Find the linear regression equation for the following data pairs (x, y): (0, 2), (2, 8), (4, 14), (6, 20), (8, 26), (10, 32), (12, 38), (14, 44)

Consider the simple linear regression model Yi = βxi + εi, i = 1, 2, ..., n, where β > 0, ∑i=1n xi2 > 0, and the uncorrelated errors εi have zero mean and finite variance σ2 (> 0). Let β̂1 = ∑i=1n ai* Yi, where ai's minimize E(∑i=1n ai Yi - β)2 with respect to scalars a1, ..., an. Let β̂2 be the ordinary least squares estimator of β. Which of the following relations is correct?

An analyst fits a multiple linear regression model Yi = β0 + β1X1i + β2X2i + β3X3i + β4X4i + εi, i = 1,2,...,n, using the method of least squares. A coordinator claims that under restrictions, a reduced model is sufficient, which can be expressed as a linear hypothesis H0: LTβ = 0 where LT is a 2 × 5 matrix testing two linear independent constraints. If the errors are independent N(0, σ2) variables, what is the distribution of the test statistic for testing H0 against HA?