Question: Dummy variable for one observation. Suppose the data set consists of n observations, (y n , X n ) and an additional observation, (y s

Dummy variable for one observation. Suppose the data set consists of n observations, (y_n, X_n) and an additional observation, (y_s, x'_s). The full data set contains a dummy variable, d, that equals zero save for one (the last) observation. Then, the full data set is

0 (Neue des) = [X] and you = [] n (Xn,s,dn,s)

It is claimed in the text that in the full regression of y_n,s on (X_n,s, d_n,s) using all n+1 observations, the slopes on X_n,s, b_n,s, and their estimated standard errors will be the same as those on X_n, b_n in the short regression of y_n on X_n, and the sum of squared residuals in the full regression will be the same as the sum of squared residuals in the short regression. That is, the last observation will be ignored. However, the R² in the full regression will not be the same as the R² in the short regression. Prove these results.

0 (Neue des) = [X] and you = [] n (Xn,s,dn,s)

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