Before revision: A regression model which is a linear combination of the explanatory variables may therefore be represented via matrix multiplication as where X is the design matrix, is a vector of the model's coefficients (one for each variable) , and y is the vector of predicted outputs for each object.
After revision: A regression model may, is a vector of random errors with mean zero be represented via matrix multiplication as where X is the design matrix, is a vector of the model's coefficients (one for each variable) , and y is the vector of predicted outputs for each object.