Difference between revisions of "Polynomial regression I"

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Through the points defining the dashed line the regression polynomial of degree 'degree' is computed and displayed.
 +
The points can be scaled by adjusting the slider 'scale'. The degree of the regression polynomial can be changed
 +
by using the slider 'degree'.
 
<jsxgraph width="700" height="500">
 
<jsxgraph width="700" height="500">
 +
var data = "406.60 428.50 429.30 426.30 434.70 415.90 419.00 408.80 410.10 408.30 420.40 415.20 409.70 408.90 411.00 410.60 409.60 409.50 409.80 413.00 417.90 415.80 415.50 421.30 423.50 426.80 426.60 427.20 433.30 435.00 442.50 447.00 450.60 448.90 446.20 443.60 446.30 448.20 452.40 451.30 451.80 459.90 464.70 467.30 463.50 466.60 461.10 464.90 467.30 458.40 458.80 463.20 462.40 461.10 465.50 461.50 458.20 460.80 459.30 445.70 425.10 437.60 438.00 436.60 437.60 437.60 438.60 443.10 446.40 445.90 450.80 451.60 457.30 456.70 455.60 454.75 453.90 451.20 450.70 446.80 443.40 448.40 451.80 449.80 449.10 447.60 448.40 450.00 443.00 440.60 437.40 435.40 432.00 430.80 429.60 437.10 440.00 438.30 435.20 436.60 435.25 433.90 436.50 436.30 437.40 441.00 445.40 450.10 449.20 450.50 455.60 452.00 451.80 456.80 455.30 457.40 457.40 461.10 459.60 462.40 463.40 464.60 469.00 472.20 471.80 470.10 465.20 470.40 468.50 468.70 469.70 472.50 474.70 472.40 475.00 476.10 473.20 471.50 472.20 471.10 472.80 470.40 470.50 472.10 471.10 468.50 465.50 465.70 465.40 466.90 468.85 470.80 474.00 478.10 480.50 481.00 479.10 476.40 469.80 471.60 470.60 467.20 473.10 471.70 474.80 477.20 474.60 475.10 475.90 475.80 472.00 470.80 469.10 464.30 463.70 467.20 467.30 467.10 465.60 462.70 449.45 436.20 466.00 467.40 467.00 471.50 469.80 474.20 476.10 477.10 480.30 478.70 478.80 479.30 479.30 478.30 477.20 480.20 484.10 488.70 492.70 492.60 491.90 491.90 495.10 494.50 494.50 496.90 496.20 498.40 498.00 496.00 497.90 495.40 497.30 495.20 499.20 500.60 497.90 499.60 497.00 498.10 496.70 491.40 487.60 486.70 487.40 489.30 485.30 501.80 485.40 491.30 495.50 501.80 504.50 502.50 505.80 510.30 511.90 509.90 508.70 510.70 512.90 512.90 513.80 516.10 512.10 511.10 505.30 505.10 505.20 508.40 510.70 511.30 514.90 517.30 519.70 521.80 524.40 526.80";
 +
data = data.split(' ');
  
