Microsoft Visual C# Statistics: The Linear Correlation Coefficient

The factors in this equation are:

1. Start Microsoft Visual Studio
2. To create a new application, on the main menu, click File -> New Project...
3. In the middle list, click Windows Forms Application
4. Change the Name to LinearCorrelationCoefficient1
5. Click OK
6. In the Solution Explorer, right-click Form1.cs and click Rename
7. Type Exercise.cs and press Enter
8. Design the form as follows:
    

   Control (Name) Text Other Properties Label   x   Label   y   Label   Values to Add:   TextBox txtX     TextBox txtY     Button btnAdd Add   ListView lvwValues   FullRowSelect: True GridLines: True View: Details Columns   (Name) Text TextAlign Width colIndex #   30 colX x Right 70 colY y Right 70 colXSquared x2 Right 90 colYSquared y2 Right 90 colXY xy Right 100 Button btnCalculate Calculate   Label   n =   TextBox txtN     Label   Σx =   TextBox txtSumX     Label   Σx2 =   TextBox txtSumXSquare     Label   Σxy =   TextBox txtSumXY     Label   Σy =   TextBox txtSumY     Label   Σy2 =   TextBox txtSumYSquare     PictureBox pbxR     Label   =   TextBox txtR     Label   Conclusion   TextBox txtConclusion     Button btnClear Clear/Reset   Button btnClose Close

9. Double-click an unoccupied area of the form
10. Return to the form and double-click the Add button
11. Return to the form
12. Double-click the Calculate button
13. Return to the form
14. Double-click the Clear/Reset button
15. Return to the form
16. Double-click the Close button
17. Change the file as follows:

    using System;
    using System.Collections.Generic;
    using System.ComponentModel;
    using System.Data;
    using System.Drawing;
    using System.Linq;
    using System.Text;
    using System.Windows.Forms;
    
    namespace LinearCorrelationCoefficient1
    {
        public partial class LinearCorrelationCoefficient : Form
        {
            List<SamplePair> pairs;
    
            public LinearCorrelationCoefficient()
            {
                InitializeComponent();
            }
    
            private void ShowPairs()
            {
                lvwValues.Items.Clear();
    
                double SumX = 0.00, SumY = 0.00,
                       SumXSquare = 0.00, SumYSquare = 0.00,
                       SumXY = 0.00;
    
                int i = 0;
                foreach( SamplePair sp in pairs)
                {
                    ListViewItem lviPair = new ListViewItem((i + 1).ToString());
    
                    lviPair.SubItems.Add(sp.x.ToString("F"));
                    lviPair.SubItems.Add(sp.y.ToString("F"));
                    lviPair.SubItems.Add(sp.xSquared.ToString("0.0000#"));
                    lviPair.SubItems.Add(sp.ySquared.ToString("0.0000#"));
                    lviPair.SubItems.Add(sp.xy.ToString("0.0000#"));
                    lvwValues.Items.Add(lviPair);
    
                    i++;
                }
    
                foreach (SamplePair sp in pairs)
                {
                    SumX += sp.x;
                    SumY += sp.y;
                    SumXSquare += (sp.x * sp.x);
                    SumYSquare += (sp.y * sp.y);
                    SumXY += (sp.x * sp.y);
                }
    
                ListViewItem lviTotals = new ListViewItem("Totals");
                lviTotals.SubItems.Add("Σx = " + SumX.ToString("F"));
                lviTotals.SubItems.Add("Σy = " + SumY.ToString("F"));
                lviTotals.SubItems.Add("Σx² = " + SumXSquare.ToString("0.0000#"));
                lviTotals.SubItems.Add("Σy² = " + SumYSquare.ToString("0.0000#"));
                lviTotals.SubItems.Add("Σxy = " + SumXY.ToString("0.0000#"));
                lvwValues.Items.Add(lviTotals);
            }
    
            private void LinearCorrelationCoefficient_Load(object sender,
            					       EventArgs e)
            {
                pairs = new List<SamplePair>();
            }
    
            private void btnAdd_Click(object sender, EventArgs e)
            {
                double x = 0.00, y = 0.00;
    
                if( txtX.Text == "" )
                {
                    MessageBox.Show("You must enter a value for x.");
                    return;
                }
    
                if (txtY.Text == "")
                {
                    MessageBox.Show("You must enter a value for y.");
                    return;
                }
    
                try
                {
                    x = double.Parse(txtX.Text);
                }
                catch (FormatException)
                {
                }
    
                try
                {
                    y = double.Parse(txtY.Text);
                }
                catch (FormatException)
                {
                }
    
                SamplePair pair = new SamplePair(x, y);
                pairs.Add(pair);
                ShowPairs();
    
                txtX.Text = "";
                txtY.Text = "";
                txtX.Focus();
    
                ShowPairs();
            }
    
            private void btnCalculate_Click(object sender, EventArgs e)
            {
                double SumX = 0.00, SumY = 0.00,
                       SumXSquare = 0.00, SumYSquare = 0.00,
                       SumXY = 0.00, r = 0.00;
    
                foreach (SamplePair sp in pairs)
                {
                    SumX += sp.x;
                    SumY += sp.y;
                    SumXSquare += (sp.x * sp.x);
                    SumYSquare += (sp.y * sp.y);
                    SumXY += (sp.x * sp.y);
                }
    
                double NTimesSumXY = pairs.Count * SumXY;
                double SumXTimesSumY = SumX * SumY;
                double SquareRoot1 = pairs.Count * SumXSquare - Math.Pow(SumX, 2);
                double SquareRoot2 = pairs.Count * SumYSquare - Math.Pow(SumY, 2);
    
                r = (NTimesSumXY - SumXTimesSumY) / (Math.Sqrt(SquareRoot1) * 
                					 Math.Sqrt(SquareRoot2));
    
                txtN.Text = pairs.Count.ToString();
                txtSumX.Text = SumX.ToString("F");
                txtSumY.Text = SumY.ToString("F");
                txtSumXSquare.Text = SumXSquare.ToString();
                txtSumYSquare.Text = SumYSquare.ToString();
                txtSumXY.Text = SumXY.ToString("F");
                
                txtR.Text = r.ToString("0.00#");
            }
    
            private void btnClear_Click(object sender, EventArgs e)
            {
                pairs.Clear();
                lvwValues.Items.Clear();
    
                txtN.Text = "";
                txtSumX.Text = "";
                txtSumY.Text = "";
                txtSumXSquare.Text = "";
                txtSumYSquare.Text = "";
                txtSumXY.Text = "";
                txtR.Text = "";
            }
    
            private void btnClose_Click(object sender, EventArgs e)
            {
                Close();
            }
        }
    
        public class SamplePair
        {
            public double x { get; set; }
            public double y { get; set; }
    
            public SamplePair(double X, double Y)
            {
                x = X;
                y = Y;
            }
    
            public double xSquared
            {
                get
                {
                    return x * x;
                }
            }
    
            public double ySquared
            {
                get
                {
                    return y * y;
                }
            }
    
            public double xy
            {
                get
                {
                    return x * y;
                }
            }
        }
    }

18. To execute, press F5
19. Enter each pair of values and click Add each time
     
    
20. After adding the values, click Calculate
     
    
21. Close the form and return to your programming environment

Application