silemus.
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  1. 23×33\times 3 determinant expansion
  2. 10Eigenvalues of a 3×33\times 3 matrix
  3. 12Eigenvector for eigenvalue 3
  4. 14Inverse of a 2×22\times 2 matrix
  5. 17Solving a 3×33\times 3 linear system
  6. 20System with no solution
  7. 21Singular matrix, det=0
  8. 22Eigenvalue zero of a matrix
  9. 27Null space of a matrix
  10. 37Volume via scalar triple product
  11. 43Characteristic polynomial, 2×22\times 2
  12. 47Orthogonal matrix check
  13. 48Gram-Schmidt second vector
  14. 49Least-squares line fit
  15. 50Coordinates in a new basis
  16. 51Distance point to plane

49Least-squares line fit

Find the least-squares line y=mx+c\displaystyle y = mx + c through (0,0)\displaystyle (0, 0), (1,1)\displaystyle (1, 1) and (2,3)\displaystyle (2, 3). Give the answer to 3 decimal places.

The best-fit line through (0,0), (1,1), (2,3) is y = 1.500x − 0.167, found from the slope formula m = (nΣxy − ΣxΣy)/(nΣx² − (Σx)²) and c = ȳ − mx̄. Check: at x=1, y ≈ 1.333, reasonably close to the actual y=1.

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