In linear regression we have real "response values" "y"1, ..., "yn", and "n" "p"-dimensional vector "covariates" x1, ..., x"n". The components of the vector x"i" are denoted "x""i"1, ..., "x""ip". If we use least squares to fit a function in the form of a hyperplane ŷ = "a" + βTx to the data (x"i", "y""i") 1 ≤ "i" ≤ "n", we could then assess the fit using the mean squared error (MSE). The MSE for given estimated parameter values "a" and β on the training set (x"i", "y""i") 1 ≤ "i" ≤ "n" is defined as