Practice — Linear Regression (6 questions)

A marketing analyst has four quarters of data on discount depth x (percentage points) and units sold y (thousands):

x:  0    10   20   30
y:  10   14   15   21

1. Compute the OLS slope and intercept by hand and write the fitted line.
2. Compute the residuals, RSS, TSS and R².
3. Compute the residual variance, the standard error of the slope and the t-statistic. With only 2 residual degrees of freedom the two-sided 5% critical value is 4.303 — is the slope statistically significant at 5%? What does that tell you about small-sample regressions?