Assignment LA - project for linear algebra PDF

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UNIVERSITI TEKNOLOGI MARAFAKULTI SAINS KOMPUTER & MATEMATIKMATLINEAR ALGEBRA IIGROUP MEMBERSNAME STUDENT NO.MUHAMMAD AFIF BIN MOHAMMADHANAPIAH2019291284MUHAMMAD IZZUDDIN BINMOHAMMAD AZMAN2019291358N4CS2482ALECTURER'S NAMEPN. NORLYDA BINTI MOHAMEDSUBMISSION DATE22 MAY 2020INTRODUCTIONThe foll...

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UNIVERSITI TEKNOLOGI MARA FAKULTI SAINS KOMPUTER & MATEMATIK

MAT523 LINEAR ALGEBRA II

GROUP MEMBERS NAME MUHAMMAD AFIF BIN MOHAMMAD HANAPIAH MUHAMMAD IZZUDDIN BIN MOHAMMAD AZMAN

N4CS2482A1

LECTURER'S NAME PN. NORLYDA BINTI MOHAMED

SUBMISSION DATE 22 MAY 2020

STUDENT NO. 2019291284 2019291358

INTRODUCTION The following data from company National Chicken Council shows the relationship between the number of chicken meat consumption in pound based on year. Hence, in this assignment we are going to use these three mathematical models which are linear model, quadratic model, cubic model and model of higher degree to find out the best fit curve curve of these data from year 2000 until 2019. Year from 2000 until 2019 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Number of chicken meat consumption 77.4 77.1 81.0 82.1 84.6 86.4 86.9 85.5 83.8 80.0 82.8 83.3 80.8 82.3 83.8 89.3 91.0 92.1 93.8 96.2

Implementation Linear model: y = a + bx The data generates a system of linear equations with the matrix representation as below:

V=

Its normal equation is

=

The least square soluton is

v=

=

=

The best fit linear curve is y = 77.9268 + 0.6745x

Error vector e = y – Mv =

||e|| = 5.89646616541351420

-

=

Quadratic model: y = a + bx + cx^2 The matrix representation of the above system is

V= Its normal equation is

=

The least square solution is

v=

=

=

The best fit quadratic curve is y = 81.3014 - 0.2457*x + 0.0438*x^2

Error vector e = y – Mv = ||e|| = 5.17138755980882081

-

=

Cubic model y = a + bx + cx^2 +dx^3 The matrix representation of the above system is

V= And its normal equation is

=

The least squares solution is

v=

=

=

The best fit cubic curve is y = 72.8547 + 4.0642x - 0.4569x^2 + 0.0158x^3

Error vector e = y – Mv =

-

Error magnitude ||e|| = 3.69864007846372544

=

Model of higher degree y = a + bx + cx^2 + dx^3 + e^4 The data generates a system of linear equations with the matrix representation as below:

V=

Its normal equation is

=

The least square soluton is

v=

=

=

The best fit linear curve is y = 77.9268 + 0.6745x

Error vector e = y – Mv =

||e|| = 2.72210641679029663

-

=

Graph best fit curve against its observed data Linear model

Quadratic model

Cubic model

Model of higher degree

Graph of the error vector against x values Linear model

Quadratic model

Cubic model

Model of higher degree

Analysis and conclusion Based on the four model above, the following error magnitudes in the approximation are obtained. TYPES OF BEST FIT CURVE Linear Quadratic Cubic Model of higher degree

ERROR MAGNITUDE 5.89646616541351420 5.17138755980882081 3.69864007846372544 2.72210641679029663

The best fit curve in this case which will give the best approximation is the model of higher degree because it has the minimum error in terms of its magnitude.

Appendix Linear model

Quadratic model

Cubic model

Model of higher degree...