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<HTML> <BODY BGCOLOR="white"> <PRE> <FONT color="green">001</FONT> /*<a name="line.1"></a> <FONT color="green">002</FONT> * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a> <FONT color="green">003</FONT> * contributor license agreements. See the NOTICE file distributed with<a name="line.3"></a> <FONT color="green">004</FONT> * this work for additional information regarding copyright ownership.<a name="line.4"></a> <FONT color="green">005</FONT> * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a> <FONT color="green">006</FONT> * (the "License"); you may not use this file except in compliance with<a name="line.6"></a> <FONT color="green">007</FONT> * the License. You may obtain a copy of the License at<a name="line.7"></a> <FONT color="green">008</FONT> *<a name="line.8"></a> <FONT color="green">009</FONT> * http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a> <FONT color="green">010</FONT> *<a name="line.10"></a> <FONT color="green">011</FONT> * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a> <FONT color="green">012</FONT> * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a> <FONT color="green">013</FONT> * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a> <FONT color="green">014</FONT> * See the License for the specific language governing permissions and<a name="line.14"></a> <FONT color="green">015</FONT> * limitations under the License.<a name="line.15"></a> <FONT color="green">016</FONT> */<a name="line.16"></a> <FONT color="green">017</FONT> <a name="line.17"></a> <FONT color="green">018</FONT> package org.apache.commons.math.stat.regression;<a name="line.18"></a> <FONT color="green">019</FONT> import java.io.Serializable;<a name="line.19"></a> <FONT color="green">020</FONT> <a name="line.20"></a> <FONT color="green">021</FONT> import org.apache.commons.math.MathException;<a name="line.21"></a> <FONT color="green">022</FONT> import org.apache.commons.math.MathRuntimeException;<a name="line.22"></a> <FONT color="green">023</FONT> import org.apache.commons.math.distribution.TDistribution;<a name="line.23"></a> <FONT color="green">024</FONT> import org.apache.commons.math.distribution.TDistributionImpl;<a name="line.24"></a> <FONT color="green">025</FONT> <a name="line.25"></a> <FONT color="green">026</FONT> /**<a name="line.26"></a> <FONT color="green">027</FONT> * Estimates an ordinary least squares regression model<a name="line.27"></a> <FONT color="green">028</FONT> * with one independent variable.<a name="line.28"></a> <FONT color="green">029</FONT> * <p><a name="line.29"></a> <FONT color="green">030</FONT> * <code> y = intercept + slope * x </code></p><a name="line.30"></a> <FONT color="green">031</FONT> * <p><a name="line.31"></a> <FONT color="green">032</FONT> * Standard errors for <code>intercept</code> and <code>slope</code> are<a name="line.32"></a> <FONT color="green">033</FONT> * available as well as ANOVA, r-square and Pearson's r statistics.</p><a name="line.33"></a> <FONT color="green">034</FONT> * <p><a name="line.34"></a> <FONT color="green">035</FONT> * Observations (x,y pairs) can be added to the model one at a time or they<a name="line.35"></a> <FONT color="green">036</FONT> * can be provided in a 2-dimensional array. The observations are not stored<a name="line.36"></a> <FONT color="green">037</FONT> * in memory, so there is no limit to the number of observations that can be<a name="line.37"></a> <FONT color="green">038</FONT> * added to the model.</p><a name="line.38"></a> <FONT color="green">039</FONT> * <p><a name="line.39"></a> <FONT color="green">040</FONT> * <strong>Usage Notes</strong>: <ul><a name="line.40"></a> <FONT color="green">041</FONT> * <li> When there are fewer than two observations in the model, or when<a name="line.41"></a> <FONT color="green">042</FONT> * there is no variation in the x values (i.e. all x values are the same)<a name="line.42"></a> <FONT color="green">043</FONT> * all statistics return <code>NaN</code>. At least two observations with<a name="line.43"></a> <FONT color="green">044</FONT> * different x coordinates are requred to estimate a bivariate regression<a name="line.44"></a> <FONT color="green">045</FONT> * model.<a name="line.45"></a> <FONT color="green">046</FONT> * </li><a name="line.46"></a> <FONT color="green">047</FONT> * <li> getters for the statistics always compute values based on the current<a name="line.47"></a> <FONT color="green">048</FONT> * set of observations -- i.e., you can get statistics, then add more data<a name="line.48"></a> <FONT color="green">049</FONT> * and get updated statistics without using a new instance. There is no<a name="line.49"></a> <FONT color="green">050</FONT> * "compute" method that updates all statistics. Each of the getters performs<a name="line.50"></a> <FONT color="green">051</FONT> * the necessary computations to return the requested statistic.</li><a name="line.51"></a> <FONT color="green">052</FONT> * </ul></p><a name="line.52"></a> <FONT color="green">053</FONT> *<a name="line.53"></a> <FONT color="green">054</FONT> * @version $Revision: 811685 $ $Date: 2009-09-05 13:36:48 -0400 (Sat, 05 Sep 2009) $<a name="line.54"></a> <FONT color="green">055</FONT> */<a name="line.55"></a> <FONT color="green">056</FONT> public class SimpleRegression implements Serializable {<a name="line.56"></a> <FONT color="green">057</FONT> <a name="line.57"></a> <FONT color="green">058</FONT> /** Serializable version identifier */<a name="line.58"></a> <FONT color="green">059</FONT> private static final long serialVersionUID = -3004689053607543335L;<a name="line.59"></a> <FONT color="green">060</FONT> <a name="line.60"></a> <FONT color="green">061</FONT> /** the distribution used to compute inference statistics. */<a name="line.61"></a> <FONT color="green">062</FONT> private TDistribution distribution;<a name="line.62"></a> <FONT color="green">063</FONT> <a name="line.63"></a> <FONT color="green">064</FONT> /** sum of x values */<a name="line.64"></a> <FONT color="green">065</FONT> private double sumX = 0d;<a name="line.65"></a> <FONT color="green">066</FONT> <a name="line.66"></a> <FONT color="green">067</FONT> /** total variation in x (sum of squared deviations from xbar) */<a name="line.67"></a> <FONT color="green">068</FONT> private double sumXX = 0d;<a name="line.68"></a> <FONT color="green">069</FONT> <a name="line.69"></a> <FONT color="green">070</FONT> /** sum of y values */<a name="line.70"></a> <FONT color="green">071</FONT> private