Trendline with no intercept

Summary

• A trendline with no intercept :

$$y=b_2x$$

• OLS fitted values: ${\hat{y}}_i=b_2x_i i=1,…,n$
• OLS residuals: $e_i=y_i-{\hat{y}}_i=y_i-b_2x_i i=1,…,n$
• Minimizing RSS gives us the no-intercept OLS formula for $b_2$ :

$$b_2= \frac{\sum_{i=1}^{n}{ x_iy_i }}{\sum_{i=1}^{n}{ x_i^2 }}$$