Esempio: regressione potenza

Funzioni > Analisi dati > Curve fitting > Esempio: regressione potenza

Utilizzare le funzioni genfit e pwrfit per adattare i dati a un modello di curva di potenza.

Utilizzo della funzione genfit

1. Definire un insieme di dati.

Fare clic per copiare questa espressione

2. Definire la funzione adattata in cui A e b sono sconosciuti.

3. Definire il vettore della funzione.

In questo esempio la funzione ln0 viene utilizzata al posto di ln perché può essere valutata circa a 0, che è una condizione necessaria per modificare i valori dei parametri riducendo al minimo l'errore. La sostituzione di ln0 con ln provoca la mancata convergenza di genfit.

4. Definire un vettore di valori ipotetici.

5. Utilizzare genfit per trovare i coefficienti della funzione di potenza.

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6. Definire una funzione utilizzando i coefficienti A e b.

7. Tracciare il grafico dei punti dati e della funzione adattata.

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Utilizzo della funzione pwrfit

1. Definire la funzione adattata in cui a, b e c sono sconosciuti.

2. Definire un vettore di valori ipotetici.

3. Utilizzare pwrfit per trovare i coefficienti della funzione di potenza.

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4. Definire una funzione utilizzando i coefficienti a, b e c.

5. Tracciare il grafico dei punti dati e della funzione adattata.

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Controllo della bontà dell'adattamento

1. Utilizzare grafici dei residui per controllare la bontà dell'adattamento dei modelli ai dati.

◦ I valori dei residui maggiori sono i seguenti:

◦ I valori dei residui minori sono i seguenti:

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2. Utilizzare la funzione corr per calcolare i coefficienti di correlazione.

L'adattamento appare molto migliore rispetto a quanto non possa indicare il grafico del residuo.

Per i dati presenti su vasta scala, in particolare i dati di potenza o esponenziali che cambiano rapidamente in corrispondenza di valori sempre maggiori di X, un grafico del residuo non è necessariamente lo strumento migliore per determinare la bontà di un adattamento.

Funzione genfit ponderata

Utilizzare funzioni locali per modificare il vettore di funzioni passato a genfit in base ad altri parametri.

1. Definire una funzione che ponderi i dati in base alle relative deviazioni standard.

L'utilizzo della forma di input del vettore per i parametri consente un semplice utilizzo della funzione ponderata per altri tipi di funzioni adattate con un numero arbitrario di parametri.

2. Scrivere un programma che restituisca la funzione genfit dei dati in base alle relative deviazioni standard.

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3. Definire un vettore di deviazioni standard.

4. Inclinare uno dei punti dati dall'insieme originale.

5. Chiamare il programma e passarvi i vettori di deviazioni standard e di valori ipotetici.

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6. Chiamare la funzione genfit senza pesi:

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7. Tracciare i grafici dei dati e delle due funzioni adattate e confrontarli.

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 <math>
 <placeholder xmlns="http://schemas.mathsoft.com/math50" />
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 </plotEquation>
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 <xyDomain scale-type="linear" auto-scale="true">
 <startValue resultRef="90">
 <real xmlns="http://schemas.mathsoft.com/math50">0</real>
 </startValue>
 <secondTickValue resultRef="91">
 <real xmlns="http://schemas.mathsoft.com/math50">1.0</real>
 </secondTickValue>
 <endValue>
 <placeholder xmlns="http://schemas.mathsoft.com/math50" />
 </endValue>
 </xyDomain>
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 <yAxis rank="1" legend-position="PlotBoundaryLeft" start="0" end="150">
 <axisLine position="origin" positionticmark="0" legendWidth="112.843333333333" />
 <axisGrid>
 <gridFrequency>11</gridFrequency>
 <gridLabels display="true" />
 <gridLines />
 <tickMarks display="true" />
 </axisGrid>
 <axisLabel />
 <markers />
 <plotEquations>
 <plotEquation>
 <math>
 <id xml:space="preserve" xmlns="http://schemas.mathsoft.com/math50">Y</id>
 </math>
 <math>
 <placeholder xmlns="http://schemas.mathsoft.com/math50" />
 </math>
 </plotEquation>
 <plotEquation>
 <math>
 <apply xmlns="http://schemas.mathsoft.com/math50">
 <id xml:space="preserve">fit</id>
 <id xml:space="preserve">m</id>
 </apply>
 </math>
 <math>
 <placeholder xmlns="http://schemas.mathsoft.com/math50" />
 </math>
 </plotEquation>
 <plotEquation>
 <math>
 <apply xmlns="http://schemas.mathsoft.com/math50">
 <id xml:space="preserve">
 fit<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">nw</Subscript>
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 <id xml:space="preserve">m</id>
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 <math>
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 <xyDomain scale-type="linear" auto-scale="true">
 <startValue>
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 <endValue>
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La funzione basata sulle deviazioni standard offre un adattamento migliore.

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