using linest function for 2nd order polynomial

B

balan

New Member
Joined
Jul 13, 2015
Messages
4
Hi All,

I am using linest function to get coefficient of 2nd order polynomial {y = (c2*x^2)+(c1*x) + c0 } for the following variable,
[TABLE="width: 128"]
<colgroup><col width="64"><col width="64"></colgroup><tbody>[TR]
[TD="class: et1, width: 64"]250[/TD]
[TD="class: et2, width: 64"]1.3 [/TD]
[/TR]
[TR]
[TD="class: et1, width: 64"]500[/TD]
[TD="class: et2, width: 64"]3.8 [/TD]
[/TR]
[TR]
[TD="class: et1, width: 64"]750[/TD]
[TD="class: et2, width: 64"]7.2 [/TD]
[/TR]
[TR]
[TD="class: et1, width: 64"]1000[/TD]
[TD="class: et2, width: 64"]11.4 [/TD]
[/TR]
[TR]
[TD="class: et1, width: 64"]1250[/TD]
[TD="class: et2, width: 64"]16.2 [/TD]
[/TR]
[TR]
[TD="class: et1, width: 64"]1500[/TD]
[TD="class: et2, width: 64"]21.6 [/TD]
[/TR]
[TR]
[TD="class: et1, width: 64"]1750[/TD]
[TD="class: et2, width: 64"]27.6 [/TD]
[/TR]
[TR]
[TD="class: et1, width: 64"]2000[/TD]
[TD="class: et2, width: 64"]34.1 [/TD]
[/TR]
[TR]
[TD="class: et1, width: 64"]2250[/TD]
[TD="class: et2, width: 64"]41.1 [/TD]
[/TR]
[TR]
[TD="class: et1, width: 64"]2500[/TD]
[TD="class: et2, width: 64"]48.6 [/TD]
[/TR]
</tbody>[/TABLE]
and using the following equation
c2 = index(linest(y,x^{1,2},1)
c1 = index(linest(y,x^{1,2},1,2)
c0 = index(linest(y,x^{1,2},1,3) and these do calculate values as
c2 = 0.0000048, c1 = 0.008 and c0 = -1.25. But when I keep input variables in row wise(as shown below), I am not able to use these equations. Looking for a help.
[TABLE="width: 640"]
<colgroup><col width="64"><col width="64"><col width="64"><col width="64"><col width="64"><col width="64"><col width="64"><col width="64"><col width="64"><col width="64"></colgroup><tbody>[TR]
[TD="class: et2, width: 64"]250.0 [/TD]
[TD="class: et2, width: 64"]500.0 [/TD]
[TD="class: et2, width: 64"]750.0 [/TD]
[TD="class: et2, width: 64"]1000.0 [/TD]
[TD="class: et2, width: 64"]1250.0 [/TD]
[TD="class: et2, width: 64"]1500.0 [/TD]
[TD="class: et2, width: 64"]1750.0 [/TD]
[TD="class: et2, width: 64"]2000.0 [/TD]
[TD="class: et2, width: 64"]2250.0 [/TD]
[TD="class: et2, width: 64"]2500.0 [/TD]
[/TR]
[TR]
[TD="class: et2, width: 64"]1.3 [/TD]
[TD="class: et2, width: 64"]3.8 [/TD]
[TD="class: et2, width: 64"]7.2 [/TD]
[TD="class: et2, width: 64"]11.4 [/TD]
[TD="class: et2, width: 64"]16.2 [/TD]
[TD="class: et2, width: 64"]21.6 [/TD]
[TD="class: et2, width: 64"]27.6 [/TD]
[TD="class: et2, width: 64"]34.1 [/TD]
[TD="class: et2, width: 64"]41.1 [/TD]
[TD="class: et2, width: 64"]48.6 [/TD]
[/TR]
</tbody>[/TABLE]

Thanks in advance for any help someone may be able to give.
[TABLE="width: 97"]
<colgroup><col width="97"></colgroup><tbody>[TR]
[TD="class: et3, width: 97"] [/TD]
[/TR]
</tbody>[/TABLE]
 

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Hello Aladin,

If I convert variables from row format to column format by using this transpose function, it works. But If I can able to use this linest function when these variables in row format, it will be better for me. Because this method I am using for finding optimum design point from 'n' set of design points.
 
Upvote 0
balan said:
Hello Aladin,

If I convert variables from row format to column format by using this transpose function, it works. But If I can able to use this linest function when these variables in row format, it will be better for me. Because this method I am using for finding optimum design point from 'n' set of design points.
Click to expand...

Vertical data...

