In eye tracking we have to compute the linear regression for pupil and gaze. The formula is: $$\begin{bmatrix} gaze_x \\ gaze_y \end{bmatrix} = \begin{bmatrix} \theta_1 \\ \theta_2 \end{bmatrix} + \begin{bmatrix} \theta_3 \\ \theta_4 \end{bmatrix}.pupil_x + \begin{bmatrix} \theta_5 \\ \theta_6 \end{bmatrix}.pupil_y $$ which I have written in form of: $gaze_x = \theta_1 + \theta_3.pupilx + \theta5.pupil_y$ and $gaze_y = \theta_2 + \theta_4.pupil_x + \theta_6.pupil_y$ There are now two questions. first is my decomposition correct? secondly $pupil_y$ and $pupil_x$ have seven values and they are equal which makes the program that computes the theta values to produce a singular vector value error. what should be done in this case?
2025-01-13 02:10:22.1736734222
Computing vector linear regression
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It turned out that the question was wrong. One assumption was added that stated $theta_4 = 0 $ and $theta_5 = 0 $. Then it is possible to do linear regression.