polynomial curve fitting: higher order models' root mean square error does not decrease The 2019 Stack Overflow Developer Survey Results Are In Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Fitting a polynomial + exponential curve of a given form to dataWhen does Mean Square Error increase?Mean Square Error & BiasNegative Mean Square ErrorRoot Mean Square Error - How did he get this number?liner regression not using mean square error to estimate parameterpolynomial curve fitting without regression (power law)What does the derivative mean in least squares curve fitting?Mean Integrated Square Errorpolynomial curve fitting and linear algebra
Can withdrawing asylum be illegal?
The following signatures were invalid: EXPKEYSIG 1397BC53640DB551
Is this wall load bearing? Blueprints and photos attached
Why did all the guest students take carriages to the Yule Ball?
What is this lever in Argentinian toilets?
How does ice melt when immersed in water?
High Q peak in frequency response means what in time domain?
Why can't wing-mounted spoilers be used to steepen approaches?
What was the last x86 CPU that did not have the x87 floating-point unit built in?
How do I add random spotting to the same face in cycles?
What information about me do stores get via my credit card?
How did passengers keep warm on sail ships?
Why is superheterodyning better than direct conversion?
Why does the Event Horizon Telescope (EHT) not include telescopes from Africa, Asia or Australia?
Can smartphones with the same camera sensor have different image quality?
Am I ethically obligated to go into work on an off day if the reason is sudden?
Simulation of a banking system with an Account class in C++
Who or what is the being for whom Being is a question for Heidegger?
Road tyres vs "Street" tyres for charity ride on MTB Tandem
Is above average number of years spent on PhD considered a red flag in future academia or industry positions?
Why can't devices on different VLANs, but on the same subnet, communicate?
Are my PIs rude or am I just being too sensitive?
Typeface like Times New Roman but with "tied" percent sign
Is every episode of "Where are my Pants?" identical?
polynomial curve fitting: higher order models' root mean square error does not decrease
The 2019 Stack Overflow Developer Survey Results Are In
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Fitting a polynomial + exponential curve of a given form to dataWhen does Mean Square Error increase?Mean Square Error & BiasNegative Mean Square ErrorRoot Mean Square Error - How did he get this number?liner regression not using mean square error to estimate parameterpolynomial curve fitting without regression (power law)What does the derivative mean in least squares curve fitting?Mean Integrated Square Errorpolynomial curve fitting and linear algebra
$begingroup$
I am trying to fit a curve for 15 data points. I started by creating a linear model and observing the root mean square difference, followed by quadratic, cubic and increasing the degree of polynomial at each iteration and also measuring the root mean square difference for each model. My data points are as follows:
x = -1.45, -1.12, -0.50, 1.40, 2.28, 3.50, 3.75, 4.50, 5.21, 5.98,6.65, 7.76, 8.56, 9.64, 10.87;
y = 4.30, 4.24, 3.10, 1.50, 5.73, 2.30, 5.31, 3.76, 7.40, 4.13, 9.45, 5.40, 12.67, 8.42, 14.86;
So far the results I got are as follows:
d - the degree of the model. d=2 is quadratic model and d=3 is cubic model
d rmsd
1 2.42613
2 1.95418
3 1.95373
4 1.91411
5 1.90665
6 1.86912
7 1.81113
8 1.80812
9 1.66018
10 1.36661
11 1.36122
12 1.75445
13 0.993169
14 1.795
15 3.52391
For degree 15, root mean square difference should be closer to zero, regardless of over fitting concerns. Reason being, if you think about it mathematically, it will be fifteen equations and fifteen unknowns and should have a solution. My question is what could have gone wrong in the polynomial curve fitting? I am just testing the linear algebra concepts here. I understand higher degree models may not be right choice.
linear-algebra statistics systems-of-equations algebraic-curves regression
asked Oct 1 '15 at 19:54
kpnanekpnane
11
$endgroup$
add a comment |
$begingroup$
I am trying to fit a curve for 15 data points. I started by creating a linear model and observing the root mean square difference, followed by quadratic, cubic and increasing the degree of polynomial at each iteration and also measuring the root mean square difference for each model. My data points are as follows:
x = -1.45, -1.12, -0.50, 1.40, 2.28, 3.50, 3.75, 4.50, 5.21, 5.98,6.65, 7.76, 8.56, 9.64, 10.87;
y = 4.30, 4.24, 3.10, 1.50, 5.73, 2.30, 5.31, 3.76, 7.40, 4.13, 9.45, 5.40, 12.67, 8.42, 14.86;
So far the results I got are as follows:
d - the degree of the model. d=2 is quadratic model and d=3 is cubic model
d rmsd
1 2.42613
2 1.95418
3 1.95373
4 1.91411
5 1.90665
6 1.86912
7 1.81113
8 1.80812
9 1.66018
10 1.36661
11 1.36122
12 1.75445
13 0.993169
14 1.795
15 3.52391
For degree 15, root mean square difference should be closer to zero, regardless of over fitting concerns. Reason being, if you think about it mathematically, it will be fifteen equations and fifteen unknowns and should have a solution. My question is what could have gone wrong in the polynomial curve fitting? I am just testing the linear algebra concepts here. I understand higher degree models may not be right choice.