double sumY = 0d;<a name="line.71"></a> <FONT color="green">072</FONT> <a name="line.72"></a> <FONT color="green">073</FONT> /** total variation in y (sum of squared deviations from ybar) */<a name="line.73"></a> <FONT color="green">074</FONT> private double sumYY = 0d;<a name="line.74"></a> <FONT color="green">075</FONT> <a name="line.75"></a> <FONT color="green">076</FONT> /** sum of products */<a name="line.76"></a> <FONT color="green">077</FONT> private double sumXY = 0d;<a name="line.77"></a> <FONT color="green">078</FONT> <a name="line.78"></a> <FONT color="green">079</FONT> /** number of observations */<a name="line.79"></a> <FONT color="green">080</FONT> private long n = 0;<a name="line.80"></a> <FONT color="green">081</FONT> <a name="line.81"></a> <FONT color="green">082</FONT> /** mean of accumulated x values, used in updating formulas */<a name="line.82"></a> <FONT color="green">083</FONT> private double xbar = 0;<a name="line.83"></a> <FONT color="green">084</FONT> <a name="line.84"></a> <FONT color="green">085</FONT> /** mean of accumulated y values, used in updating formulas */<a name="line.85"></a> <FONT color="green">086</FONT> private double ybar = 0;<a name="line.86"></a> <FONT color="green">087</FONT> <a name="line.87"></a> <FONT color="green">088</FONT> // ---------------------Public methods--------------------------------------<a name="line.88"></a> <FONT color="green">089</FONT> <a name="line.89"></a> <FONT color="green">090</FONT> /**<a name="line.90"></a> <FONT color="green">091</FONT> * Create an empty SimpleRegression instance<a name="line.91"></a> <FONT color="green">092</FONT> */<a name="line.92"></a> <FONT color="green">093</FONT> public SimpleRegression() {<a name="line.93"></a> <FONT color="green">094</FONT> this(new TDistributionImpl(1.0));<a name="line.94"></a> <FONT color="green">095</FONT> }<a name="line.95"></a> <FONT color="green">096</FONT> <a name="line.96"></a> <FONT color="green">097</FONT> /**<a name="line.97"></a> <FONT color="green">098</FONT> * Create an empty SimpleRegression using the given distribution object to<a name="line.98"></a> <FONT color="green">099</FONT> * compute inference statistics.<a name="line.99"></a> <FONT color="green">100</FONT> * @param t the distribution used to compute inference statistics.<a name="line.100"></a> <FONT color="green">101</FONT> * @since 1.2<a name="line.101"></a> <FONT color="green">102</FONT> */<a name="line.102"></a> <FONT color="green">103</FONT> public SimpleRegression(TDistribution t) {<a name="line.103"></a> <FONT color="green">104</FONT> super();<a name="line.104"></a> <FONT color="green">105</FONT> setDistribution(t);<a name="line.105"></a> <FONT color="green">106</FONT> }<a name="line.106"></a> <FONT color="green">107</FONT> <a name="line.107"></a> <FONT color="green">108</FONT> /**<a name="line.108"></a> <FONT color="green">109</FONT> * Adds the observation (x,y) to the regression data set.<a name="line.109"></a> <FONT color="green">110</FONT> * <p><a name="line.110"></a> <FONT color="green">111</FONT> * Uses updating formulas for means and sums of squares defined in<a name="line.111"></a> <FONT color="green">112</FONT> * "Algorithms for Computing the Sample Variance: Analysis and<a name="line.112"></a> <FONT color="green">113</FONT> * Recommendations", Chan, T.F., Golub, G.H., and LeVeque, R.J.<a name="line.113"></a> <FONT color="green">114</FONT> * 1983, American Statistician, vol. 37, pp. 242-247, referenced in<a name="line.114"></a> <FONT color="green">115</FONT> * Weisberg, S. "Applied Linear Regression". 2nd Ed. 1985.</p><a name="line.115"></a> <FONT color="green">116</FONT> *<a name="line.116"></a> <FONT color="green">117</FONT> *<a name="line.117"></a> <FONT color="green">118</FONT> * @param x independent variable value<a name="line.118"></a> <FONT color="green">119</FONT> * @param y dependent variable value<a name="line.119"></a> <FONT color="green">120</FONT> */<a name="line.120"></a> <FONT color="green">121</FONT> public void addData(double x, double y) {<a name="line.121"></a> <FONT color="green">122</FONT> if (n == 0) {<a name="line.122"></a> <FONT color="green">123</FONT> xbar = x;<a name="line.123"></a> <FONT color="green">124</FONT> ybar = y;<a name="line.124"></a> <FONT color="green">125</FONT> } else {<a name="line.125"></a> <FONT color="green">126</FONT> double dx = x - xbar;<a name="line.126"></a> <FONT color="green">127</FONT> double dy = y - ybar;<a name="line.127"></a> <FONT color="green">128</FONT> sumXX += dx * dx * (double) n / (n + 1d);<a name="line.128"></a> <FONT color="green">129</FONT> sumYY += dy * dy * (double) n / (n + 1d);<a name="line.129"></a> <FONT color="green">130</FONT> sumXY += dx * dy * (double) n / (n + 1d);<a name="line.130"></a> <FONT color="green">131</FONT> xbar += dx / (n + 1.0);<a name="line.131"></a> <FONT color="green">132</FONT> ybar += dy / (n + 1.0);<a name="line.132"></a> <FONT color="green">133</FONT> }<a name="line.133"></a> <FONT color="green">134</FONT> sumX += x;<a name="line.134"></a> <FONT color="green">135</FONT> sumY += y;<a name="line.135"></a> <FONT color="green">136</FONT> n++;<a name="line.136"></a> <FONT color="green">137</FONT> <a name="line.137"></a> <FONT color="green">138</FONT> if (n > 2) {<a name="line.138"></a> <FONT color="green">139</FONT> distribution.setDegreesOfFreedom(n - 2);<a name="line.139"></a> <FONT color="green">140</FONT> }<a name="line.140"></a> <FONT color="green">141</FONT> }<a name="line.141"></a> <FONT color="green">142</FONT> <a name="line.142"></a> <FONT color="green">143</FONT> <a name="line.143"></a> <FONT color="green">144</FONT> /**<a name="line.144"></a> <FONT color="green">145</FONT> * Removes the observation (x,y) from the regression data set.<a name="line.145"></a> <FONT color="green">146</FONT> * <p><a name="line.146"></a> <FONT color="green">147</FONT> * Mirrors the addData method. This method permits the use of<a name="line.147"></a> <FONT color="green">148</FONT> * SimpleRegression instances in streaming mode where the regression<a name="line.148"></a> <FONT color="green">149</FONT> * is applied to a sliding "window" of observations, however the caller is<a name="line.149"></a> <FONT color="green">150</FONT> * responsible for maintaining the set of observations in the window.