Untitled Quiz

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).