Partial Least Squares:
Partial least squares regression is an addition of the multiple linear regression models. In its simple form, a linear model details out the linear relationship between a dependent (response) variable Y, and a set of predictor variables, the X's, so that
Y = a0 + a1X1 + a2X2 + ... + apXp
In this equation, for the intercept, a0 is the regression coefficient and the ai values are the regression coefficients for variables 1 through p worked out from the data.
For instance, you could calculate approximately a person's height as a function of the person's weight and gender. One can also use linear regression to predict the relevant regression coefficients from a sample of data, which can measure height, weight, and observing the subjects' gender.
For data analysis problems, predictions of the linear relationships between variables are sufficient to explain the experimental data, and to make rational predictions for new observations.
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