Mixing
How to choose degree for polynomial regression?
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I know how to perform polynomial regression. But is there any method to use for estimating the degree of the polynomial that is best suited? Some kind of meta-regression.
With best suited I mean the grade that has the highest probability of being the true degree of the source for the data.
For example, if we look at this picture we can easily "see" that a polynomial of degree 4 would fit nicely:
A more generalized question is if there is any method to determine if the source is polynomial at all or if it is exponential or something else.
statistics regression regression-analysis
asked Jan 11 at 0:45
BromanBroman
1034
$endgroup$
add a comment |
$begingroup$
I know how to perform polynomial regression. But is there any method to use for estimating the degree of the polynomial that is best suited? Some kind of meta-regression.
With best suited I mean the grade that has the highest probability of being the true degree of the source for the data.
For example, if we look at this picture we can easily "see" that a polynomial of degree 4 would fit nicely:
A more generalized question is if there is any method to determine if the source is polynomial at all or if it is exponential or something else.
statistics regression regression-analysis
asked Jan 11 at 0:45
BromanBroman
1034
$endgroup$
$begingroup$
@saulspatz Fixed. Thanks.
$endgroup$
– Broman
Jan 11 at 1:38
1
$begingroup$
The keyword you're looking for is "model selection." In general there are various approaches to decide which model (in this case, which degree) is better, such as AIC, BIC, or cross validation.
$endgroup$
– angryavian
Jan 11 at 1:43
1
$begingroup$
I think cross-validation is a popular technique for this.
$endgroup$
– littleO
Jan 11 at 2:36
$begingroup$
Polynomial regression is only really of use for interpolation, and can be disastrous for extrapolation
$endgroup$
– Henry
Jan 11 at 8:19
add a comment |
$begingroup$
I know how to perform polynomial regression. But is there any method to use for estimating the degree of the polynomial that is best suited? Some kind of meta-regression.
With best suited I mean the grade that has the highest probability of being the true degree of the source for the data.
For example, if we look at this picture we can easily "see" that a polynomial of degree 4 would fit nicely:
A more generalized question is if there is any method to determine if the source is polynomial at all or if it is exponential or something else.
statistics regression regression-analysis
asked Jan 11 at 0:45
BromanBroman
1034
$endgroup$
I know how to perform polynomial regression. But is there any method to use for estimating the degree of the polynomial that is best suited? Some kind of meta-regression.
With best suited I mean the grade that has the highest probability of being the true degree of the source for the data.
For example, if we look at this picture we can easily "see" that a polynomial of degree 4 would fit nicely:
A more generalized question is if there is any method to determine if the source is polynomial at all or if it is exponential or something else.
statistics regression regression-analysis
statistics regression regression-analysis
asked Jan 11 at 0:45
BromanBroman
1034
asked Jan 11 at 0:45
BromanBroman
1034
edited Jan 11 at 9:53
Broman
asked Jan 11 at 0:45
BromanBroman
1034
asked Jan 11 at 0:45
BromanBroman
1034
asked Jan 11 at 0:45
BromanBroman
1034
1034
$begingroup$
@saulspatz Fixed. Thanks.
$endgroup$
– Broman
Jan 11 at 1:38
1
$begingroup$
The keyword you're looking for is "model selection." In general there are various approaches to decide which model (in this case, which degree) is better, such as AIC, BIC, or cross validation.
$endgroup$
– angryavian
Jan 11 at 1:43
1
$begingroup$
I think cross-validation is a popular technique for this.
$endgroup$
– littleO
Jan 11 at 2:36
$begingroup$
Polynomial regression is only really of use for interpolation, and can be disastrous for extrapolation
$endgroup$
– Henry
Jan 11 at 8:19
add a comment |
$begingroup$
@saulspatz Fixed. Thanks.
$endgroup$
– Broman
Jan 11 at 1:38
1
$begingroup$
The keyword you're looking for is "model selection." In general there are various approaches to decide which model (in this case, which degree) is better, such as AIC, BIC, or cross validation.
$endgroup$
– angryavian
Jan 11 at 1:43
1
$begingroup$
I think cross-validation is a popular technique for this.
$endgroup$
– littleO
Jan 11 at 2:36
$begingroup$
Polynomial regression is only really of use for interpolation, and can be disastrous for extrapolation
$endgroup$
– Henry
Jan 11 at 8:19
$begingroup$
@saulspatz Fixed. Thanks.
$endgroup$
– Broman
Jan 11 at 1:38
$begingroup$
@saulspatz Fixed. Thanks.
$endgroup$
– Broman
Jan 11 at 1:38
1
1
$begingroup$
The keyword you're looking for is "model selection." In general there are various approaches to decide which model (in this case, which degree) is better, such as AIC, BIC, or cross validation.
$endgroup$
– angryavian
Jan 11 at 1:43
$begingroup$
The keyword you're looking for is "model selection." In general there are various approaches to decide which model (in this case, which degree) is better, such as AIC, BIC, or cross validation.
$endgroup$
– angryavian
Jan 11 at 1:43
1
1
$begingroup$
I think cross-validation is a popular technique for this.
$endgroup$
– littleO
Jan 11 at 2:36
$begingroup$
I think cross-validation is a popular technique for this.
$endgroup$
– littleO
Jan 11 at 2:36
$begingroup$
Polynomial regression is only really of use for interpolation, and can be disastrous for extrapolation
$endgroup$
– Henry
Jan 11 at 8:19
$begingroup$
Polynomial regression is only really of use for interpolation, and can be disastrous for extrapolation
$endgroup$
– Henry
Jan 11 at 8:19
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
An alternative to
polynomial regression
is to a fit with
Chebychev polynomials,
which essentially is a
least squares fit.
