List of top Statistics, Econometrics & Mathematical Economics Questions on Regression Analysis asked in GATE XH-C1

Consider a simple pooled regression model: y_it = β₀ + β₁x_it + vit where v_it = μ_i + ∈_it and Cov(x_it, μ_i) ≠ 0. Here, μ_i captures the unknown individual specific effects and it is the idiosyncratic error uncorrelated with both x_it and μ_i. If the parameters of this model are estimated using the ordinary least squares (OLS) method, then the estimated slope coefficient will be

For the function \(F: \R^2 → \R\) specified as F(x, y) = x³ - y³ + 9xy, which of the following options is/are correct

Consider a regression model \( y = \beta_0 + \beta x + u \) where the continuous variable \( y \) is regressed on a dummy variable \( x \), which takes the value either 1 or 0. However, the model was estimated using the instrumental variable (IV) estimation method, wherein the indicator variable \( z \) is used as an instrument of \( x \). Let \( \bar{y}_1 \) and \( \bar{y}_0 \) be the sample averages of \( y \) when \( z \) takes the value 1 and 0, respectively. Let \( \bar{x}_1 \) and \( \bar{x}_0 \) be the sample averages of \( x \) when \( z \) takes the value 1 and 0, respectively. Let \( \bar{y}_1 \) and \( \bar{y}_0 \) be the sample averages of \( y \) when \( x \) takes the value 1 and 0, respectively. Let \( \bar{z}_1 \) and \( \bar{z}_0 \) be the sample averages of \( z \) when \( x \) takes the value 1 and 0, respectively. Then the estimated coefficient of \( \beta_{IV} \) is:

Consider two regression models estimated on a sample of 350 observations.
\[ y = \beta_0 + \beta_1 x_1 + \beta_2 x_2 + \beta_3 x_3 + \beta_4 x_4 + \beta_5 x_5 + u \quad \text{--------(1)} \] \[ y = \alpha_0 + \alpha_1 x_1 + \alpha_2 x_2 + v \quad \text{--------(2)} \] The \( R^2 \) in model (1) is \( R^2_1 = 0.3521 \) and in model (2) is \( R^2_2 = 0.2314 \). The value of the test statistic to test the \( H_0: \beta_3 = \beta_4 = \beta_5 = 0 \) is _________ (round off to three decimal places).