Suppose that (n=100) i.i.d. observations for (left(Y_{i}, X_{i} ight)) yield the following regression results: [ begin{equation*} hat{Y}=32.1+66.8

Suppose that \(n=100\) i.i.d. observations for \(\left(Y_{i}, X_{i}\right)\) yield the following regression results:

\[ \begin{equation*} \hat{Y}=32.1+66.8 X, S E R=15.1, R^{2}=0.81 \tag{15.1} \end{equation*} \]

Another researcher is interested in the same regression, but he makes an error when he enters the data into his regression program: He enters each observation twice, so he has 200 observations (with observation 1 entered twice, observation 2 entered twice, and so forth).

a. Using these 200 observations, what results will be produced by his regression program? (Hint: Write the "incorrect" values of the sample means, variances, and covariances of \(Y\) and \(X\) as functions of the "correct" values. Use these to determine the regression statistics.)

\[ \begin{aligned} & \hat{Y}=\Longrightarrow+\Longrightarrow X, S E R=\Longrightarrow, R^{2}= \\ & (\square)(\square) \end{aligned} \]

b. Which (if any) of the internal validity conditions are violated?