## Saturday, 29 August 2015

### Maps, hurricanes and linear regression equation (correlation) in OpenWebGIS using JavaScript

When you create your maps with the help of online services, sometimes you surely want not only to see your data on the map, but also to make at least some mathematical analysis. For example, to create a chart reflecting the change in the data and to estimate how much your data is correlated in some attributes and to construct a linear regression equation. Not every online service for maps creation provides such an opportunity. In OpenWebGIS you can do it. In this article, we'll start talking about how you can do it yourself in your service using JavaScript language.
The whole code you can see in the function "ApplyChart" in the file "table.htm", if you download the javascript code using the menu item of OpenWebGIS "JavascriptSourceCode".

But this function is very large, since it solves many tasks, depending on the user's choice, but at the moment we are only interested in the process of calculating the correlation and linear regression equation coefficients. Next, we will describe user`s actions that involve the appropriate function blocks of "ApplyChart".
So let us start with the choice of data in the example of which we will show a mathematical calculation. We offer to take the data on hurricanes in the North Atlantic in 2004. Let's take the information about the three hurricanes of this season: IVAN, CHARLEY and JEANNE. We have put these hurricanes tracks on the OpenWebGIS map .The result is shown in Figure 1.
 Figure 1

You can open the map in this link. Further in order the users could analyze the data of the layer "Hurricanes2004", they must select the name of the layer (in this case select the layer "Hurricanes2004") with which we will work in the list of "Editable Layer" and click on the menu item "Edit->Open attribute table".  After that the new window will open (or Tab) "table.htm" and the user will see what is shown in Figure 2.
 Figure 2

Next, the user must specify which layer attributes will be used for creating the chart on the X axis and on the Y axis. Let`s suppose for example the attribute "PRESSURE" is along the X axis and the wind speed "WIND_MPH" is along the Y axis. In order to get a calculation of the correlation coefficient and the regression equation, the user must activate the "get line regression equation (y/x)" option.

Now finally we will turn to the JavaScript code. To describe it, we need to know the identifier of the "select" element in which we select an attribute on the X axis: id = "fieldChartX", on the Y axis:       id = "fieldChartY". Checkbox element ID for activating the process of correlation calculation is:      id = "id_CorrRegV".

For creating charts in OpenWebGIS the canvas element is used. So everything that in ApplyChart function refers to the correlation calculation begins with this:

`if(document.getElementById ('id_CorrRegV'). checked == true) {`

Be sure to have checked whether the user has specified the attributes for the X and Y axes and report the error to the user:
```var atX=document.getElementById("fieldChartX").value;
var atY=document.getElementById("fieldChartY").value
if(atX=="0"||atY=="0")
```
It is also important to check that the selected attributes of the analyzed layer contain numeric data and their number on the axes is equal to:
```var countV1 = 0; var feat1 = '';
var mLayers=window.opener.edilayerMainLayer;
countV1=mLayers.features.length;
feat1=mLayers.features;
var atrY=document.getElementById("fieldChartY").value;
if(isNaN(mLayers.features[0].attributes[atrY]*1)==true)
{alert("Error value is string "); return;}

var countV2 = 0; var feat2 = '';

countV2 = mLayers.features.length; feat2 = mLayers.features;
var atrX=document.getElementById("fieldChartX").value;
if(isNaN(mLayers.features[0].attributes[atrX]*1)==true)
{alert("Error value is string "); return;}
if (countV1!=countV2)
{alert("number of first value not equal number of second value"); return;}

```

After reviewing the code given above the question raises - What is the meaning of these expressions: "window.opener.edilayerMainLayer" and "mLayers.features"? To understand this, it is necessary to bear in mind that in OpenWebGIS to create maps and layers on the map, JavaScript is used. More about this you can see in the article "Heatmap, JavaScript, Openlayers and canvas". So in expression "window.opener.edilayerMainLayer" we appeal to the global variable "edilayerMainLayer", created in the main window ("opengis_eng.html") using the function "SeteditlayerMain(editlayerM)". This variable is qual to the analyzing layer (in this case, "Hurricanes2004") and its contents. Using the expression "mLayers.features" we obtain an array of all features (points, lines, polygons with their attributes, in this case it is the pressure and speed of the wind). In order to make it clearer what "features" are, we suggest to look at the documentation  of the object "OpenLayers.Feature" with the help of which every element of the array is created. But in your case you do not have to use OpenLayers and  instead of an array "mLayers.features" there can be any other array containing your data.