    data = "406.60 428.50 429.30 426.30 434.70 415.90 419.00 408.80 410.10 408.30 420.40 415.20 409.70 408.90 411.00 410.60 409.60 409.50 409.80 413.00 417.90 415.80 415.50 421.30 423.50 426.80 426.60 427.20 433.30 435.00 442.50 447.00 450.60 448.90 446.20 443.60 446.30 448.20 452.40 451.30 451.80 459.90 464.70 467.30 463.50 466.60 461.10 464.90 467.30 458.40 458.80 463.20 462.40 461.10 465.50 461.50 458.20 460.80 459.30 445.70 425.10 437.60 438.00 436.60 437.60 437.60 438.60 443.10 446.40 445.90 450.80 451.60 457.30 456.70 455.60 454.75 453.90 451.20 450.70 446.80 443.40 448.40 451.80 449.80 449.10 447.60 448.40 450.00 443.00 440.60 437.40 435.40 432.00 430.80 429.60 437.10 440.00 438.30 435.20 436.60 435.25 433.90 436.50 436.30 437.40 441.00 445.40 450.10 449.20 450.50 455.60 452.00 451.80 456.80 455.30 457.40 457.40 461.10 459.60 462.40 463.40 464.60 469.00 472.20 471.80 470.10 465.20 470.40 468.50 468.70 469.70 472.50 474.70 472.40 475.00 476.10 473.20 471.50 472.20 471.10 472.80 470.40 470.50 472.10 471.10 468.50 465.50 465.70 465.40 466.90 468.85 470.80 474.00 478.10 480.50 481.00 479.10 476.40 469.80 471.60 470.60 467.20 473.10 471.70 474.80 477.20 474.60 475.10 475.90 475.80 472.00 470.80 469.10 464.30 463.70 467.20 467.30 467.10 465.60 462.70 449.45 436.20 466.00 467.40 467.00 471.50 469.80 474.20 476.10 477.10 480.30 478.70 478.80 479.30 479.30 478.30 477.20 480.20 484.10 488.70 492.70 492.60 491.90 491.90 495.10 494.50 494.50 496.90 496.20 498.40 498.00 496.00 497.90 495.40 497.30 495.20 499.20 500.60 497.90 499.60 497.00 498.10 496.70 491.40 487.60 486.70 487.40 489.30 485.30 501.80 485.40 491.30 495.50 501.80 504.50 502.50 505.80 510.30 511.90 509.90 508.70 510.70 512.90 512.90 513.80 516.10 512.10 511.10 505.30 505.10 505.20 508.40 510.70 511.30 514.90 517.30 519.70 521.80 524.40 526.80";
+
var datax = [];
    data = data.split(' ');
+
for (i = 0; i < data.length; i++)  {  
    datax = [];
+
    datax[i] = i;
    for (i = 0; i < data.length; i++)  {  
+
    data[i] = (parseFloat(data[i])-450.0);  
        data[i] = (parseFloat(data[i])-450.0);  
+
}
        datax[i] = i;
+
        }
+
var brd = JXG.JSXGraph.initBoard('jxgbox', {boundingbox:[-2, 100, data.length+2, -70], grid: false, axis:true});
      
+
 
 +
brd.suspendUpdate();
 +
var s = brd.create('slider',[[10,70],[80,70],[0,1,1]],{name:'scale'});    
 +
var deg = brd.create('slider',[[10,90],[80,90],[1,1,10]],{name:'degree',snapWidth:1});      
  
brd = JXG.JSXGraph.initBoard('jxgbox', {boundingbox:[-2, 100, data.length+2, -70], grid: false, axis:true});
+
var curve = brd.create('curve',[[],[]],{strokeColor:'gray',strokeWidth:2, dash:2});
s = brd.createElement('slider',[[10,70],[100,70],[0,1,1]]);   
 
deg = brd.createElement('slider',[[10,90],[100,90],[1,1,10]],{name:'degree',snapWidth:1});   
 
curve = brd.createElement('curve',[datax,[]],{strokeColor:'gray',dash:2});    
 
 
curve.updateDataArray = function() {
 
curve.updateDataArray = function() {
 
     var i, len = data.length;
 
     var i, len = data.length;
     for(i=0;i<len;i++) { this.dataY[i] = s.Value()*data[i]; }
+
    this.dataX = datax.slice(0,len);
 +
     for (i=0; i<len; i++) {
 +
      this.dataY[i] = s.Value()*data[i];  
 +
    }
 
}
 
}
regressionPolynomial = JXG.Math.Numerics.regressionPolynomial(deg,datax,curve.dataY); // generateFunction();
+
curve.update(); // Needed for correct glider position
  
reg = brd.createElement('functiongraph',[regressionPolynomial],{strokeColor:'black'});     
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var regressionPolynomial = JXG.Math.Numerics.regressionPolynomial(deg, datax, curve.dataY);
brd.createElement('glider',[100,30,reg],{strokeColor:'black'});   
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var reg = brd.create('functiongraph',[regressionPolynomial],{strokeColor:'blue', strokeWidth:4});     
regD = brd.createElement('functiongraph',[brd.D(regressionPolynomial)],{strokeColor:'red'});     
+
brd.create('glider',[100,30,reg],{strokeColor:'black'});     
  
t = brd.createElement('text',[20,40,
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t = brd.create('text',[20,40,
 
             function(){ return "r(x) = " + regressionPolynomial.getTerm();}
 
             function(){ return "r(x) = " + regressionPolynomial.getTerm();}
 
             ],
 
             ],
             {strokeColor:'black',fontSize:'14px'});     
+
             {strokeColor:'black',fontSize:18});     
  
