In modeling the effect of an impurity on crystal growth the following equation is used:G-GLGo-G KLCM(1)where C is the impurity concentration, Gi is a limiting growth rate, Go is the growthrate of the crystal with no impurity present and KL and M are model parameters. Thetable below shows the values of growth rates G for several impurity concentrations C,for the values of Go = 310-3ml/min and G1 = 1.810-3ml/min.75 100 125C(ppm)G(ml/min)x 103 2.5 2.2 2.04 1.9550Recall that in the multiple linear regression approach (generalized least squares method),we write the general linear model asy = coxo + C1x1+c2x2+ + CmXm(2)which is equivalent toAc = y,whereX11yi1.y2(4)1УтThen we use the following linear algebra operation to find the parameters co, c1,C2, *, Cm:c= [A"A]*[A"y](5)(a) Using the multiple linear regression approach (generalized least squares method),write the model in the general linear formy = coxo +C1x1+c2x2 +.+ CmXm(6)and then specify the form of the parameters co, c1, C2, ,Cm:(b) To obtain the parameters of the model, the following linear algebra operation is re-quired,c= [A"A]*[A"y](7)define the matrices A and y for this case including size and content.

a) Using multiple linear regression and given data the model is written in the general form as…

(a) Using the multiple linear regression approach (generalized least squares method), write the model in the general linear form y = co*o + C1*1+CC2X2+ +Cm*m (6) and then specify the form of the parameters co, c1, c2, ,Cm: (b) To obtain the parameters of the model, the following linear algebra operation is re- quired, e= [A"A]*[A*y] (7) define the matrices A and y for this case including size and content.

(a) Using the multiple linear regression approach (generalized least squares method), write the model in the general linear form y = coo + C11+CC2X2+ +Cmm (6) and then specify the form of the parameters co, c1, c2, ,Cm: (b) To obtain the parameters of the model, the following linear algebra operation is re- quired, e= [A"A][A*y] (7) define the matrices A and y for this case including size and content.

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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Question

100%

In modeling the effect of an impurity on crystal growth the following equation is used:
G-GL
Go-G KLCM
(1)
where C is the impurity concentration, Gi is a limiting growth rate, Go is the growth
rate of the crystal with no impurity present and KL and M are model parameters. The
table below shows the values of growth rates G for several impurity concentrations C,
for the values of Go = 310-3ml/min and G1 = 1.810-3ml/min.
75 100 125
C(ppm)
G(ml/min)x 103 2.5 2.2 2.04 1.95
50
Recall that in the multiple linear regression approach (generalized least squares method),
we write the general linear model as
y = coxo + C1x1+c2x2+ + CmXm
(2)
which is equivalent to
Ac = y,
where
X1
1
yi
1.
y2
(4)
1
Ут
Then we use the following linear algebra operation to find the parameters co, c1,
C2, *, Cm:
c= [A"A]*[A"y]
(5)
(a) Using the multiple linear regression approach (generalized least squares method),
write the model in the general linear form
y = coxo +C1x1+c2x2 +.+ CmXm
(6)
and then specify the form of the parameters co, c1, C2, ,Cm:
(b) To obtain the parameters of the model, the following linear algebra operation is re-
quired,
c= [A"A]*[A"y]
(7)
define the matrices A and y for this case including size and content.

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