a). Derive the 4 x 4 system of equations required to fit the modely = f(x; co, C1, C2, C3) = co+ qr+c2r + C3r +e,by minimizing the mean squared error, based on a data set{(ci, y), i = 1,2, .,n}.b). For the data set generated from the model: {(1.2, 2.25), (1.4, 3.2), (1.6, 3.17),(1.8, 4.08), (2, 4.5), (2.2, 5.54), (2.4, 6.57), (2.6, 7.92), (2.8, 9.33), (3, 10.66)},calculate the estimates of co, C1, C2, C3.

a) There are n data points. (Taking points sequentially ) yi=c0+c1·xi+c2·xi2+c3·xi3 for all…

a). Derive the 4 x 4 system of equations required to fit the model y = f(r; co, C1, C2, C3) = co+ C1r+c2r? + Car +e, by minimizing the mean squared error, based on a data set {(ri, y4), i = 1,2,,n}. ... b). For the data set generated from the model: {(1.2, 2.25), (1.4, 3.2), (1.6, 3.17), (1.8, 4.08), (2, 4.5), (2.2, 5.54), (2.4, 6.57), (2.6, 7.92), (2.8, 9.33), (3, 10.66)}, calculate the estimates of cCo, C1, C2, C3.

a). Derive the 4 x 4 system of equations required to fit the model y = f(r; co, C1, C2, C3) = co+ C1r+c2r? + Car +e, by minimizing the mean squared error, based on a data set {(ri, y4), i = 1,2,,n}. ... b). For the data set generated from the model: {(1.2, 2.25), (1.4, 3.2), (1.6, 3.17), (1.8, 4.08), (2, 4.5), (2.2, 5.54), (2.4, 6.57), (2.6, 7.92), (2.8, 9.33), (3, 10.66)}, calculate the estimates of cCo, C1, C2, C3.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

a). Derive the 4 x 4 system of equations required to fit the model
y = f(x; co, C1, C2, C3) = co+ qr+c2r + C3r +e,
by minimizing the mean squared error, based on a data set
{(ci, y), i = 1,2, .,n}.
b). For the data set generated from the model: {(1.2, 2.25), (1.4, 3.2), (1.6, 3.17),
(1.8, 4.08), (2, 4.5), (2.2, 5.54), (2.4, 6.57), (2.6, 7.92), (2.8, 9.33), (3, 10.66)},
calculate the estimates of co, C1, C2, C3.

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