Consider the simple linear regression model, 𝑦 = 𝛽 0 + 𝛽 1 𝑥 + 𝑢 . The algebraic expression for the intercept parameter estimate is 𝛽 ^ 0 = 𝑦 ¯ − 𝛽 ^ 1 𝑥 ¯ (1). The algebraic expression for the slope parameter estimate is 𝛽 ^ 1 = ∑ ( 𝑥 𝑖 − 𝑥 ¯ ) ( 𝑦 𝑖 − 𝑦 ¯ ) / ∑ ( 𝑥 𝑖 − 𝑥 ¯ ) 2 (2). A fitted value for y when  𝑥 = 𝑥 𝑖  is defined as: 𝑦 ^ 𝑖 = 𝛽 ^ 0 + 𝛽 ^ 1 𝑥 𝑖 . The residual for observation i is defined as: 𝑢 ^ 𝑖 = 𝑦 𝑖 = 𝑦 ^ 𝑖 . Which of the following statements is correct?