linear-algebra statistics systems-of-equations algebraic-curves regression
asked Oct 1 '15 at 19:54
kpnanekpnane
11
$endgroup$
$begingroup$
Your fitting is incorrect if (as you have stated) all $x$ values are distinct. The 14th degree best fit polynomial will interpolate all data points exactly.
$endgroup$
– hardmath
Oct 1 '15 at 21:58
add a comment |
$begingroup$
I am trying to fit a curve for 15 data points. I started by creating a linear model and observing the root mean square difference, followed by quadratic, cubic and increasing the degree of polynomial at each iteration and also measuring the root mean square difference for each model. My data points are as follows:
x = -1.45, -1.12, -0.50, 1.40, 2.28, 3.50, 3.75, 4.50, 5.21, 5.98,6.65, 7.76, 8.56, 9.64, 10.87;
y = 4.30, 4.24, 3.10, 1.50, 5.73, 2.30, 5.31, 3.76, 7.40, 4.13, 9.45, 5.40, 12.67, 8.42, 14.86;
So far the results I got are as follows:
d - the degree of the model. d=2 is quadratic model and d=3 is cubic model
d rmsd
1 2.42613
2 1.95418
3 1.95373
4 1.91411
5 1.90665
6 1.86912
7 1.81113
8 1.80812
9 1.66018
10 1.36661
11 1.36122
12 1.75445
13 0.993169
14 1.795
15 3.52391
For degree 15, root mean square difference should be closer to zero, regardless of over fitting concerns. Reason being, if you think about it mathematically, it will be fifteen equations and fifteen unknowns and should have a solution. My question is what could have gone wrong in the polynomial curve fitting? I am just testing the linear algebra concepts here. I understand higher degree models may not be right choice.
linear-algebra statistics systems-of-equations algebraic-curves regression
asked Oct 1 '15 at 19:54
kpnanekpnane
11
$endgroup$
I am trying to fit a curve for 15 data points. I started by creating a linear model and observing the root mean square difference, followed by quadratic, cubic and increasing the degree of polynomial at each iteration and also measuring the root mean square difference for each model. My data points are as follows:
x = -1.45, -1.12, -0.50, 1.40, 2.28, 3.50, 3.75, 4.50, 5.21, 5.98,6.65, 7.76, 8.56, 9.64, 10.87;
y = 4.30, 4.24, 3.10, 1.50, 5.73, 2.30, 5.31, 3.76, 7.40, 4.13, 9.45, 5.40, 12.67, 8.42, 14.86;
So far the results I got are as follows:
d - the degree of the model. d=2 is quadratic model and d=3 is cubic model
d rmsd
1 2.42613
2 1.95418
3 1.95373
4 1.91411
5 1.90665
6 1.86912
7 1.81113
8 1.80812
9 1.66018
10 1.36661
11 1.36122
12 1.75445
13 0.993169
14 1.795
15 3.52391
For degree 15, root mean square difference should be closer to zero, regardless of over fitting concerns. Reason being, if you think about it mathematically, it will be fifteen equations and fifteen unknowns and should have a solution. My question is what could have gone wrong in the polynomial curve fitting? I am just testing the linear algebra concepts here. I understand higher degree models may not be right choice.
linear-algebra statistics systems-of-equations algebraic-curves regression
linear-algebra statistics systems-of-equations algebraic-curves regression
asked Oct 1 '15 at 19:54
kpnanekpnane
11
asked Oct 1 '15 at 19:54
kpnanekpnane
11
asked Oct 1 '15 at 19:54
kpnanekpnane
11
asked Oct 1 '15 at 19:54
kpnanekpnane
11
asked Oct 1 '15 at 19:54
kpnanekpnane
11
11
$begingroup$
Your fitting is incorrect if (as you have stated) all $x$ values are distinct. The 14th degree best fit polynomial will interpolate all data points exactly.
