Question

section A. Multiple choice questions: [50 marks] Indicate the correct answer in the box provided. 1. To decide whether $y_i = \beta_1 + \beta_2x_i + e_i$, or $ln y_i = \beta_1 + \beta_2x_i + e_i$ fits the data better, you cannot consult the regression $R^2$ because: a. the natural logarithm of $y_i$, $ln y_i$, may be negative for $0 < y_i < 1$. b. the TSS are not measured in the same units between the two models. c. the slope no longer indicates the effect of a unit change of $x_i$ on $y_i$ in the log- linear model. d. the regression $R^2$ can be greater than one in the second model. 2. Suppose that the variable $x_3$ has been omitted from the following regression equation: $y_i = \beta_1 + \beta_2x_{2i} + \beta_3x_{3i} + e_i$ where $\beta_2$ is the estimator obtained when $x_3$ is omitted from the equation. The bias of $\beta_2$ is positive if: a. $\beta_3 > 0$ and $x_2$ and $x_3$ are positively correlated. b. $\beta_3 < 0$ and $x_2$ and $x_3$ are positively correlated. c. $\beta_3 > 0$ and $x_2$ and $x_3$ are negatively correlated. d. $\beta_3 = 0$ and $x_2$ and $x_3$ are negatively correlated.

          section A. Multiple choice questions: [50 marks]
Indicate the correct answer in the box provided.
1. To decide whether $y_i = \beta_1 + \beta_2x_i + e_i$, or $ln y_i = \beta_1 + \beta_2x_i + e_i$ fits the data better, you
cannot consult the regression $R^2$ because:
a. the natural logarithm of $y_i$, $ln y_i$, may be negative for $0 < y_i < 1$.
b. the TSS are not measured in the same units between the two models.
c. the slope no longer indicates the effect of a unit change of $x_i$ on $y_i$ in the log-
linear model.
d. the regression $R^2$ can be greater than one in the second model.
2. Suppose that the variable $x_3$ has been omitted from the following regression equation:
$y_i = \beta_1 + \beta_2x_{2i} + \beta_3x_{3i} + e_i$
where $\beta_2$ is the estimator obtained when $x_3$ is omitted from the equation. The bias of $\beta_2$
is positive if:
a. $\beta_3 > 0$ and $x_2$ and $x_3$ are positively correlated.
b. $\beta_3 < 0$ and $x_2$ and $x_3$ are positively correlated.
c. $\beta_3 > 0$ and $x_2$ and $x_3$ are negatively correlated.
d. $\beta_3 = 0$ and $x_2$ and $x_3$ are negatively correlated.

section A. Multiple choice questions: [50 marks]
Indicate the correct answer in the box provided.
1. To decide whether yi = β1 + β2xi + ei, or ln yi = β1 + β2xi + ei fits the data better, you
cannot consult the regression R^2 because:
a. the natural logarithm of yi, ln yi, may be negative for 0 < yi < 1.
b. the TSS are not measured in the same units between the two models.
c. the slope no longer indicates the effect of a unit change of xi on yi in the log-
linear model.
d. the regression R^2 can be greater than one in the second model.
2. Suppose that the variable x3 has been omitted from the following regression equation:
yi = β1 + β2x2i + β3x3i + ei
where β2 is the estimator obtained when x3 is omitted from the equation. The bias of β2
is positive if:
a. β3 > 0 and x2 and x3 are positively correlated.
b. β3 < 0 and x2 and x3 are positively correlated.
c. β3 > 0 and x2 and x3 are negatively correlated.
d. β3 = 0 and x2 and x3 are negatively correlated.

Added by Harry B.

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