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 : ($\sum xy$)
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

$$ \begin{aligned} S_{xx}=\sum_{i=1}^n x_i^2- \frac{(\sum_i x_i)^2}{n} \end{aligned} $$

$$ \begin{aligned} S_{xy}=\sum_{i=1}^n x_iy_i- \frac{(\sum_i x_i)(\sum_i y_i)}{n} \end{aligned} $$

$$ \begin{aligned} b=\frac{S_{xy}}{S_{xx}} \end{aligned} $$

$$ \begin{aligned} a=\overline{y}-b \overline{x} \end{aligned} $$

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