5) The linear regression model y = a₀ + a₁x is applied to the data in the table shown below. What is the value of the sum squared error function S(a₀, a₁), when a₀ = 1, a₁ = 2?
6) The linear regression model y = a₀ + a₁x is to be fitted to the data in the table shown below. What is the optimal regression model obtained by minimizing sum squared error?
a) y = 1.01 – 2.10x b) y = 1.01 + 2.10x c) y = 1.01 – 0.98x d) y = 1.01 + 0.98x
7) The linear regression model y = a₀ + a₁x₁ + a₂x₂ + … + aₚxₚ is to be fitted to a set of N training data points having p attributes each. Let X be an N × (p+1) vector of input values (augmented by 1’s), Y be an N × 1 vector of target values, and q be a (p+1) × 1 vector of parameter values (a₀, a₁, a₂, …, aₚ). If the sum squared error is minimized for obtaining the optimal regression model, which of the following equation holds?
10) In principal component analysis, the projected lower-dimensional space corresponds to:
a) Subset of the original coordinate axis b) Eigenvectors of the data covariance matrix c) Eigenvectors of the data distance matrix d) Orthogonal vectors to the original coordinate axis
