Simple Linear Regression From sum and sum of squares
Use this calculator to fit a simple linear regression model from summarized data.
| Simple Linear Regression | |
|---|---|
| No. of Pairs of Observations ($n$) | |
| Sum of X : ($\sum x$) | |
| Sum of Y : ($\sum y$) | |
| Sum of X squares : ($\sum x^2$) | |
| Sum of Y squares : ($\sum y^2$) | |
| Sum of product of X and Y : ($\sum xy$) | |
| Results | |
| Mean of X ($\overline{x}$) | |
| Mean of Y ($\overline{y}$) | |
| Sxx ($S_{xx}$) | |
| Syy ($S_{yy}$) | |
| Sxy ($S_{xy}$) | |
| Correlation between X and Y ($r$) | |
| Intercept ($\hat{\beta}_0$) | |
| Slope ($\hat{\beta}_1$) | |
| Regression equation | |
Simple Linear Regression
Another method
$$ \begin{aligned} S_{xx}=\sum_{i=1}^n x_i^2- \frac{(\sum_i x_i)^2}{n} \end{aligned} $$
$$ \begin{aligned} S_{xy}=\sum_{i=1}^n x_iy_i- \frac{(\sum_i x_i)(\sum_i y_i)}{n} \end{aligned} $$
$$ \begin{aligned} b=\frac{S_{xy}}{S_{xx}} \end{aligned} $$
$$ \begin{aligned} a=\overline{y}-b \overline{x} \end{aligned} $$