Usually the coefficients
will decrease from the
low order terms,
and you can stop when
the coefficients
get small enough.
You can then convert from
Chebychev form to
polynomial form.
Hope this is
hand-wavey enough.
answered Jan 11 at 2:20
marty cohenmarty cohen
73.5k549128
$endgroup$
add a comment |
$begingroup$
AIC or BIC is the right path to go. These criteria helps you to determine the model that best approximates the generating mechanism. Another, more basic approach is Ramsey RESET test for model misspecification. For example, see here http://lipas.uwasa.fi/~sjp/Teaching/ecm/lectures/ecmc8.pdf
answered Jan 14 at 8:21
V. VancakV. Vancak
11.1k2926
$endgroup$
add a comment |
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
An alternative to
polynomial regression
is to a fit with
Chebychev polynomials,
which essentially is a
least squares fit.
Usually the coefficients
will decrease from the
low order terms,
and you can stop when
the coefficients
get small enough.
You can then convert from
Chebychev form to
polynomial form.
Hope this is
hand-wavey enough.
answered Jan 11 at 2:20
marty cohenmarty cohen
73.5k549128
$endgroup$
add a comment |
$begingroup$
An alternative to
polynomial regression
is to a fit with
Chebychev polynomials,
which essentially is a
least squares fit.
Usually the coefficients
will decrease from the
low order terms,
and you can stop when
the coefficients
get small enough.
You can then convert from
Chebychev form to
polynomial form.
Hope this is
hand-wavey enough.
answered Jan 11 at 2:20
marty cohenmarty cohen
73.5k549128
$endgroup$
add a comment |
$begingroup$
An alternative to
polynomial regression
is to a fit with
Chebychev polynomials,
which essentially is a
least squares fit.
Usually the coefficients
will decrease from the
low order terms,
and you can stop when
the coefficients
get small enough.
You can then convert from
Chebychev form to
polynomial form.
Hope this is
hand-wavey enough.
answered Jan 11 at 2:20
marty cohenmarty cohen
73.5k549128
$endgroup$
An alternative to
polynomial regression
is to a fit with
Chebychev polynomials,
which essentially is a
least squares fit.
Usually the coefficients
will decrease from the
low order terms,
and you can stop when
the coefficients
get small enough.
You can then convert from
Chebychev form to
polynomial form.
Hope this is
hand-wavey enough.
answered Jan 11 at 2:20
marty cohenmarty cohen
73.5k549128
answered Jan 11 at 2:20
marty cohenmarty cohen
73.5k549128
answered Jan 11 at 2:20
marty cohenmarty cohen
73.5k549128
answered Jan 11 at 2:20
marty cohenmarty cohen
73.5k549128
73.5k549128
add a comment |
add a comment |
$begingroup$
AIC or BIC is the right path to go. These criteria helps you to determine the model that best approximates the generating mechanism. Another, more basic approach is Ramsey RESET test for model misspecification. For example, see here http://lipas.uwasa.fi/~sjp/Teaching/ecm/lectures/ecmc8.pdf
answered Jan 14 at 8:21
V. VancakV. Vancak
11.1k2926
$endgroup$
add a comment |
$begingroup$
AIC or BIC is the right path to go. These criteria helps you to determine the model that best approximates the generating mechanism. Another, more basic approach is Ramsey RESET test for model misspecification. For example, see here http://lipas.uwasa.fi/~sjp/Teaching/ecm/lectures/ecmc8.pdf
answered Jan 14 at 8:21
V. VancakV. Vancak
11.1k2926
$endgroup$
add a comment |
$begingroup$
AIC or BIC is the right path to go. These criteria helps you to determine the model that best approximates the generating mechanism. Another, more basic approach is Ramsey RESET test for model misspecification. For example, see here http://lipas.uwasa.fi/~sjp/Teaching/ecm/lectures/ecmc8.pdf
answered Jan 14 at 8:21
V. VancakV. Vancak
11.1k2926
$endgroup$
AIC or BIC is the right path to go. These criteria helps you to determine the model that best approximates the generating mechanism. Another, more basic approach is Ramsey RESET test for model misspecification. For example, see here http://lipas.uwasa.fi/~sjp/Teaching/ecm/lectures/ecmc8.pdf
answered Jan 14 at 8:21
V. VancakV. Vancak
11.1k2926
answered Jan 14 at 8:21
V. VancakV. Vancak
11.1k2926
answered Jan 14 at 8:21
V. VancakV. Vancak
11.1k2926
answered Jan 14 at 8:21
V. VancakV. Vancak
11.1k2926
11.1k2926
add a comment |
add a comment |
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$begingroup$
@saulspatz Fixed. Thanks.
$endgroup$
– Broman
Jan 11 at 1:38
1
$begingroup$
The keyword you're looking for is "model selection." In general there are various approaches to decide which model (in this case, which degree) is better, such as AIC, BIC, or cross validation.
$endgroup$
– angryavian
Jan 11 at 1:43
1
$begingroup$
I think cross-validation is a popular technique for this.
$endgroup$
– littleO
Jan 11 at 2:36
$begingroup$
Polynomial regression is only really of use for interpolation, and can be disastrous for extrapolation
$endgroup$
– Henry
Jan 11 at 8:19