Question:

(10 points) Suppose you build a simple linear regression model Y_i = ?₀ + ?₁ x_i + ?_i based on n = 20 data points (x₁, y₁), (x₂, y₂), …, (x₂₀, y₂₀). Recall that the regression model estimates the unknown parameters ?₀ and ?₁ with b₀ and b₁. You then seek to validate your model by looking at the residuals e_i = y_i ?? y^_i, where y^_i = b₀ + b₁ x_i are the predicted Y values. Consider the following possible residual graphs that you might encounter.

(A) (B)

(C) (D)

(a) For each of the four graphs, determine whether it suggests a problem in your regression model. If so, what is the nature of the problem?