</p><a name="line.150"></a> <FONT color="green">151</FONT> *<a name="line.151"></a> <FONT color="green">152</FONT> * The method has no effect if there are no points of data (i.e. n=0)<a name="line.152"></a> <FONT color="green">153</FONT> *<a name="line.153"></a> <FONT color="green">154</FONT> * @param x independent variable value<a name="line.154"></a> <FONT color="green">155</FONT> * @param y dependent variable value<a name="line.155"></a> <FONT color="green">156</FONT> */<a name="line.156"></a> <FONT color="green">157</FONT> public void removeData(double x, double y) {<a name="line.157"></a> <FONT color="green">158</FONT> if (n > 0) {<a name="line.158"></a> <FONT color="green">159</FONT> double dx = x - xbar;<a name="line.159"></a> <FONT color="green">160</FONT> double dy = y - ybar;<a name="line.160"></a> <FONT color="green">161</FONT> sumXX -= dx * dx * (double) n / (n - 1d);<a name="line.161"></a> <FONT color="green">162</FONT> sumYY -= dy * dy * (double) n / (n - 1d);<a name="line.162"></a> <FONT color="green">163</FONT> sumXY -= dx * dy * (double) n / (n - 1d);<a name="line.163"></a> <FONT color="green">164</FONT> xbar -= dx / (n - 1.0);<a name="line.164"></a> <FONT color="green">165</FONT> ybar -= dy / (n - 1.0);<a name="line.165"></a> <FONT color="green">166</FONT> sumX -= x;<a name="line.166"></a> <FONT color="green">167</FONT> sumY -= y;<a name="line.167"></a> <FONT color="green">168</FONT> n--;<a name="line.168"></a> <FONT color="green">169</FONT> <a name="line.169"></a> <FONT color="green">170</FONT> if (n > 2) {<a name="line.170"></a> <FONT color="green">171</FONT> distribution.setDegreesOfFreedom(n - 2);<a name="line.171"></a> <FONT color="green">172</FONT> }<a name="line.172"></a> <FONT color="green">173</FONT> }<a name="line.173"></a> <FONT color="green">174</FONT> }<a name="line.174"></a> <FONT color="green">175</FONT> <a name="line.175"></a> <FONT color="green">176</FONT> /**<a name="line.176"></a> <FONT color="green">177</FONT> * Adds the observations represented by the elements in<a name="line.177"></a> <FONT color="green">178</FONT> * <code>data</code>.<a name="line.178"></a> <FONT color="green">179</FONT> * <p><a name="line.179"></a> <FONT color="green">180</FONT> * <code>(data[0][0],data[0][1])</code> will be the first observation, then<a name="line.180"></a> <FONT color="green">181</FONT> * <code>(data[1][0],data[1][1])</code>, etc.</p><a name="line.181"></a> <FONT color="green">182</FONT> * <p><a name="line.182"></a> <FONT color="green">183</FONT> * This method does not replace data that has already been added. The<a name="line.183"></a> <FONT color="green">184</FONT> * observations represented by <code>data</code> are added to the existing<a name="line.184"></a> <FONT color="green">185</FONT> * dataset.</p><a name="line.185"></a> <FONT color="green">186</FONT> * <p><a name="line.186"></a> <FONT color="green">187</FONT> * To replace all data, use <code>clear()</code> before adding the new<a name="line.187"></a> <FONT color="green">188</FONT> * data.</p><a name="line.188"></a> <FONT color="green">189</FONT> *<a name="line.189"></a> <FONT color="green">190</FONT> * @param data array of observations to be added<a name="line.190"></a> <FONT color="green">191</FONT> */<a name="line.191"></a> <FONT color="green">192</FONT> public void addData(double[][] data) {<a name="line.192"></a> <FONT color="green">193</FONT> for (int i = 0; i < data.length; i++) {<a name="line.193"></a> <FONT color="green">194</FONT> addData(data[i][0], data[i][1]);<a name="line.194"></a> <FONT color="green">195</FONT> }<a name="line.195"></a> <FONT color="green">196</FONT> }<a name="line.196"></a> <FONT color="green">197</FONT> <a name="line.197"></a> <FONT color="green">198</FONT> <a name="line.198"></a> <FONT color="green">199</FONT> /**<a name="line.199"></a> <FONT color="green">200</FONT> * Removes observations represented by the elements in <code>data</code>.<a name="line.200"></a> <FONT color="green">201</FONT> * <p><a name="line.201"></a> <FONT color="green">202</FONT> * If the array is larger than the current n, only the first n elements are<a name="line.202"></a> <FONT color="green">203</FONT> * processed. This method permits the use of SimpleRegression instances in<a name="line.203"></a> <FONT color="green">204</FONT> * streaming mode where the regression is applied to a sliding "window" of<a name="line.204"></a> <FONT color="green">205</FONT> * observations, however the caller is responsible for maintaining the set<a name="line.205"></a> <FONT color="green">206</FONT> * of observations in the window.</p><a name="line.206"></a> <FONT color="green">207</FONT> * <p><a name="line.207"></a> <FONT color="green">208</FONT> * To remove all data, use <code>clear()</code>.</p><a name="line.208"></a> <FONT color="green">209</FONT> *<a name="line.209"></a> <FONT color="green">210</FONT> * @param data array of observations to be removed<a name="line.210"></a> <FONT color="green">211</FONT> */<a name="line.211"></a> <FONT color="green">212</FONT> public void removeData(double[][] data) {<a name="line.212"></a> <FONT color="green">213</FONT> for (int i = 0; i < data.length && n > 0; i++) {<a name="line.213"></a> <FONT color="green">214</FONT> removeData(data[i][0], data[i][1]);<a name="line.214"></a> <FONT color="green">215</FONT> }<a name="line.215"></a> <FONT color="green">216</FONT> }<a name="line.216"></a> <FONT color="green">217</FONT> <a name="line.217"></a> <FONT color="green">218</FONT> /**<a name="line.218"></a> <FONT color="green">219</FONT> * Clears all data from the model.<a name="line.219"></a> <FONT color="green">220</FONT> */<a name="line.220"></a> <FONT color="green">221</FONT> public void clear() {<a name="line.221"></a> <FONT color="green">222</FONT> sumX = 0d;<a name="line.222"></a> <FONT color="green">223</FONT> sumXX = 0d;<a name="line.223"></a> <FONT color="green">224</FONT> sumY = 0d;<a name="line.224"></a> <FONT color="green">225</FONT> sumYY = 0d;<a name="line.225"></a> <FONT color="green">226</FONT> sumXY = 0d;<a name="line.226"></a> <FONT color="green">227</FONT> n = 0;<a name="line.227"></a> <FONT color="green">228</FONT> }<a name="line.228"></a> <FONT color="green">229</FONT> <a name="line.229"></a> <FONT color="green">230</FONT> /**<a name="line.230"></a> <FONT color="green">231</FONT> * Returns the number of observations that have been added to the model.<a name="line.231"></a> <FONT color="green">232</FONT> *<a name="line.232"></a> <FONT color="green">233</FONT> * @return n number of observations that have been added.