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Bartlett's Three Group Regression.

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Model II regression should be used when the two variables in the regression equation are random and subject to error, i.e. not controlled by the researcher. Model I regression using ordinary least squares underestimates the slope of the linear relationship between the variables when they both contain error. According to Sokal and Rohlf (1995), the subject of Model II regression is one on which research and controversy are continuing and definitive recommendations are difficult to make.

BARTREGRESS is a Model II procedure. It is an approach to estimate the functional relationship in Model II by estimating the slope from segments of the sample arrayed by magnitude of the x variate. Ricker (1973) argues that this method yield biased estimates of functional relationships. Its main handicap is that the regression lines are not the same depending on whether the grouping (into three groups) is made based on x or y. The regression line is not guaranteed to pass through the centroid of the scatter of points and the slope estimator is not symmetric. However, here it is developed the computational procedure to all those people interested on it.

[B,BINT] = BARTREGRESS(X,Y,ALPHA) returns the vector B of regression coefficients in the linear Model, a matrix BINT of the given confidence intervals for B, and the N three groups size vector.

BARTREGRESS treats NaNs in X or Y as missing values, and removes them.

Syntax: [b,bint,n] = Bartregress(x,y,alpha)

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