1 consider the model yt beta0 beta1 xt

Question

1. Consider the model Y_t = β₀ + β₁ X_t + ε_t, where t = 1,..., n.  If the errors ε_t are not correlated, then the OLS estimates of  β₀  and β₁  will be unbiased.

2. In the following regression model ln Y_i = β₀ + β₁ X_1i + β₂ ln X_2i + ε_i, all β_k coefficients measure the elasticities of the Y variable with the respective X variables, because the Y variable appears in a logarithmic form. 

3. If we want to capture a curvature in the relationship between Y_i and X_i, we have to use a quadratic model, where the slope is not constant everywhere and changes according to the value of Xi at which it is being assessed. 

4. If a hypothesis is rejected at the 0.10 level of significance, it may not be rejected at the 0.05 level of significance.

5. If β₁  is positive in the equation 

(1)  Y_i = β₀ + β₁ X_1i + β₂ X_2i + ε_i, it can never be negative in the equation

(2)  Y_i = β₀ + β₁ X_1i + β₂ X_2i + β₃ X_3i + ε_i,.