$endgroup$
– hardmath
Oct 1 '15 at 21:58
add a comment |
$begingroup$
Your fitting is incorrect if (as you have stated) all $x$ values are distinct. The 14th degree best fit polynomial will interpolate all data points exactly.
$endgroup$
– hardmath
Oct 1 '15 at 21:58
$begingroup$
Your fitting is incorrect if (as you have stated) all $x$ values are distinct. The 14th degree best fit polynomial will interpolate all data points exactly.
$endgroup$
– hardmath
Oct 1 '15 at 21:58
$begingroup$
Your fitting is incorrect if (as you have stated) all $x$ values are distinct. The 14th degree best fit polynomial will interpolate all data points exactly.
$endgroup$
– hardmath
Oct 1 '15 at 21:58
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
I tried working out the same as you using Excel. My results agree with yours up to $d=11$. From that point on we begin to differ. The reason is that the difference in size of the values becomes so great that no meaningful analysis is possible. In Excel, by the time you are trying to work with $d=11$ you have to find the 11th power of each x-value and these range from $4.9 times 10^-4$ to $2.5 times 10^9$. Depending on the software you are using to find the fit, it will fail earlier or later, but eventually the results will start to be meaningless.
answered Oct 2 '15 at 0:20
tomitomi
6,21411232
$endgroup$
add a comment |
Your Answer
StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "69"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);
else
createEditor();
);
function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader:
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
,
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);
);
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f1460080%2fpolynomial-curve-fitting-higher-order-models-root-mean-square-error-does-not-d%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
I tried working out the same as you using Excel. My results agree with yours up to $d=11$. From that point on we begin to differ. The reason is that the difference in size of the values becomes so great that no meaningful analysis is possible. In Excel, by the time you are trying to work with $d=11$ you have to find the 11th power of each x-value and these range from $4.9 times 10^-4$ to $2.5 times 10^9$. Depending on the software you are using to find the fit, it will fail earlier or later, but eventually the results will start to be meaningless.
answered Oct 2 '15 at 0:20
tomitomi
6,21411232
$endgroup$
add a comment |
$begingroup$
I tried working out the same as you using Excel. My results agree with yours up to $d=11$. From that point on we begin to differ. The reason is that the difference in size of the values becomes so great that no meaningful analysis is possible. In Excel, by the time you are trying to work with $d=11$ you have to find the 11th power of each x-value and these range from $4.9 times 10^-4$ to $2.5 times 10^9$. Depending on the software you are using to find the fit, it will fail earlier or later, but eventually the results will start to be meaningless.
answered Oct 2 '15 at 0:20
tomitomi
6,21411232
$endgroup$
add a comment |
$begingroup$
I tried working out the same as you using Excel. My results agree with yours up to $d=11$. From that point on we begin to differ. The reason is that the difference in size of the values becomes so great that no meaningful analysis is possible. In Excel, by the time you are trying to work with $d=11$ you have to find the 11th power of each x-value and these range from $4.9 times 10^-4$ to $2.5 times 10^9$. Depending on the software you are using to find the fit, it will fail earlier or later, but eventually the results will start to be meaningless.
answered Oct 2 '15 at 0:20
tomitomi
6,21411232
$endgroup$
I tried working out the same as you using Excel. My results agree with yours up to $d=11$. From that point on we begin to differ. The reason is that the difference in size of the values becomes so great that no meaningful analysis is possible. In Excel, by the time you are trying to work with $d=11$ you have to find the 11th power of each x-value and these range from $4.9 times 10^-4$ to $2.5 times 10^9$. Depending on the software you are using to find the fit, it will fail earlier or later, but eventually the results will start to be meaningless.
answered Oct 2 '15 at 0:20
tomitomi
6,21411232
edited Oct 2 '15 at 14:22
answered Oct 2 '15 at 0:20
tomitomi
6,21411232
answered Oct 2 '15 at 0:20
tomitomi
6,21411232
answered Oct 2 '15 at 0:20
tomitomi
6,21411232
6,21411232
add a comment |
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f1460080%2fpolynomial-curve-fitting-higher-order-models-root-mean-square-error-does-not-d%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
$begingroup$
Your fitting is incorrect if (as you have stated) all $x$ values are distinct. The 14th degree best fit polynomial will interpolate all data points exactly.
$endgroup$
– hardmath
Oct 1 '15 at 21:58