[See Solution] Consider the following estimated sample regression equation: \haty_i=12+6 x_i 1-3 x_i 2 Determine which of the following statements are true,


Question: Consider the following estimated sample regression equation:

\[\hat{y}_{i}=12+6 x_{i 1}-3 x_{i 2}\]

Determine which of the following statements are true, which are false, and which are indeterminate

Explain your answer.

  1. When \(x_{i 2}\) increases by 1 unit, \(\hat{y}_{i}\) increases by 3 units.
  2. For a given \(x_{i 2}\), when \(x_{i 1}\) increases by 1 unit, \(\hat{y}_{i}\) increases by 6 units.
  3. \(Y\) is more strongly correlated with \(X_{1}\) than with \(X_{2}\) because the coefficient of \(X_{1}\) is larger?
  4. It is possible that the coefficient 6 might not be significantly different from 0 and that the coefficient -3 could be significantly different from 0 if we tested each coefficient using \(\alpha\).

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