Question

Which of the following offsets is used in linear least squares fitting technique? (Assuming \(Y\sim X\))?

Answer

Vertical Offsets

In a linear regression setting, the most commonly used method to find the coefficients is by minimizing the sum of squares of residuals. The sum of squares of residuals is defined as: \[R^2 = \sum[y_i- \hat{y_i}]^2\]. And \(y_i - \hat{y_i}\) is nothing but vertical offset.

To find the coefficients, let’s say for: \(y = \beta_0 + \beta_1x\), minimize \(R^2\) by differentiating with respect to \(\beta_0\) and \(\beta_1\) and equating the resulting equations to zero.

Thanks for reading. If you find a correction, hit me up on Twitter and if you like the question, how about a tip: PayPal TipJar