Regression Analysis and Curve Fitting by John Homan

Author:John Homan [Homan, John]
Language: eng
Format: azw3
Published: 2016-05-14T04:00:00+00:00

a∑X7.

. 5 rows

.

a∑X4……………………………………..en -∑Y

. 6 columns

Page 149:

Example:

Find the 50th. degree Equation:

50th Degree:

a1∑X100 + a2∑X99……………………………………a51X59-∑YX50

a1∑X99+

+aX -∑YX 51 Rows

a1∑X50 +a2X49………………………………………+ a51n -∑Y

52 columns

We shall now derive the defining summation equations for a Cubic Regression using a traditional method of proof.

Genberal regression Equations for a Cubic:

aX3 + bX2 + cX + d = Y

[1] Express as the sum of errors:

S = (aX3 + bX2 + cX + d - Y )2 = 0

[2] Differentiating in respect to a:

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DS/Da = 2(aX3 + bX2 + cX + d - Y )(X3) = 0

[3] Cancelling zero and multiply/ express as summation:

(aX6 + bX5 + cX4 + d X3 - Y X3 ) = 0

a∑X6 + b∑X5 + c∑X4 + d ∑X3 - ∑Y X3 = 0

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