linReg

A console application that's able to find the best-fit linear equation $y_i = ax_i + b$
for a two-dimensional samples dataset using the least-squares approach.
$x_i$ and $y_i$ are independent and dependent values from the dataset, respectively.
$a$ - the slope of the line.
$b$ - the y-intercept.

Expressions used by Statistics.dll

Slope coefficient equation:
$$a = \frac{\sum\limits_{i=1}^n (x_i - \bar x)(y_i - \bar y)} {\sum\limits_{i=1}^n (x_i - \bar x)^2}$$

y-intercept coefficient equation:
$$b = \bar y - (a \bar x)$$

Definition of the coefficient of determination: $$R^2 = 1 - \frac{SS_{res}} {SS_{tot}}$$

Residual sum of squares: $$SS_{res} = \sum_{i=1}^n (y_i - f_i)^2$$ Where $f_i$ is fitted value equal to $x_i * a + b$.

Total sum of squares: $$SS_{tot} = \sum_{i=1}^n (y_i - \bar y)^2$$

Dependencies

.NET 8.0