = 0.0;
for(int i = 0;i<=n-1;i++) // sum of all x^2
ans = ans +x[i]*x[i];
return ans;
}

/*
output:
0 0
1 6.88
1.5 15.48
2 27.52
2.5 43
3 61.92
3.27 73.56
3.496 84.08
3.5 84.28
3.524 85.44
3.732 95.82
4 110.1
4.5 139.3
5 172
y = 31.3589x+ -23.2485
r = 0.928284

*/

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