Korrelasjon, samvarians, samvariasjon, R^2

Owned by BL
Last updated: 15.Jan 2024
2 min read

Generelt

  • JMP default: uses either the Row-wise, Pairwise, or REML methods.
  • Row-wise:
    • JMP usage: estimation is used for data tables with no missing values.
    • Row-wise estimation does not use observations with missing values, so rows that contain missing cells are deleted before the method is applied. This method is useful for excluding any observations that have missing data. Row-wise estimation was the only estimation method available prior to JMP 8, so it can also be used to check compatibility with JMP versions prior to JMP 8.
  • Pairwise: 
    • JMP usage: Pairwise estimation is used for data tables with missing values and either more than 10 columns, more than 5,000 rows, or more columns than rows.
    • Pair-wise estimation uses all of the data, even if missing values are present. This estimation method performs correlations for all rows for each pair of columns with nonmissing values. It is most useful when a data table has missing values and either more columns than rows, more than 10 columns, or more than 5,000 rows.
  • REML 
    • JMP usage: estimation is used otherwise.
    • Restricted maximum likelihood (REML) estimation uses all of the data, even if missing values are present. Due to a bias-correction factor, this method is slow if the dataset is large and there are many missing values. Therefore, REML is most useful for smaller datasets. If there are no missing cells in the data, then the REML and ML estimates are equivalent and equal to the sample covariance matrix. If there are missing cells, REML’s variance and covariance estimates are less biased than the estimates from ML estimation. For more information, see REML.

Manuell beregning

  • Variabel: R^2
    • R=r-kvadrat.
  • Formler:
    • R=(Zx-Zy)/n
    • R=((x-(gjsn x)(y-(gjsn y)))/((n-1)*Sx*Sy)
    • Manuelt:
      • Korrelasjon=(Sum((x-xgjsn)*(y-ygjsn)))/((n-1)*Sx*Sy)
        • Sum((x-xgjsn)*(y-ygjsn))
          • For hvert datapar x og y.
          • x=x-verdi.
          • y=y-verdi
        • Sx=standardavvik for x
        • Sy=standardavvik for y
        • n=antall datapar
  • Viser hvorvidt samvariansen er større enn tilfeldighet.
  • Beregnes etter totalt utvalg og sannsynlighet for tilfeldig utslag.
  • Regnes som (sum(avvik*avvik))/((n-1)*Sx*Sy).
  • Korrelasjon.xlsx
  • Korrelasjon på kalkulator:
    • x-verdi
    • Hvit "input"
    • y-verdi
    • Sigma
    • gjsn:
      • Trykk Rød shift
      • Trykk 4
      • Trykk Rød shift
      • Trykk K\swap
      • Resultatet er korrelasjon, R2

Undertemaer:

Korrelasjon:

Samvarians:

Samvariasjon:

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