Need some tips, pls help
Hello,
I need some tips to resolve this problem:
We have a quadratic form z = a(x ^ 2) + bxy + c(y ^ 2) + dx + ey + f. The equation can be normalized, by dividing with a nonzero coefficient (for example f <> 0). Set {(x, y): z = 0} are called conic sections.It can be seen with the contour function. The planets have elliptical orbits.Here are 10 observations of positions of planets.
X 1.02 .95 .87 .77 .67 .56 .44 .30 .16 .01
Y 0.39 .32 .27 .22 .18 .15 .13 .12 .13 .15
a) Determine the coefficients of the quadratic form that approximates the data
in the sense of least squares taking a coefficient equal to 1 and solving
superiorly 10 × 5 system. Draw the orbit and the 10 points.
b) This problem is nearly rank deficient. To see the effect, disturb the data slightly by adding each point coordonate a random number uniformly distributed in the interval [-0005, 0005]. Calculate the new coefficients for the perturbed data. Draw the new orbit
on the same schedule with the old one. Comment on the differences between
coefficients and orbitals
Thank you very much,
Bobby
I need some tips to resolve this problem:
We have a quadratic form z = a(x ^ 2) + bxy + c(y ^ 2) + dx + ey + f. The equation can be normalized, by dividing with a nonzero coefficient (for example f <> 0). Set {(x, y): z = 0} are called conic sections.It can be seen with the contour function. The planets have elliptical orbits.Here are 10 observations of positions of planets.
X 1.02 .95 .87 .77 .67 .56 .44 .30 .16 .01
Y 0.39 .32 .27 .22 .18 .15 .13 .12 .13 .15
a) Determine the coefficients of the quadratic form that approximates the data
in the sense of least squares taking a coefficient equal to 1 and solving
superiorly 10 × 5 system. Draw the orbit and the 10 points.
b) This problem is nearly rank deficient. To see the effect, disturb the data slightly by adding each point coordonate a random number uniformly distributed in the interval [-0005, 0005]. Calculate the new coefficients for the perturbed data. Draw the new orbit
on the same schedule with the old one. Comment on the differences between
coefficients and orbitals
Thank you very much,
Bobby
0
Comments
Then I would draw it.