<a name="line.233"></a> <FONT color="green">234</FONT> */<a name="line.234"></a> <FONT color="green">235</FONT> public long getN() {<a name="line.235"></a> <FONT color="green">236</FONT> return n;<a name="line.236"></a> <FONT color="green">237</FONT> }<a name="line.237"></a> <FONT color="green">238</FONT> <a name="line.238"></a> <FONT color="green">239</FONT> /**<a name="line.239"></a> <FONT color="green">240</FONT> * Returns the "predicted" <code>y</code> value associated with the<a name="line.240"></a> <FONT color="green">241</FONT> * supplied <code>x</code> value, based on the data that has been<a name="line.241"></a> <FONT color="green">242</FONT> * added to the model when this method is activated.<a name="line.242"></a> <FONT color="green">243</FONT> * <p><a name="line.243"></a> <FONT color="green">244</FONT> * <code> predict(x) = intercept + slope * x </code></p><a name="line.244"></a> <FONT color="green">245</FONT> * <p><a name="line.245"></a> <FONT color="green">246</FONT> * <strong>Preconditions</strong>: <ul><a name="line.246"></a> <FONT color="green">247</FONT> * <li>At least two observations (with at least two different x values)<a name="line.247"></a> <FONT color="green">248</FONT> * must have been added before invoking this method. If this method is<a name="line.248"></a> <FONT color="green">249</FONT> * invoked before a model can be estimated, <code>Double,NaN</code> is<a name="line.249"></a> <FONT color="green">250</FONT> * returned.<a name="line.250"></a> <FONT color="green">251</FONT> * </li></ul></p><a name="line.251"></a> <FONT color="green">252</FONT> *<a name="line.252"></a> <FONT color="green">253</FONT> * @param x input <code>x</code> value<a name="line.253"></a> <FONT color="green">254</FONT> * @return predicted <code>y</code> value<a name="line.254"></a> <FONT color="green">255</FONT> */<a name="line.255"></a> <FONT color="green">256</FONT> public double predict(double x) {<a name="line.256"></a> <FONT color="green">257</FONT> double b1 = getSlope();<a name="line.257"></a> <FONT color="green">258</FONT> return getIntercept(b1) + b1 * x;<a name="line.258"></a> <FONT color="green">259</FONT> }<a name="line.259"></a> <FONT color="green">260</FONT> <a name="line.260"></a> <FONT color="green">261</FONT> /**<a name="line.261"></a> <FONT color="green">262</FONT> * Returns the intercept of the estimated regression line.<a name="line.262"></a> <FONT color="green">263</FONT> * <p><a name="line.263"></a> <FONT color="green">264</FONT> * The least squares estimate of the intercept is computed using the<a name="line.264"></a> <FONT color="green">265</FONT> * <a href="http://www.xycoon.com/estimation4.htm">normal equations</a>.<a name="line.265"></a> <FONT color="green">266</FONT> * The intercept is sometimes denoted b0.</p><a name="line.266"></a> <FONT color="green">267</FONT> * <p><a name="line.267"></a> <FONT color="green">268</FONT> * <strong>Preconditions</strong>: <ul><a name="line.268"></a> <FONT color="green">269</FONT> * <li>At least two observations (with at least two different x values)<a name="line.269"></a> <FONT color="green">270</FONT> * must have been added before invoking this method. If this method is<a name="line.270"></a> <FONT color="green">271</FONT> * invoked before a model can be estimated, <code>Double,NaN</code> is<a name="line.271"></a> <FONT color="green">272</FONT> * returned.<a name="line.272"></a> <FONT color="green">273</FONT> * </li></ul></p><a name="line.273"></a> <FONT color="green">274</FONT> *<a name="line.274"></a> <FONT color="green">275</FONT> * @return the intercept of the regression line<a name="line.275"></a> <FONT color="green">276</FONT> */<a name="line.276"></a> <FONT color="green">277</FONT> public double getIntercept() {<a name="line.277"></a> <FONT color="green">278</FONT> return getIntercept(getSlope());<a name="line.278"></a> <FONT color="green">279</FONT> }<a name="line.279"></a> <FONT color="green">280</FONT> <a name="line.280"></a> <FONT color="green">281</FONT> /**<a name="line.281"></a> <FONT color="green">282</FONT> * Returns the slope of the estimated regression line.<a name="line.282"></a> <FONT color="green">283</FONT> * <p><a name="line.283"></a> <FONT color="green">284</FONT> * The least squares estimate of the slope is computed using the<a name="line.284"></a> <FONT color="green">285</FONT> * <a href="http://www.xycoon.com/estimation4.htm">normal equations</a>.<a name="line.285"></a> <FONT color="green">286</FONT> * The slope is sometimes denoted b1.</p><a name="line.286"></a> <FONT color="green">287</FONT> * <p><a name="line.287"></a> <FONT color="green">288</FONT> * <strong>Preconditions</strong>: <ul><a name="line.288"></a> <FONT color="green">289</FONT> * <li>At least two observations (with at least two different x values)<a name="line.289"></a> <FONT color="green">290</FONT> * must have been added before invoking this method. If this method is<a name="line.290"></a> <FONT color="green">291</FONT> * invoked before a model can be estimated, <code>Double.NaN</code> is<a name="line.291"></a> <FONT color="green">292</FONT> * returned.<a name="line.292"></a> <FONT color="green">293</FONT> * </li></ul></p><a name="line.293"></a> <FONT color="green">294</FONT> *<a name="line.294"></a> <FONT color="green">295</FONT> * @return the slope of the regression line<a name="line.295"></a> <FONT color="green">296</FONT> */<a name="line.296"></a> <FONT color="green">297</FONT> public double getSlope() {<a name="line.297"></a> <FONT color="green">298</FONT> if (n < 2) {<a name="line.298"></a> <FONT color="green">299</FONT> return Double.NaN; //not enough data<a name="line.299"></a> <FONT color="green">300</FONT> }<a name="line.300"></a> <FONT color="green">301</FONT> if (Math.abs(sumXX) < 10 * Double.MIN_VALUE) {<a name="line.301"></a> <FONT color="green">302</FONT> return Double.NaN; //not enough variation in x<a name="line.302"></a> <FONT color="green">303</FONT> }<a name="line.303"></a> <FONT color="green">304</FONT> return sumXY / sumXX;<a name="line.304"></a> <FONT color="green">305</FONT> }<a name="line.305"></a> <FONT color="green">306</FONT> <a name="line.306"></a> <FONT color="green">307</FONT> /**<a name="line.307"></a> <FONT color="green">308</FONT> * Returns the <a href="http://www.xycoon.com/SumOfSquares.htm"><a name="line.308"></a> <FONT color="green">309</FONT> * sum of squared errors</a> (SSE) associated with the regression<a name="line.309"></a> <FONT color="green">310</FONT> * model.