excel polynomial
DESCRIPTION
polynomialTRANSCRIPT
determination of polynomials fro data sets
X Y1 280 277.4 280.8
2.6 203.1 217.0 197.83.1 193 189.1 192.23.9 165 153.7 177.25.6 183 182.8 179.56.1 240.2 233.1 219.87.3 410.3 456.3 450.78 705.2 662.5 678.5
9.2 1152.9 1160.8 1156.2
a b
Polynomial Y=A4*x^4+A3*x^3+A2*x^2+A1*x^+A0 4th order
Polynomial Y=A5*x^5+A4*x^4+A3*x^3+A2*x^2+A1*x^+A0 5th order
Example: Polynomial 4th Order
=INDEX(LINEST(b,a^{1,2,3,4}),5) =INDEX(LINEST(b,a^{1,2,3,4}),4)
Coefficient A0
1,2,3,4 for Poly 4th order
a is the name of the range of data x-value (here cell C6 to C14)(highlight cells, click on insert, click on name, click on define, type the name for this range of cells)b is the name of the range of data y-value (here cell D6 to D14)
Example: Polynomial 5th Order
=INDEX(LINEST(b,a^{1,2,3,4,5}),6) =INDEX(LINEST(b,a^{1,2,3,4,5}),5)
Calculated from Polynomial 4th
order
Calculated from Polynomial 5th
order
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f(x) = − 1.9860E-01 x⁴ + 8.1851E+00 x³ − 5.7282E+01 x² + 8.9217E+01 x + 2.3746E+02
Data with Polynomial 4th Order
Coefficient A0
1,2,3,4,5 for Poly 5th order
a is the name of the range of data x-value (here cell C6 to C14)
b is the name of the range of data y-value (here cell D6 to D14)
A0 A1 A2 A3 A42.3746E+02 8.9217E+01 -5.7282E+01 8.1851E+00 -1.9860E-01
A0 A1 A2 A3 A4 A56.0138E+02 -5.4192E+02 2.8461E+02 -7.0982E+01 8.0146E+00 -3.1396E-01
=INDEX(LINEST(b,a^{1,2,3,4}),4) =INDEX(LINEST(b,a^{1,2,3,4}),3)
Coefficient A1 Coefficient A2
=INDEX(LINEST(b,a^{1,2,3,4}),2)
Coefficient A3range of data x-value (here cell C6 to C14)
=INDEX(LINEST(b,a^{1,2,3,4}),1)click on define, type the name for this range of cells)
range of data y-value (here cell D6 to D14)Coefficient A4
=INDEX(LINEST(b,a^{1,2,3,4,5}),5) =INDEX(LINEST(b,a^{1,2,3,4,5}),4)
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f(x) = − 1.9860E-01 x⁴ + 8.1851E+00 x³ − 5.7282E+01 x² + 8.9217E+01 x + 2.3746E+02
Data with Polynomial 4th Order
0 1 2 3 4 5 6 7 8 9 100
200
400
600
800
1000
1200
1400
f(x) = − 3.1396E-01 x⁵ + 8.0146E+00 x⁴ − 7.0982E+01 x³ + 2.8461E+02 x² − 5.4192E+02 x + 6.0138E+02
Data with Polynomial 5th Order
Coefficient A1 Coefficient A2
=INDEX(LINEST(b,a^{1,2,3,4,5}),3)
Coefficient A3range of data x-value (here cell C6 to C14)
=INDEX(LINEST(b,a^{1,2,3,4,5}),2)
range of data y-value (here cell D6 to D14)Coefficient A4
=INDEX(LINEST(b,a^{1,2,3,4,5}),1)
Coefficient A5
compare excel Polynomial
and calculated polynomial
0 1 2 3 4 5 6 7 8 9 100
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1400
f(x) = − 3.1396E-01 x⁵ + 8.0146E+00 x⁴ − 7.0982E+01 x³ + 2.8461E+02 x² − 5.4192E+02 x + 6.0138E+02
Data with Polynomial 5th Order