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 \(b_2\) :

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