<a name="line.310"></a> <FONT color="green">311</FONT> * <p><a name="line.311"></a> <FONT color="green">312</FONT> * The sum is computed using the computational formula</p><a name="line.312"></a> <FONT color="green">313</FONT> * <p><a name="line.313"></a> <FONT color="green">314</FONT> * <code>SSE = SYY - (SXY * SXY / SXX)</code></p><a name="line.314"></a> <FONT color="green">315</FONT> * <p><a name="line.315"></a> <FONT color="green">316</FONT> * where <code>SYY</code> is the sum of the squared deviations of the y<a name="line.316"></a> <FONT color="green">317</FONT> * values about their mean, <code>SXX</code> is similarly defined and<a name="line.317"></a> <FONT color="green">318</FONT> * <code>SXY</code> is the sum of the products of x and y mean deviations.<a name="line.318"></a> <FONT color="green">319</FONT> * </p><p><a name="line.319"></a> <FONT color="green">320</FONT> * The sums are accumulated using the updating algorithm referenced in<a name="line.320"></a> <FONT color="green">321</FONT> * {@link #addData}.</p><a name="line.321"></a> <FONT color="green">322</FONT> * <p><a name="line.322"></a> <FONT color="green">323</FONT> * The return value is constrained to be non-negative - i.e., if due to<a name="line.323"></a> <FONT color="green">324</FONT> * rounding errors the computational formula returns a negative result,<a name="line.324"></a> <FONT color="green">325</FONT> * 0 is returned.</p><a name="line.325"></a> <FONT color="green">326</FONT> * <p><a name="line.326"></a> <FONT color="green">327</FONT> * <strong>Preconditions</strong>: <ul><a name="line.327"></a> <FONT color="green">328</FONT> * <li>At least two observations (with at least two different x values)<a name="line.328"></a> <FONT color="green">329</FONT> * must have been added before invoking this method. If this method is<a name="line.329"></a> <FONT color="green">330</FONT> * invoked before a model can be estimated, <code>Double,NaN</code> is<a name="line.330"></a> <FONT color="green">331</FONT> * returned.<a name="line.331"></a> <FONT color="green">332</FONT> * </li></ul></p><a name="line.332"></a> <FONT color="green">333</FONT> *<a name="line.333"></a> <FONT color="green">334</FONT> * @return sum of squared errors associated with the regression model<a name="line.334"></a> <FONT color="green">335</FONT> */<a name="line.335"></a> <FONT color="green">336</FONT> public double getSumSquaredErrors() {<a name="line.336"></a> <FONT color="green">337</FONT> return Math.max(0d, sumYY - sumXY * sumXY / sumXX);<a name="line.337"></a> <FONT color="green">338</FONT> }<a name="line.338"></a> <FONT color="green">339</FONT> <a name="line.339"></a> <FONT color="green">340</FONT> /**<a name="line.340"></a> <FONT color="green">341</FONT> * Returns the sum of squared deviations of the y values about their mean.<a name="line.341"></a> <FONT color="green">342</FONT> * <p><a name="line.342"></a> <FONT color="green">343</FONT> * This is defined as SSTO<a name="line.343"></a> <FONT color="green">344</FONT> * <a href="http://www.xycoon.com/SumOfSquares.htm">here</a>.</p><a name="line.344"></a> <FONT color="green">345</FONT> * <p><a name="line.345"></a> <FONT color="green">346</FONT> * If <code>n < 2</code>, this returns <code>Double.NaN</code>.</p><a name="line.346"></a> <FONT color="green">347</FONT> *<a name="line.347"></a> <FONT color="green">348</FONT> * @return sum of squared deviations of y values<a name="line.348"></a> <FONT color="green">349</FONT> */<a name="line.349"></a> <FONT color="green">350</FONT> public double getTotalSumSquares() {<a name="line.350"></a> <FONT color="green">351</FONT> if (n < 2) {<a name="line.351"></a> <FONT color="green">352</FONT> return Double.NaN;<a name="line.352"></a> <FONT color="green">353</FONT> }<a name="line.353"></a> <FONT color="green">354</FONT> return sumYY;<a name="line.354"></a> <FONT color="green">355</FONT> }<a name="line.355"></a> <FONT color="green">356</FONT> <a name="line.356"></a> <FONT color="green">357</FONT> /**<a name="line.357"></a> <FONT color="green">358</FONT> * Returns the sum of squared deviations of the x values about their mean.<a name="line.358"></a> <FONT color="green">359</FONT> *<a name="line.359"></a> <FONT color="green">360</FONT> * If <code>n < 2</code>, this returns <code>Double.NaN</code>.</p><a name="line.360"></a> <FONT color="green">361</FONT> *<a name="line.361"></a> <FONT color="green">362</FONT> * @return sum of squared deviations of x values<a name="line.362"></a> <FONT color="green">363</FONT> */<a name="line.363"></a> <FONT color="green">364</FONT> public double getXSumSquares() {<a name="line.364"></a> <FONT color="green">365</FONT> if (n < 2) {<a name="line.365"></a> <FONT color="green">366</FONT> return Double.NaN;<a name="line.366"></a> <FONT color="green">367</FONT> }<a name="line.367"></a> <FONT color="green">368</FONT> return sumXX;<a name="line.368"></a> <FONT color="green">369</FONT> }<a name="line.369"></a> <FONT color="green">370</FONT> <a name="line.370"></a> <FONT color="green">371</FONT> /**<a name="line.371"></a> <FONT color="green">372</FONT> * Returns the sum of crossproducts, x<sub>i</sub>*y<sub>i</sub>.<a name="line.372"></a> <FONT color="green">373</FONT> *<a name="line.373"></a> <FONT color="green">374</FONT> * @return sum of cross products<a name="line.374"></a> <FONT color="green">375</FONT> */<a name="line.375"></a> <FONT color="green">376</FONT> public double getSumOfCrossProducts() {<a name="line.376"></a> <FONT color="green">377</FONT> return sumXY;<a name="line.377"></a> <FONT color="green">378</FONT> }<a name="line.378"></a> <FONT color="green">379</FONT> <a name="line.379"></a> <FONT color="green">380</FONT> /**<a name="line.380"></a> <FONT color="green">381</FONT> * Returns the sum of squared deviations of the predicted y values about<a name="line.381"></a> <FONT color="green">382</FONT> * their mean (which equals the mean of y).<a name="line.382"></a> <FONT color="green">383</FONT> * <p><a name="line.383"></a> <FONT color="green">384</FONT> * This is usually abbreviated SSR or SSM. It is defined as SSM<a name="line.384"></a> <FONT color="green">385</FONT> * <a href="http://www.xycoon.com/SumOfSquares.htm">here</a></p><a name="line.385"></a> <FONT color="green">386</FONT> * <p><a name="line.386"></a> <FONT color="green">387</FONT> * <strong>Preconditions</strong>: <ul><a name="line.387"></a> <FONT color="green">388</FONT> * <li>At least two observations (with at least two different x values)<a name="line.388"></a> <FONT color="green">389</FONT> * must have been added before invoking this method. If this method is<a name="line.389"></a> <FONT color="green">390</FONT> * invoked before a model can be estimated, <code>Double.NaN</code> is<a name="line.390"></a> <FONT color="green">391</FONT> * returned.