Given a data set $D={\{(-1,0),(1,-2),(2,-1),(3,1)}\}$ which consists of $(x, y)$ pairs. Consider a linear regression model of the form $y = {\theta}^Tx + {\theta}_0$ where $\theta = 0.5 $ and $\theta_0 = -1$
Compute the gradient contribution of each point with respect to the regression line.
Hi, I'm struggling to understand how to answer this question. Currently the limits of my understanding are that a squared error of each data point can be calculated by $(y - prediction)^2$
- I don't understand exactly what it means by "with respect to the regression line". I can calculate the gradient of the regression line with respect to x but I'm not sure if that is what I'm meant to do.
- I understand that each point will have a squared error that will ideally be minimised, but I'm also struggling with the conceptual understanding of what gradient contribution actually means.
- In the answers, each contribution is a pair of numbers, I am also confused about why this is the case.
The answers are $(3,-3), (3,3), (4,2), (-3,-1)$ Any help understanding this question would be greatly appreciated. The wider context is machine learning and I'm very new to it. Thank you.