A bivariate regression between y_t and x_t has the form y_t = a + bx_t + e_t where e_t is the error. Recall that the hat in (for example) indicates an estimate.

Write down an expression for the estimated residual (the error) _t,, theb write down expressions for the Total, Explained and Residual Sum of Squares (TSS, ESS, RSS).

R² may be defined as

Explain what this expression means, then show how R² is related to TSS, ESS and RSS, and list and briefly explain three problems with R² as a goodness of fit measure

2 R2 = 1 - =e, =- )^ Et=1