Untitled Quiz

<p>It takes into account features like simultaneity (A)</p> Signup and view all the answers

<p>Dependent variable (D)</p> Signup and view all the answers

<p>Linearity in the parameters of the model (A)</p> Signup and view all the answers

<p>Arbitrary transformations of regressor variables (A)</p> Signup and view all the answers

<p>They account for potential interaction among variables (A)</p> Signup and view all the answers

<p>The intercept of the regression line (A)</p> Signup and view all the answers

<p>To estimate the model parameters accurately (A)</p> Signup and view all the answers

<p>It provides a method for estimating the coefficients (B)</p> Signup and view all the answers

<p>Their mean should be zero for an unbiased model (B)</p> Signup and view all the answers

<p>The unexplained variation in Y (D)</p> Signup and view all the answers

<p>There is no correlation (D)</p> Signup and view all the answers

<p>To account for unobserved factors affecting the dependent variable (B)</p> Signup and view all the answers

<p>$k + 1$ (C)</p> Signup and view all the answers

<p>Total variation is equal to the explained variation plus the unexplained variation. (B)</p> Signup and view all the answers

<p>The intercept term, $eta_1$. (B)</p> Signup and view all the answers

<p>It centers the data around the mean. (D)</p> Signup and view all the answers

<p>$Y_t - ar{Y} = eta_2(X_{2t} - ar{X_2}) + ...$ (C)</p> Signup and view all the answers

<p>The mean of the dependent variable $Y$. (A)</p> Signup and view all the answers

<p>$ ext{TSS} = ext{sum of }(Y_t - ar{Y})^2$ (D)</p> Signup and view all the answers

<p>The difference between the individual error and the average error. (A)</p> Signup and view all the answers

<p>Substituting the mean into the squared deviations. (D)</p> Signup and view all the answers

<p>$RB$ (C)</p> Signup and view all the answers

<p>u is normally distributed (C)</p> Signup and view all the answers

<p>$Rβ - r ~ N(0, σ² R(X'X)^{-1} R')$ (A)</p> Signup and view all the answers

<p>A projection matrix that follows idempotent properties (C)</p> Signup and view all the answers

<p>Total Sum of Squares (C)</p> Signup and view all the answers

<p>Rβ = r (C)</p> Signup and view all the answers

<p>The unknown value of σ² (D)</p> Signup and view all the answers

<p>It must have full column rank. (D)</p> Signup and view all the answers

<p>To select models and compare their fit (B)</p> Signup and view all the answers

<p>It decreases when increasing the number of predictors in the model. (A)</p> Signup and view all the answers

<p>They must have zero mean. (C)</p> Signup and view all the answers

<p>Schwarz Criterion (C)</p> Signup and view all the answers

<p>Explained Sum of Squares (A)</p> Signup and view all the answers

<p>$var(m) = E(a'uu'a) = ho^2 \alpha'\alpha$ (B)</p> Signup and view all the answers

<p>$X'a = c$ (C)</p> Signup and view all the answers

<p>It is a best linear unbiased estimator (BLUE) of $c'\beta$. (D)</p> Signup and view all the answers

<p>$H_0: \beta_1 = 0$ (B)</p> Signup and view all the answers

<p>It indicates constant returns to scale. (D)</p> Signup and view all the answers

<p>It is the same linear combination of the <em>β</em>'s. (D)</p> Signup and view all the answers

<p>It is an estimated prediction of Y. (C)</p> Signup and view all the answers

<p>Inversion of $(X'X)$ multiplied by the constrained equation. (C)</p> Signup and view all the answers

The statistical analysis of economic data, used to model economic relationships and make predictions.

A model that predicts a dependent variable (regressand) based on a linear combination of 2 or more independent variables (regressors).

The dependent variable in a regression model. It's the variable being predicted.

The independent variables in a regression model. They explain the changes in the regressand.

When variables in a model influence each other at the same time, making it impossible to isolate cause and effect.

A model where the relationship between the variables is linear, meaning changes in the regressors directly result in proportional changes in the regressand.

A model that predicts one dependent variable using several independent variables, but doesn't consider relationships between the independent variables.

A system of equations that model multiple dependent variables and their relationships, accounting for simultaneous influences.

The total variation of the dependent variable (Y) around its mean, measuring the overall spread of the data.

The variation in the dependent variable (Y) that is explained by the regression model, capturing how well the independent variables predict the outcome.

The variation in the dependent variable (Y) that is not explained by the regression model, representing the unexplained variation in the data.

The principle that the total variation in the dependent variable (Y) can be broken down into two components: the variation explained by the regression model (ESS) and the variation not explained by the model (RSS).

A way to express the regression equation using deviations of variables from their respective means, simplifying the calculations and highlighting the relationship between variables.

A matrix used to transform the data to the deviation form, ensuring the transformation preserves the essential properties and enables simpler calculations.

By applying the transformation matrix (A), all variables in the regression equation are expressed as deviations from their means, eliminating the intercept term (β_1) and simplifying the equation.

An idempotent matrix, when applied twice, yields the same result as applying it once. In this context, it ensures that transforming the data twice doesn't change the deviation form, guaranteeing the stability of the transformation and simplifying the calculations.

The linear model expressing the relationship between a dependent variable (y) and multiple independent variables (X). It includes the coefficient vector (β) and error term (e).

The matrix A, when multiplied by itself, results in the same matrix (A * A = A). This means applying A twice has the same effect as applying it once.

Breaking down the total variation in the dependent variable (TSS) into explained variation by the model (ESS) and unexplained variation (RSS).

Measures the proportion of the total variation in the dependent variable that is explained by the regressors in the model.

Adjusted for the number of independent variables in the model, providing a better measure of the model's fit when comparing models with differing predictors.

A measure used for model selection, weighing the model's fit (RSS/n) with the complexity of the model (k/n).

Similar to AIC, it prioritizes simpler models by including a penalty that increases with sample size.

In a matrix, the columns are linearly independent, meaning no column can be expressed as a linear combination of the others.

An estimator that, on average, produces the true value of the parameter being estimated.

An estimator that is both unbiased and has the smallest variance among all possible linear unbiased estimators.

A weighted sum of the regression coefficients (β's).

The best linear unbiased estimate of the expected value of Y (the regressand), obtained by plugging in the corresponding X values into the regression equation.

A statistical procedure used to determine whether there is enough evidence to reject a null hypothesis about the population parameter.

A hypothesis test that examines whether a regressor has predictive power for the regressand.

A production function where increasing inputs proportionally results in the same proportional increase in output.

Determines if the difference between two coefficients is significant enough to conclude they are not the same.

The probability distribution of a linear combination of regression coefficients (Rβ), which is determined by the distribution of the error terms (u) in the regression model.

A statistical model that predicts a dependent variable (Y) using a linear combination of independent variables (X's).

To derive the sampling distribution of Rβ, we need to assume normality of the error terms (u) in addition to the standard assumptions of zero mean and constant variance.

If the error terms follow a normal distribution, then the linear combination of regression coefficients, Rβ, also follows a normal distribution with a mean of RB and a variance of σ² R(X'X)⁻¹ R'.

When testing a null hypothesis about a linear combination of regression coefficients (Rβ), we can use the F-distribution to assess the evidence against the null hypothesis.

An equation that describes the relationship between the regression coefficients (β) and the data (X and Y) by minimizing SRSS.

When the regressors (X) and the residuals (e) have no linear relationship, indicating that the model is capturing the influence of the regressors on the dependent variable.

Since the variance of the error terms (σ²) is unknown, we can estimate it using the residual sum of squares (e'e) divided by the degrees of freedom (n-k).