<a name="line.391"></a> <FONT color="green">392</FONT> * </li></ul></p><a name="line.392"></a> <FONT color="green">393</FONT> *<a name="line.393"></a> <FONT color="green">394</FONT> * @return sum of squared deviations of predicted y values<a name="line.394"></a> <FONT color="green">395</FONT> */<a name="line.395"></a> <FONT color="green">396</FONT> public double getRegressionSumSquares() {<a name="line.396"></a> <FONT color="green">397</FONT> return getRegressionSumSquares(getSlope());<a name="line.397"></a> <FONT color="green">398</FONT> }<a name="line.398"></a> <FONT color="green">399</FONT> <a name="line.399"></a> <FONT color="green">400</FONT> /**<a name="line.400"></a> <FONT color="green">401</FONT> * Returns the sum of squared errors divided by the degrees of freedom,<a name="line.401"></a> <FONT color="green">402</FONT> * usually abbreviated MSE.<a name="line.402"></a> <FONT color="green">403</FONT> * <p><a name="line.403"></a> <FONT color="green">404</FONT> * If there are fewer than <strong>three</strong> data pairs in the model,<a name="line.404"></a> <FONT color="green">405</FONT> * or if there is no variation in <code>x</code>, this returns<a name="line.405"></a> <FONT color="green">406</FONT> * <code>Double.NaN</code>.</p><a name="line.406"></a> <FONT color="green">407</FONT> *<a name="line.407"></a> <FONT color="green">408</FONT> * @return sum of squared deviations of y values<a name="line.408"></a> <FONT color="green">409</FONT> */<a name="line.409"></a> <FONT color="green">410</FONT> public double getMeanSquareError() {<a name="line.410"></a> <FONT color="green">411</FONT> if (n < 3) {<a name="line.411"></a> <FONT color="green">412</FONT> return Double.NaN;<a name="line.412"></a> <FONT color="green">413</FONT> }<a name="line.413"></a> <FONT color="green">414</FONT> return getSumSquaredErrors() / (n - 2);<a name="line.414"></a> <FONT color="green">415</FONT> }<a name="line.415"></a> <FONT color="green">416</FONT> <a name="line.416"></a> <FONT color="green">417</FONT> /**<a name="line.417"></a> <FONT color="green">418</FONT> * Returns <a href="http://mathworld.wolfram.com/CorrelationCoefficient.html"><a name="line.418"></a> <FONT color="green">419</FONT> * Pearson's product moment correlation coefficient</a>,<a name="line.419"></a> <FONT color="green">420</FONT> * usually denoted r.<a name="line.420"></a> <FONT color="green">421</FONT> * <p><a name="line.421"></a> <FONT color="green">422</FONT> * <strong>Preconditions</strong>: <ul><a name="line.422"></a> <FONT color="green">423</FONT> * <li>At least two observations (with at least two different x values)<a name="line.423"></a> <FONT color="green">424</FONT> * must have been added before invoking this method. If this method is<a name="line.424"></a> <FONT color="green">425</FONT> * invoked before a model can be estimated, <code>Double,NaN</code> is<a name="line.425"></a> <FONT color="green">426</FONT> * returned.<a name="line.426"></a> <FONT color="green">427</FONT> * </li></ul></p><a name="line.427"></a> <FONT color="green">428</FONT> *<a name="line.428"></a> <FONT color="green">429</FONT> * @return Pearson's r<a name="line.429"></a> <FONT color="green">430</FONT> */<a name="line.430"></a> <FONT color="green">431</FONT> public double getR() {<a name="line.431"></a> <FONT color="green">432</FONT> double b1 = getSlope();<a name="line.432"></a> <FONT color="green">433</FONT> double result = Math.sqrt(getRSquare());<a name="line.433"></a> <FONT color="green">434</FONT> if (b1 < 0) {<a name="line.434"></a> <FONT color="green">435</FONT> result = -result;<a name="line.435"></a> <FONT color="green">436</FONT> }<a name="line.436"></a> <FONT color="green">437</FONT> return result;<a name="line.437"></a> <FONT color="green">438</FONT> }<a name="line.438"></a> <FONT color="green">439</FONT> <a name="line.439"></a> <FONT color="green">440</FONT> /**<a name="line.440"></a> <FONT color="green">441</FONT> * Returns the <a href="http://www.xycoon.com/coefficient1.htm"><a name="line.441"></a> <FONT color="green">442</FONT> * coefficient of determination</a>,<a name="line.442"></a> <FONT color="green">443</FONT> * usually denoted r-square.<a name="line.443"></a> <FONT color="green">444</FONT> * <p><a name="line.444"></a> <FONT color="green">445</FONT> * <strong>Preconditions</strong>: <ul><a name="line.445"></a> <FONT color="green">446</FONT> * <li>At least two observations (with at least two different x values)<a name="line.446"></a> <FONT color="green">447</FONT> * must have been added before invoking this method. If this method is<a name="line.447"></a> <FONT color="green">448</FONT> * invoked before a model can be estimated, <code>Double,NaN</code> is<a name="line.448"></a> <FONT color="green">449</FONT> * returned.<a name="line.449"></a> <FONT color="green">450</FONT> * </li></ul></p><a name="line.450"></a> <FONT color="green">451</FONT> *<a name="line.451"></a> <FONT color="green">452</FONT> * @return r-square<a name="line.452"></a> <FONT color="green">453</FONT> */<a name="line.453"></a> <FONT color="green">454</FONT> public double getRSquare() {<a name="line.454"></a> <FONT color="green">455</FONT> double ssto = getTotalSumSquares();<a name="line.455"></a> <FONT color="green">456</FONT> return (ssto - getSumSquaredErrors()) / ssto;<a name="line.456"></a> <FONT color="green">457</FONT> }<a name="line.457"></a> <FONT color="green">458</FONT> <a name="line.458"></a> <FONT color="green">459</FONT> /**<a name="line.459"></a> <FONT color="green">460</FONT> * Returns the <a href="http://www.xycoon.com/standarderrorb0.htm"><a name="line.460"></a> <FONT color="green">461</FONT> * standard error of the intercept estimate</a>,<a name="line.461"></a> <FONT color="green">462</FONT> * usually denoted s(b0).<a name="line.462"></a> <FONT color="green">463</FONT> * <p><a name="line.463"></a> <FONT color="green">464</FONT> * If there are fewer that <strong>three</strong> observations in the<a name="line.464"></a> <FONT color="green">465</FONT> * model, or if there is no variation in x, this returns<a name="line.465"></a> <FONT color="green">466</FONT> * <code>Double.NaN</code>.