Control+shift+enter, not just enter:

=INDEX(LINEST(A1:A10,B1:B10^{1,2}),1)

Horizontal data...

Control+shift+enter, not just enter:

=INDEX(LINEST(TRANSPOSE(A1:J1),TRANSPOSE(A2:J2)^{1,2}),1)

Both produce the same outcome.
 
Upvote 0
HI Aladin,

Thank You for your reply. It works well and saves lot of time during my optimization study.

Many thanks once again.
 
Upvote 0
balan said:
Hi All,

I am using linest function to get coefficient of 2nd order polynomial {y = (c2*x^2)+(c1*x) + c0 } for the following variable,
[TABLE="width: 128"]
<tbody>[TR]
[TD="class: et1, width: 64"]250[/TD]
[TD="class: et2, width: 64"]1.3[/TD]
[/TR]
[TR]
[TD="class: et1, width: 64"]500[/TD]
[TD="class: et2, width: 64"]3.8[/TD]
[/TR]
[TR]
[TD="class: et1, width: 64"]750[/TD]
[TD="class: et2, width: 64"]7.2[/TD]
[/TR]
[TR]
[TD="class: et1, width: 64"]1000[/TD]
[TD="class: et2, width: 64"]11.4[/TD]
[/TR]
[TR]
[TD="class: et1, width: 64"]1250[/TD]
[TD="class: et2, width: 64"]16.2[/TD]
[/TR]
[TR]
[TD="class: et1, width: 64"]1500[/TD]
[TD="class: et2, width: 64"]21.6[/TD]
[/TR]
[TR]
[TD="class: et1, width: 64"]1750[/TD]
[TD="class: et2, width: 64"]27.6[/TD]
[/TR]
[TR]
[TD="class: et1, width: 64"]2000[/TD]
[TD="class: et2, width: 64"]34.1[/TD]
[/TR]
[TR]
[TD="class: et1, width: 64"]2250[/TD]
[TD="class: et2, width: 64"]41.1[/TD]
[/TR]
[TR]
[TD="class: et1, width: 64"]2500[/TD]
[TD="class: et2, width: 64"]48.6[/TD]
[/TR]
</tbody>[/TABLE]
and using the following equation
c2 = index(linest(y,x^{1,2},1)
c1 = index(linest(y,x^{1,2},1,2)
c0 = index(linest(y,x^{1,2},1,3) and these do calculate values as
c2 = 0.0000048, c1 = 0.008 and c0 = -1.25. But when I keep input variables in row wise(as shown below), I am not able to use these equations. Looking for a help.
[TABLE="width: 640"]
<tbody>[TR]
[TD="class: et2, width: 64"]250.0[/TD]
[TD="class: et2, width: 64"]500.0[/TD]
[TD="class: et2, width: 64"]750.0[/TD]
[TD="class: et2, width: 64"]1000.0[/TD]
[TD="class: et2, width: 64"]1250.0[/TD]
[TD="class: et2, width: 64"]1500.0[/TD]
[TD="class: et2, width: 64"]1750.0[/TD]
[TD="class: et2, width: 64"]2000.0[/TD]
[TD="class: et2, width: 64"]2250.0[/TD]
[TD="class: et2, width: 64"]2500.0[/TD]
[/TR]
[TR]
[TD="class: et2, width: 64"]1.3[/TD]
[TD="class: et2, width: 64"]3.8[/TD]
[TD="class: et2, width: 64"]7.2[/TD]
[TD="class: et2, width: 64"]11.4[/TD]
[TD="class: et2, width: 64"]16.2[/TD]
[TD="class: et2, width: 64"]21.6[/TD]
[TD="class: et2, width: 64"]27.6[/TD]
[TD="class: et2, width: 64"]34.1[/TD]
[TD="class: et2, width: 64"]41.1[/TD]
[TD="class: et2, width: 64"]48.6[/TD]
[/TR]
</tbody>[/TABLE]

Thanks in advance for any help someone may be able to give.
[TABLE="width: 97"]
<tbody>[TR]
[TD="class: et3, width: 97"][/TD]
[/TR]
</tbody>[/TABLE]
Click to expand...

Hi

Another option

Since the data and the exponents array must be orthogonal, if your data is in horizontal rows, like in the second table, use like:

c2 = index(linest(y,x^{1;2},1)
 
Upvote 0
pgc01 said:
Hi

Another option

Since the data and the exponents array must be orthogonal, if your data is in horizontal rows, like in the second table, use like:

c2 = index(linest(y,x^{1;2},1)
Click to expand...

Good idea... Adding the missing paren:

=INDEX(LINEST(A1:J1,A2:J2^{1;2}),1)
 
Upvote 0
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