Get to the calculation of the correlation  coefficient and the coefficients of the regression equation. But first, we must refresh our memory on the mathematical theory of it. Please read about Correlation and dependence. So the sample correlation coefficient is written in Figure 3:
 Figure 3

where x and y are the sample means of X and Y, and sx and sy are the sample standard deviations of X and Y. To make these calculations using JavaScript, we have to loop over all the elements of the array "feat1" equal to "mLayers.features":
```var mean1 = 0; var mean2 = 0; sumV1V2 = 0; squaredVal1 = 0; squaredVal2 = 0;
var fielY=document.getElementById("fieldChartY").value;
var fielX=document.getElementById("fieldChartX").value;
for (var i = 0; i< feat1.length; i ++)
{
mean1 + = parseFloat (feat1[i].attributes[fielY]);
sumV1V2+=parseFloat(feat1[i].attributes[fielY])*
parseFloat(feat2[i].attributes[fielX]);
squaredVal1+=parseFloat(feat1[i].attributes[fielY])*
parseFloat(feat1[i].attributes[fielY]);
mean2 + = parseFloat (feat2[i].attributes [fielX]);
squaredVal2+=parseFloat(feat2[i].attributes[fielX])*
parseFloat(feat2[i].attributes[fielX]);
}
```

After passing this "for" loop, calculate the means of X and Y:
```mean1 = mean1 / feat1.length;
mean2 = mean2 / feat2.length;
```

Then calculate the variance of X and Y:
```sumV1V2 = sumV1V2 / feat1.length;
variance1 = (squaredVal1 / feat1.length) - (mean1 * mean1);
variance2 = (squaredVal2 / feat1.length) - (mean2 * mean2);
Finally calculate the sample correlation coefficient:
CoefCorr=(sumV1V2-(mean1*mean2))/(Math.pow(variance1,0.5)*Math.pow(variance2,0.5));
```

Where "Math.pow(variance1,0.5)" and "Math.pow(variance2,0.5)" is standard deviations sx and sy .
Function "Math.pow" - is exponentiation function. Expression "Math.pow(variance1,0.5)" according to the rules of mathematics is equivalent to the square root of variance1.
Calculate the regression coefficients according to the rules:
 Figure 4

 Figure 5

In javascript syntax it will be:
```var b = (sumV1V2-(mean1*mean2))/variance2;
var a = mean1-b * mean2;
```

The results are recorded in the item "textarea" element:
```if (document.getElementById ('id_CorrRegV'). checked == true)
{
var DivAreaLeg = document.createElement ("textarea");
DivAreaLeg.id = "id_correlDiv_textarea";
DivAreaLeg.style.width=250;
DivAreaLeg.style.height=80;
if(!document.getElementById("id_correlDiv_textarea"))
{document.getElementById("id_correlDiv").appendChild(DivAreaLeg);}
document.getElementById("id_correlDiv_textarea").value=
'correlation coefficient:'+CoefCorr+'\n'+'varianceY:'+
variance1+'\n'+'varianceX:'+variance2+'\n'+
'regression equation:'+document.getElementById("fieldChartY").value+'='+
a+'+'+b+'*'+document.getElementById("fieldChartX").value;

parseFloat(window.opener.edilayerMainLayer.features[0].attributes[fieldSel2]);
context.fillRect (LenX * 0 +40, NumberChartC, 3, 3);
context.beginPath (); context.moveTo(LenX * 0 +40, NumberChartC);
var var_last=window.opener.edilayerMainLayer.features.length-1;
parseFloat(window.opener.edilayerMainLayer.features[var_last].attributes[fieldSel2]);
context.lineTo(LenX*((arrayFeat2.length-1)) + 40, NumberChartC2);
context.stroke ();
}
```

Here, the variable "context" is the context of canvas element in which our chart is creating. On page "table.htm" it is defined as follows:
```var myWinChartKV = window;
var drawingCanvas0 = myWinChartKV.document.getElementById ('id_canvas1Chart');
var context = drawingCanvas0.getContext ('2d');
```

But we are not going to tell about the chart creating using the canvas element in this article, because it is a topic for another article.
So the function "ApplyChart()" (parts of which we have described above) is linked to the button "Create Chart". After the user selects the axes X and Y and activates the option "get line regression equation (y / x)" and clicks "Create Chart" button - the user will see the result as shown in Figure 6.
 Figure 6

Pay your attention to a textarea element (in the lower left corner), there all calculated coefficients and variances are listed.
As can be seen, the regression equation:
WIND_MPH = 1456.3434664919223-1.4083907778030962 * PRESSURE,
and correlation coefficient= -0.954741767863270 describe well the identified dependence of wind speed and pressure in hurricanes. The user can customize the chart style (using the "open options of chart") such as shown in Figure 7. How to do it with the help of JavaScript we will discuss in other articles.
 Figure 7

But attention! In this article we used the data on the three hurricanes at the same time only as an example for the calculation of regression and correlation coefficient. And the resulting linear relationship can not be used for any scientific conclusions. In fact, it is desirable to analyze the data on hurricanes separately. Also depending on the time passed since the beginning of the hurricane and depending on the location within the hurricane, pressure and wind speed have much more complex relationship. The relationship is linear only in some track parts. It can be seen from Figures 8 and 9.
 Figure 8 - Wind Speed, Gust, and Sea Level Pressure at Cape Lookout, NC during Hurricane Irene (taken from the site of NOAA http://www.ndbc.noaa.gov/hurricanes/2011/irene/)

 Figure 9 - Pressure and Winds in hurricanes,

That's all, I wish you success in the automation of mathematical calculations and creating charts and maps using JavaScript.