</p><a name="line.466"></a> <FONT color="green">467</FONT> *<a name="line.467"></a> <FONT color="green">468</FONT> * @return standard error associated with intercept estimate<a name="line.468"></a> <FONT color="green">469</FONT> */<a name="line.469"></a> <FONT color="green">470</FONT> public double getInterceptStdErr() {<a name="line.470"></a> <FONT color="green">471</FONT> return Math.sqrt(<a name="line.471"></a> <FONT color="green">472</FONT> getMeanSquareError() * ((1d / (double) n) + (xbar * xbar) / sumXX));<a name="line.472"></a> <FONT color="green">473</FONT> }<a name="line.473"></a> <FONT color="green">474</FONT> <a name="line.474"></a> <FONT color="green">475</FONT> /**<a name="line.475"></a> <FONT color="green">476</FONT> * Returns the <a href="http://www.xycoon.com/standerrorb(1).htm">standard<a name="line.476"></a> <FONT color="green">477</FONT> * error of the slope estimate</a>,<a name="line.477"></a> <FONT color="green">478</FONT> * usually denoted s(b1).<a name="line.478"></a> <FONT color="green">479</FONT> * <p><a name="line.479"></a> <FONT color="green">480</FONT> * If there are fewer that <strong>three</strong> data pairs in the model,<a name="line.480"></a> <FONT color="green">481</FONT> * or if there is no variation in x, this returns <code>Double.NaN</code>.<a name="line.481"></a> <FONT color="green">482</FONT> * </p><a name="line.482"></a> <FONT color="green">483</FONT> *<a name="line.483"></a> <FONT color="green">484</FONT> * @return standard error associated with slope estimate<a name="line.484"></a> <FONT color="green">485</FONT> */<a name="line.485"></a> <FONT color="green">486</FONT> public double getSlopeStdErr() {<a name="line.486"></a> <FONT color="green">487</FONT> return Math.sqrt(getMeanSquareError() / sumXX);<a name="line.487"></a> <FONT color="green">488</FONT> }<a name="line.488"></a> <FONT color="green">489</FONT> <a name="line.489"></a> <FONT color="green">490</FONT> /**<a name="line.490"></a> <FONT color="green">491</FONT> * Returns the half-width of a 95% confidence interval for the slope<a name="line.491"></a> <FONT color="green">492</FONT> * estimate.<a name="line.492"></a> <FONT color="green">493</FONT> * <p><a name="line.493"></a> <FONT color="green">494</FONT> * The 95% confidence interval is</p><a name="line.494"></a> <FONT color="green">495</FONT> * <p><a name="line.495"></a> <FONT color="green">496</FONT> * <code>(getSlope() - getSlopeConfidenceInterval(),<a name="line.496"></a> <FONT color="green">497</FONT> * getSlope() + getSlopeConfidenceInterval())</code></p><a name="line.497"></a> <FONT color="green">498</FONT> * <p><a name="line.498"></a> <FONT color="green">499</FONT> * If there are fewer that <strong>three</strong> observations in the<a name="line.499"></a> <FONT color="green">500</FONT> * model, or if there is no variation in x, this returns<a name="line.500"></a> <FONT color="green">501</FONT> * <code>Double.NaN</code>.</p><a name="line.501"></a> <FONT color="green">502</FONT> * <p><a name="line.502"></a> <FONT color="green">503</FONT> * <strong>Usage Note</strong>:<br><a name="line.503"></a> <FONT color="green">504</FONT> * The validity of this statistic depends on the assumption that the<a name="line.504"></a> <FONT color="green">505</FONT> * observations included in the model are drawn from a<a name="line.505"></a> <FONT color="green">506</FONT> * <a href="http://mathworld.wolfram.com/BivariateNormalDistribution.html"><a name="line.506"></a> <FONT color="green">507</FONT> * Bivariate Normal Distribution</a>.</p><a name="line.507"></a> <FONT color="green">508</FONT> *<a name="line.508"></a> <FONT color="green">509</FONT> * @return half-width of 95% confidence interval for the slope estimate<a name="line.509"></a> <FONT color="green">510</FONT> * @throws MathException if the confidence interval can not be computed.<a name="line.510"></a> <FONT color="green">511</FONT> */<a name="line.511"></a> <FONT color="green">512</FONT> public double getSlopeConfidenceInterval() throws MathException {<a name="line.512"></a> <FONT color="green">513</FONT> return getSlopeConfidenceInterval(0.05d);<a name="line.513"></a> <FONT color="green">514</FONT> }<a name="line.514"></a> <FONT color="green">515</FONT> <a name="line.515"></a> <FONT color="green">516</FONT> /**<a name="line.516"></a> <FONT color="green">517</FONT> * Returns the half-width of a (100-100*alpha)% confidence interval for<a name="line.517"></a> <FONT color="green">518</FONT> * the slope estimate.<a name="line.518"></a> <FONT color="green">519</FONT> * <p><a name="line.519"></a> <FONT color="green">520</FONT> * The (100-100*alpha)% confidence interval is </p><a name="line.520"></a> <FONT color="green">521</FONT> * <p><a name="line.521"></a> <FONT color="green">522</FONT> * <code>(getSlope() - getSlopeConfidenceInterval(),<a name="line.522"></a> <FONT color="green">523</FONT> * getSlope() + getSlopeConfidenceInterval())</code></p><a name="line.523"></a> <FONT color="green">524</FONT> * <p><a name="line.524"></a> <FONT color="green">525</FONT> * To request, for example, a 99% confidence interval, use<a name="line.525"></a> <FONT color="green">526</FONT> * <code>alpha = .01</code></p><a name="line.526"></a> <FONT color="green">527</FONT> * <p><a name="line.527"></a> <FONT color="green">528</FONT> * <strong>Usage Note</strong>:<br><a name="line.528"></a> <FONT color="green">529</FONT> * The validity of this statistic depends on the assumption that the<a name="line.529"></a> <FONT color="green">530</FONT> * observations included in the model are drawn from a<a name="line.530"></a> <FONT color="green">531</FONT> * <a href="http://mathworld.wolfram.com/BivariateNormalDistribution.html"><a name="line.531"></a> <FONT color="green">532</FONT> * Bivariate Normal Distribution</a>.</p><a name="line.532"></a> <FONT color="green">533</FONT> * <p><a name="line.533"></a> <FONT color="green">534</FONT> * <strong> Preconditions:</strong><ul><a name="line.534"></a> <FONT color="green">535</FONT> * <li>If there are fewer that <strong>three</strong> observations in the<a name="line.535"></a> <FONT color="green">536</FONT> * model, or if there is no variation in x, this returns<a name="line.536"></a> <FONT color="green">537</FONT> * <code>Double.NaN</code>.<a name="line.537"></a> <FONT color="green">538</FONT> * </li><a name="line.538"></a> <FONT color="green">539</FONT> * <li><code>(0 < alpha < 1)</code>; otherwise an<a name="line.539"></a> <FONT color="green">540</FONT> * <code>IllegalArgumentException</code> is thrown.<a name="line.540"></a> <FONT color="green">541</FONT> * </li></ul></p><a name="line.541"></a> <FONT color="green">542</FONT> *<a name="line.542"></a> <FONT color="green">543</FONT> * @param alpha the desired significance level<a name="line.543"></a> <FONT color="green">544</FONT> * @return half-width of 95% confidence interval for the slope estimate<a name="line.544"></a> <FONT color="green">545</FONT> * @throws MathException if the confidence interval can not be computed.