The mean squared error loss quantifies the error between a target variable and an estimate for its value.
The train error is the error commited by a machine-learning model on the dataset it was trained on. The test error is the error commited on another dataset...
In machine-learning, a target value is an output value to a supervised learning problem.
The residual is the error vector between the true output vector and its estimate :
An hyperparameter is a parameter of the machine-learning algorithm. While the parameters are learned by the machine-learning algorithm, an hyperparameter dictates how the algorithm learns.
In machine-learning, a feature is an input variable to a supervised learning problem.
Given our usual dataset made of input vectors and output values, the design matrix is the matrix whose rows are the input vectors.