Econometrics Test #1

The problem with R^2

-R^2 goes up every time you add independent variables to your regression equation. -Because of the way it is calculated, R^2 goes up even if we add independent variables that have little or no explanatory power. -To remedy this problem, statistical programs generate a statistic called "Adjusted R^2."

Given Incomei = 10 + 1.5Agei + ei, interpret the model A) A one year increase in age is expected to lead to a 1.5 increase in income B) A 1.5 increase in age is expected to lead to a 1 increase in income C) A 1.5 increase in income is expected to lead to a 1 unit increase in age D) Income is 10

A

If we decrease the significance level (alpha) all else being equal, the power of the test will: A) Decrease B) Increase C) Won't change D) It depends - need more information

A

Name the concept: The variance of ei is the same for every observation. A) Homoscedasticity B) Heteroscedasticity C) Consistency D) Bias

A

The error term A) Contains all other factors that affect the dependent variable. B) Contains all other factors that affect the independent variable. C) Contains all other factors that affect the intercept. D) Is a random variable with no relation to other variables.

A

Multicollinearity

A multiple regression equation is flawed because two variables thought to be independent are actually correlated to be independent

the concept of consistency in OLS estimations:

An estimator is a consistent estimator if the distribution of B1hat shrinks closer and closer to the true value (B1) as the sample size increases (as we get more data), as long as the exogeneity condition holds true.

An omitted variable bias problem occurs when: A) We fail to include an independent variable that is not correlated with the dependent variable but is correlated with the main independent variable of interest. B) We fail to include an independent variable that is correlated with the main independent variable of interest and the error term. C) We fail to include the main independent variable of interest in the model. D) We fail to include an independent variable that is correlated with the error term but is not correlated with the main independent variable of interest.

B

In which case would we choose to a one-sided alternative hypothesis over a two-sided alternative hypothesis? A) It does not matter what type of alternative hypothesis we specify. B) Choose a one sided alternative hypothesis when the theory and literature suggests either that the coefficient should be greater than zero or that the coefficient should be less than zero. C) We choose a one sided alternative hypothesis when we have a large sample size. D) We choose a one sided alternative hypothesis when we specify a low (0.01) alpha.

B

When an independent variable is exogenous A) It is correlated with the error term B) It is not correlated with the error term C) It is correlated with the slope D) It is not correlated with the slope

B

Which of the following are used to describe the goodness of fit for a model? A) The coefficient of the regression B) R^2 C) The standard error of the coefficient D) The constant

B

If the measurement error is in the independent variable, then A) We don't need to worry about bias, the measurement error will be reflected in the error term. B) The bigger the measurement error, the bigger the variance of the error term. C) We will have a case of attenuation bias, where the coefficient will be closer to 0 than it should be. D) We will have a case of attenuation bias, where the coefficient is larger than it should be.

C

What should we do when we have multicollinearity? A) Ignore it no matter what. B) Drop some of the independent variables. C) Consider testing whether the highly collinear variables are jointly significant. D) Add more independent variables in order to reduce multicollinearity

C

In a case where there is multicollinearity in the model A) Independent variables have strong linear relationships with each other B) The variance of the estimates increases when we have multicollinearity. C) Multicollinearity will lead to bias. D) Both A and B E) Both A and C

D

Assume that we are looking at the effect of education on wages, which of the following factors could most likely lead to endogeneity? A) Height B) Religion C) Number of siblings D) Intelligence

D)

equation for R^2

ESS/TSS

Total sum of squares (TSS) =

Explained sum of squares (ESS) + Residual sum of squares (RSS)

The Classical Assumptions:

Linear, Zero Population Mean, Explanatory Variables Uncorrelated with Error, Error Term is Uncorrelated with Itself, Error has Constant Variance (Homoscedasticity), No Perfect Multicollinearity, error term normally distributed

the residual value:

The difference between the estimated Y and the actual Y

Ordinary least squares (OLS):

a regression estimate technique that calculates the coefficients so as to minimize the sum of the squared residuals

Outlier

an observation that lies outside the range of the rest of the observations

type II error

failing to reject a false null hypothesis

true/false: Type I errors occur when we fail to reject a null hypothesis even when it is false.

false

true/false: The residual for observation i is eihat = Yihat - Yi

false: other way around

true/false: Measurement error in the dependent variable causes our beta-hat estimates to be biased.

false; it causes it to be less precise and standard error bigger, but not biased.

true/false: The higher the variance of X in our sample, the higher the variance of B1hat.

false; they are inversely related

how to create a variable in stata:

gen

multivariate regression coefficient:

indicates the change in the dependent variable associated with a one-unit increase in the independent variable in question, holding constant the other independent variables in the equation

Does the unit of measurement of the variables matter?

no

type I error

rejecting a true null hypothesis

endogeneity

situations in which an explanatory variable is correlated with the error term; something out of one's control (ex height)

R^2 (coefficient of determination)

the most commonly used measure of fit

true/false: An independent variable is endogenous if changes in it are related to factors in the error term

true

true/false: If an analysis cannot be replicated, it cannot be trusted

true

true/false: Outliers are a bigger problem when we have a smaller sample size than when we have a bigger sample size.

true

true/false: Statistical projects should document both the data and the methods used to arrive at the conclusion.

true

true/false: The probability a continuous random variable is near some value is defined by its probability density function.

true