 +
brd.unsuspendUpdate();
 
</jsxgraph>
 
</jsxgraph>
  
 
===The underlying JavaScript code===
 
===The underlying JavaScript code===
<source lang="xml">
+
<source lang="javascript">
 +
var data = "406.60 428.50 429.30 426.30 434.70 415.90 ... many points ... 521.80 524.40 526.80";
 +
data = data.split(' ');
 +
var datax = [];
 +
for (i = 0; i < data.length; i++)  {
 +
    data[i] = (parseFloat(data[i])-450.0);
 +
    datax[i] = i;
 +
}
 +
   
 +
var brd = JXG.JSXGraph.initBoard('jxgbox', {boundingbox:[-2, 100, data.length+2, -70], grid: false, axis:true});
 +
brd.suspendUpdate();
 +
var s = brd.create('slider',[[10,70],[80,70],[0,1,1]],{name:'scale'});   
 +
var deg = brd.create('slider',[[10,90],[80,90],[1,1,10]],{name:'degree',snapWidth:1});   
 +
curve.updateDataArray = function() {
 +
    var i, len = data.length;
 +
    this.dataX = datax.slice(0,len);
 +
    for (i=0; i<len; i++) {
 +
      this.dataY[i] = s.Value()*data[i];
 +
    }
 +
}
 +
curve.update(); // Needed for correct glider position
 +
 
 +
var regressionPolynomial = JXG.Math.Numerics.regressionPolynomial(deg, datax, curve.dataY);
 +
var reg = brd.create('functiongraph',[regressionPolynomial],{strokeColor:'blue', strokeWidth:4});   
 +
brd.create('glider',[100,30,reg],{strokeColor:'black'});   
 +
 
 +
t = brd.create('text',[20,40,
 +
            function(){ return "r(x) = " + regressionPolynomial.getTerm();}
 +
            ],
 +
            {strokeColor:'black',fontSize:18});   
 +
brd.unsuspendUpdate();
 
</source>
 
</source>
  
 
[[Category:Examples]]
 
[[Category:Examples]]

Latest revision as of 18:04, 21 November 2013

Through the points defining the dashed line the regression polynomial of degree 'degree' is computed and displayed. The points can be scaled by adjusting the slider 'scale'. The degree of the regression polynomial can be changed by using the slider 'degree'.

The underlying JavaScript code

var data = "406.60 428.50 429.30 426.30 434.70 415.90 ... many points ... 521.80 524.40 526.80";
data = data.split(' ');
var datax = [];
for (i = 0; i < data.length; i++)  { 
    data[i] = (parseFloat(data[i])-450.0); 
    datax[i] = i;
}
    
var brd = JXG.JSXGraph.initBoard('jxgbox', {boundingbox:[-2, 100, data.length+2, -70], grid: false, axis:true});
brd.suspendUpdate();
var s = brd.create('slider',[[10,70],[80,70],[0,1,1]],{name:'scale'});     
var deg = brd.create('slider',[[10,90],[80,90],[1,1,10]],{name:'degree',snapWidth:1});     
curve.updateDataArray = function() {
    var i, len = data.length;
    this.dataX = datax.slice(0,len); 
    for (i=0; i<len; i++) {
       this.dataY[i] = s.Value()*data[i]; 
    }
}
curve.update(); // Needed for correct glider position

var regressionPolynomial = JXG.Math.Numerics.regressionPolynomial(deg, datax, curve.dataY);
var reg = brd.create('functiongraph',[regressionPolynomial],{strokeColor:'blue', strokeWidth:4});     
brd.create('glider',[100,30,reg],{strokeColor:'black'});     

t = brd.create('text',[20,40,
            function(){ return "r(x) = " + regressionPolynomial.getTerm();}
            ],
            {strokeColor:'black',fontSize:18});     
brd.unsuspendUpdate();