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Linear AlgebraMediumOrthogonality & Least Squares

Orthogonality & Least Squares · Medium problem

A spring's stretch is believed to be proportional to the applied force, stretch =k⋅force= k\cdot\text{force}. Three trials give (force, stretch) =(1,3),(2,5),(4,9)= (1,3), (2,5), (4,9) in consistent units. Using the least-squares value of kk (minimizing the sum of squared errors over all three trials), predict the stretch at a force of 99.