Regression Least Squares Fitting

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Latex Code

                                    y_{i}=\alpha + \beta (x_{i} - \bar{x}) + \epsilon_{i} \\ \hat{\alpha}=\bar{y} \\ \hat{\beta}=\frac{s^{2}_{xy}}{s^{2}_{x}}

Introduction

$y_{i}=\alpha + \beta (x_{i} - \bar{x}) + \epsilon_{i} \\ \hat{\alpha}=\bar{y} \\ \hat{\beta}=\frac{s^{2}_{xy}}{s^{2}_{x}}$

To fit a straight line by least squares to n pairs of points (xi,yi), model the observations y by the above equation $y_{i}=\alpha + \beta (x_{i} - \bar{x}) + \epsilon_{i}$ .

Statistics of $s^{2}_{x},s^{2}_{y},s^{2}_{xy}$ is defined as
$s^{2}_{x}=\frac{1}{n}\sum (x_{i}-\bar{x})^{2}$
$s^{2}_{y}=\frac{1}{n}\sum (y_{i}-\bar{y})^{2}$
$s^{2}_{xy}=\frac{1}{n}\sum (x_{i}-\bar{x})(y_{i}-\bar{y})$

Regression Least Squares Fitting

Latex Code

Introduction

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