10.8 Question bank

Multiple choice

QB 10.1 In the regression \(y = \beta_0 + \beta_1 D + u\) where \(D\) is a dummy, \(\beta_0\) is

  1. the mean of \(y\) in the whole sample
  2. the mean of \(y\) in the group with \(D = 0\)
  3. the mean of \(y\) in the group with \(D = 1\)
  4. the difference between the two group means

QB 10.2 A categorical variable with six categories requires

  1. six dummies and an intercept
  2. five dummies and an intercept
  3. six dummies and no intercept, or five and an intercept
  4. one variable coded 1 to 6

QB 10.3 In \(y = \beta_0 + \beta_1 x + \beta_2 D + \beta_3(xD) + u\), the slope for the group with \(D = 1\) is

  1. \(\beta_1\)    b. \(\beta_3\)    c. \(\beta_1 + \beta_3\)    d. \(\beta_1 + \beta_2 + \beta_3\)

QB 10.4 A regression of \(y\) on a single dummy variable is equivalent to

  1. a one-sample \(t\)-test
  2. a paired \(t\)-test
  3. a two-sample \(t\)-test assuming equal variances
  4. a chi-squared test

QB 10.5 The Chow test compares

  1. two coefficients within one regression
  2. a pooled regression against separate regressions for each group
  3. two different dependent variables
  4. \(R^2\) across two models with different sample sizes

Short reasoning

QB 10.6 Explain why including a dummy for every category alongside an intercept is an arithmetic problem rather than a statistical one.

QB 10.7 A researcher reports that switching the base group “changed the results”. What has actually changed, and what has not?

QB 10.8 Why does the interacted regression give the same \(F\) statistic as fitting two separate regressions? State what the interacted version tells you that the split does not.

QB 10.9 A study interacts a treatment dummy with baseline income and finds a significant interaction. Explain what that means in words, and give the two equivalent readings of the coefficient.

QB 10.10 Explain why a large sample makes a Chow test more likely to reject even when the two groups are economically almost identical.

QB 10.11 In a regression of crop yield on rainfall with an irrigation dummy and its interaction, the interaction coefficient is negative. Interpret this, and say why it is economically plausible.

QB 10.12 A colleague argues that since a dummy regression is just a \(t\)-test, nothing is gained by using regression. Give two things regression can do that the \(t\)-test cannot.

Numerical

QB 10.13 A log-wage regression on a public-sector dummy gives a coefficient of 0.28. Compute the exact percentage premium and explain why \(28\%\) would be the wrong figure to report.

QB 10.14 For \(\widehat{y} = 40 + 6x + 15D - 2(xD)\), compute the predicted value for both groups at \(x = 5\) and \(x = 10\), and find the value of \(x\) at which the groups are predicted to be equal.

QB 10.15 A Chow test on two groups of 80 and 120 observations, with a regression containing an intercept and three slopes, gives \(\text{SSR}_P = 940\), \(\text{SSR}_1 = 310\) and \(\text{SSR}_2 = 505\). Compute \(F\) and state its degrees of freedom.

QB 10.16 Three regional dummies are entered with the North as base, giving coefficients of \(-0.14\) (South), \(0.09\) (East) and \(-0.22\) (West) on log output. What is the predicted difference in log output between the South and the West, and which region has the highest predicted output?