<a name="line.545"></a> <FONT color="green">546</FONT> */<a name="line.546"></a> <FONT color="green">547</FONT> public double getSlopeConfidenceInterval(double alpha)<a name="line.547"></a> <FONT color="green">548</FONT> throws MathException {<a name="line.548"></a> <FONT color="green">549</FONT> if (alpha >= 1 || alpha <= 0) {<a name="line.549"></a> <FONT color="green">550</FONT> throw MathRuntimeException.createIllegalArgumentException(<a name="line.550"></a> <FONT color="green">551</FONT> "out of bounds significance level {0}, must be between {1} and {2}",<a name="line.551"></a> <FONT color="green">552</FONT> alpha, 0.0, 1.0);<a name="line.552"></a> <FONT color="green">553</FONT> }<a name="line.553"></a> <FONT color="green">554</FONT> return getSlopeStdErr() *<a name="line.554"></a> <FONT color="green">555</FONT> distribution.inverseCumulativeProbability(1d - alpha / 2d);<a name="line.555"></a> <FONT color="green">556</FONT> }<a name="line.556"></a> <FONT color="green">557</FONT> <a name="line.557"></a> <FONT color="green">558</FONT> /**<a name="line.558"></a> <FONT color="green">559</FONT> * Returns the significance level of the slope (equiv) correlation.<a name="line.559"></a> <FONT color="green">560</FONT> * <p><a name="line.560"></a> <FONT color="green">561</FONT> * Specifically, the returned value is the smallest <code>alpha</code><a name="line.561"></a> <FONT color="green">562</FONT> * such that the slope confidence interval with significance level<a name="line.562"></a> <FONT color="green">563</FONT> * equal to <code>alpha</code> does not include <code>0</code>.<a name="line.563"></a> <FONT color="green">564</FONT> * On regression output, this is often denoted <code>Prob(|t| > 0)</code><a name="line.564"></a> <FONT color="green">565</FONT> * </p><p><a name="line.565"></a> <FONT color="green">566</FONT> * <strong>Usage Note</strong>:<br><a name="line.566"></a> <FONT color="green">567</FONT> * The validity of this statistic depends on the assumption that the<a name="line.567"></a> <FONT color="green">568</FONT> * observations included in the model are drawn from a<a name="line.568"></a> <FONT color="green">569</FONT> * <a href="http://mathworld.wolfram.com/BivariateNormalDistribution.html"><a name="line.569"></a> <FONT color="green">570</FONT> * Bivariate Normal Distribution</a>.</p><a name="line.570"></a> <FONT color="green">571</FONT> * <p><a name="line.571"></a> <FONT color="green">572</FONT> * If there are fewer that <strong>three</strong> observations in the<a name="line.572"></a> <FONT color="green">573</FONT> * model, or if there is no variation in x, this returns<a name="line.573"></a> <FONT color="green">574</FONT> * <code>Double.NaN</code>.</p><a name="line.574"></a> <FONT color="green">575</FONT> *<a name="line.575"></a> <FONT color="green">576</FONT> * @return significance level for slope/correlation<a name="line.576"></a> <FONT color="green">577</FONT> * @throws MathException if the significance level can not be computed.<a name="line.577"></a> <FONT color="green">578</FONT> */<a name="line.578"></a> <FONT color="green">579</FONT> public double getSignificance() throws MathException {<a name="line.579"></a> <FONT color="green">580</FONT> return 2d * (1.0 - distribution.cumulativeProbability(<a name="line.580"></a> <FONT color="green">581</FONT> Math.abs(getSlope()) / getSlopeStdErr()));<a name="line.581"></a> <FONT color="green">582</FONT> }<a name="line.582"></a> <FONT color="green">583</FONT> <a name="line.583"></a> <FONT color="green">584</FONT> // ---------------------Private methods-----------------------------------<a name="line.584"></a> <FONT color="green">585</FONT> <a name="line.585"></a> <FONT color="green">586</FONT> /**<a name="line.586"></a> <FONT color="green">587</FONT> * Returns the intercept of the estimated regression line, given the slope.<a name="line.587"></a> <FONT color="green">588</FONT> * <p><a name="line.588"></a> <FONT color="green">589</FONT> * Will return <code>NaN</code> if slope is <code>NaN</code>.</p><a name="line.589"></a> <FONT color="green">590</FONT> *<a name="line.590"></a> <FONT color="green">591</FONT> * @param slope current slope<a name="line.591"></a> <FONT color="green">592</FONT> * @return the intercept of the regression line<a name="line.592"></a> <FONT color="green">593</FONT> */<a name="line.593"></a> <FONT color="green">594</FONT> private double getIntercept(double slope) {<a name="line.594"></a> <FONT color="green">595</FONT> return (sumY - slope * sumX) / n;<a name="line.595"></a> <FONT color="green">596</FONT> }<a name="line.596"></a> <FONT color="green">597</FONT> <a name="line.597"></a> <FONT color="green">598</FONT> /**<a name="line.598"></a> <FONT color="green">599</FONT> * Computes SSR from b1.<a name="line.599"></a> <FONT color="green">600</FONT> *<a name="line.600"></a> <FONT color="green">601</FONT> * @param slope regression slope estimate<a name="line.601"></a> <FONT color="green">602</FONT> * @return sum of squared deviations of predicted y values<a name="line.602"></a> <FONT color="green">603</FONT> */<a name="line.603"></a> <FONT color="green">604</FONT> private double getRegressionSumSquares(double slope) {<a name="line.604"></a> <FONT color="green">605</FONT> return slope * slope * sumXX;<a name="line.605"></a> <FONT color="green">606</FONT> }<a name="line.606"></a> <FONT color="green">607</FONT> <a name="line.607"></a> <FONT color="green">608</FONT> /**<a name="line.608"></a> <FONT color="green">609</FONT> * Modify the distribution used to compute inference statistics.<a name="line.609"></a> <FONT color="green">610</FONT> * @param value the new distribution<a name="line.610"></a> <FONT color="green">611</FONT> * @since 1.2<a name="line.611"></a> <FONT color="green">612</FONT> */<a name="line.612"></a> <FONT color="green">613</FONT> public void setDistribution(TDistribution value) {<a name="line.613"></a> <FONT color="green">614</FONT> distribution = value;<a name="line.614"></a> <FONT color="green">615</FONT> <a name="line.615"></a> <FONT color="green">616</FONT> // modify degrees of freedom<a name="line.616"></a> <FONT color="green">617</FONT> if (n > 2) {<a name="line.617"></a> <FONT color="green">618</FONT> distribution.setDegreesOfFreedom(n - 2);<a name="line.618"></a> <FONT color="green">619</FONT> }<a name="line.619"></a> <FONT color="green">620</FONT> }<a name="line.620"></a> <FONT color="green">621</FONT> }<a name="line.621"></a> </PRE> </BODY> </HTML>