RegCoeff(R1, R2) = ( k+1) × 1 coefficient vector B RegCov(R1, R2) = ( k+1) × ( k+1) matrix MS Res( X T X) -1 which is the covariance matrix for the regression coefficients Here R1 is an n × k array containing the X sample data and R2 is an n × 1 array containing the Y sample data.ĭIAGHAT(R1) = n × 1 column array containing the diagonal of the hat matrixĬORE(R1) = ( k+1) × (k+1) matrix ( X T X) -1 which makes up the core of the hat matrix Real Statistics Excel Functions: The Real Statistics Resource Pack contains the following array functions. Thus R 2 can also be calculated by the formula: If this has the value c then the desired value of R 2 is the square root of 1–1/ c. It turns out that R 2 = RSquare(R1, j) can also be calculated by first finding the correlation matrix for R1, then taking its inverse and then selecting the jth element on the diagonal. There is also a second form of the RSquare function in which RSquare(R1, j) = R 2 where the X data consist of all the columns in R1 except the jth column and the Y data consist of the jth column of R1. Similarly, you can use SSRegTot(R1, R2) and its value will be equivalent to SSRegTot(R2). Here R1 is an n × k array containing the X sample data and R2 is an n × 1 array containing the Y sample data.Ī second R2 parameter can be used with each of the df functions above, although this parameter is not used. Real Statistics Excel Functions: The Real Statistics Resource Pack supplies the following functions.
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