Deck 3: Bivariate Ols: the Foundation of Econometric Analysis

Question 1

The residual for observation i is e_ihat = Y_ihat - Y_i

Answer 1

True

Question 2

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

Answer 2

True

Question 3

Violating the homoscedasticity condition will cause our OLS estimates of $\beta$ ₁hat to be biased.

Answer 3

False

Question 4

Outliers are a bigger problem when we have a smaller sample size than when we have a bigger sample size.

Question 5

The higher the correlation of the error term and the independent variable, the closer the expected value of B1hat is to the true value.

Question 6

The higher the variance of X in our sample, the higher the variance of B1hat.

Question 7

Suppose we estimate a model in which salary in thousands of Euros is the dependent variable and years of education is the independent variable. We get a result that says Income-hat = 20 + 2 Years Education. Which of the following is correct:

A) Two years of education increases income by one.
B) An extra year of education is expected to increase income by 2.
C) An individual with 10 years of education is expected to have an income of 20.
D) The expected income for someone with 0 years of education is 2.

Question 8

A residual measures:

A) The unobservable error term, $\varepsilon$ .
B) The distance between the actual value and the predicted value.
C) The distance between $\beta$ -hat and the actual value of $\beta$ .
D) The expected value of the dependent variable.

Question 9

Please look at the equation below and pick the best answer $$\hat { \beta } _ { 1 } = \frac { \sum _ { i = 1 } ^ { N } \left( X _ { i } - \bar { X } \right) \left( Y _ { i } - \bar { Y } \right) } { \sum _ { i = 1 } ^ { N } \left( X _ { i } - \bar { X } \right) ^ { 2 } }$$

A) B1hat will be positive if Y tends to be above its mean when X tends to be above its mean.
B) The sign of B1 will be the same sign as the denominator.
C) Xi can never equal X-bar for any observation
D) B1hat will be positive if Xi is always above X-bar.

Question 10

In OLS with a large sample, the coefficient estimates will be:

A) Correct
B) Normally distributed.
C) Centered on zero.
D) Correct

Question 11

An estimate of beta1 is said to be unbiased if

A) Beta1-hat is normally distributed
B) The coefficient distribution is narrow.
C) The average value of the distribution of B1-hat is equal to the true value.
D) The coefficient distribution is wide.

Question 12

Name the concept: The variance of e_i is the same for every observation.

A) Homoscedasticity
B) Heteroscedasticity
C) Consistency
D) Bias

Question 13

Which of the following are used to describe the goodness of fit for a model?

A) The coefficient of the regression
B) R²
C) The standard error of the coefficient
D) The constant

Question 14

Imagine we have two separate models, Model 1 and Model 2. The R² for Model 1 is 0.8 and the R² for Model 2 is 0.4.

A) Model 1 is a better model than Model 2
B) Model 2 is a better model than Model 1
C) R² is neither necessary nor sufficient for analysis to be useful

Question 15

Please briefly describe the concept of an outlier and explain some strategies for dealing with outliers.

Question 16

Please explain why residuals need to be squared in process of generating OLS coefficients.

Question 17

OLS does not automatically produce unbiased estimates. Please briefly explain the condition that must be satisfied for OLS to produce unbiased estimates.

Question 18

Please explain the concept of consistency in OLS estimations.

Question 19

Please list and give a short description of the two sources of randomness in the coefficient estimates.