Linear Regression

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In statistics, linear regression is an approach to modeling the relationship between a scalar dependent variable y and one or more explanatory variables denoted X. The case of one explanatory variable is called simple linear regression.&#160;Linear regression models are often fitted using the least squares approach.<div><br/></div><div><div>Linear regression has many practical uses. Most applications fall into one of the following two broad categories:</div><div><ul><li>If the goal is <span class="GINGER_SOFTWARE_mark">prediction</span>, or forecasting, or reduction, linear regression can be used to fit a predictive model to an observed data set of y and X values. After developing such a model, if an additional value of X is then given without its accompanying value of y, the fitted model can be used to make a prediction of the value of y.</li><li>Given a variable y and a number of variables X1,<span class="GINGER_SOFTWARE_mark"> ...</span>, Xp that may be related to <span class="GINGER_SOFTWARE_mark">y</span>, linear regression analysis can be applied to quantify the strength of the relationship between <span class="GINGER_SOFTWARE_mark">y</span> and the Xj, to assess which Xj may have no relationship with <span class="GINGER_SOFTWARE_mark">y</span> at all, and to identify which subsets of the Xj contain redundant information about <span class="GINGER_SOFTWARE_mark">y</span>.</li></ul><div><br/></div><div><a href="http://en.wikipedia.org/wiki/Linear_regression">http://en.wikipedia.org/wiki/Linear_regression</a><br/></div></div></div><div><br/></div><div>Expected input: List of points</div><div>Expected output: JSON object with slope and offset</div>
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