Response distribution at each X

In experiments, the values of the explanatory variable, X, are controlled by the experimenter. Several response measurements are often made at each distinct value of X.

At any single value of X, the repeated response measurements can be considered as a univariate data set and can be modelled as a random sample from some distribution — commonly a normal distribution. The characteristics of the distribution will often depend on the value of X.

The collection of distributions of Y at different values of X comprise a model for the complete bivariate data set called a regression model.

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