Session 3

Question 1

mean of the probability distribution

Answer 1

mu (u) true mean sample mean = x-bar

Question 2

law of large numbers

Answer 2

as the number of observations drawn increases, the mean of x-bar (sample mean) eventually approaches the mean mu (true mean of population) as closely as you specified.

Question 3

standard deviation =

Answer 3

= square root of the variance

Question 4

variance

Answer 4

is the avg squared deviation of the values of the variable from their mean

Question 5

3 assumptions on linear regression model under which OLS gives appropriate estimator

Answer 5

1. conditional distribution of Ui given Xi has a mean of zero (other factors contained in Ui are unrelated to Xi – that is, given a value of Xi, the mean of the distribution of these other factors is 0). IN other words, the error term Ui has a condition mean zero given Xi:E(Ui|Xi) = 0. 2. (Xi, Yi), i = 1,….n. Are independently and identically distributed. 3. large outliers are unlikely in other words 1. OLS estimator is unbiased, b/c error term has conditional mean of 0 2. Xi and Yi are independent and indentically distributed 3. large outliers unlikely.

Question 6

if the least squares assumptions hold then the OLS estimators of the slope and intercept are: _____, _______, and have a ______

Answer 6

if the least squares assumptions hold then the OLS estimators of the slope and intercept are: unbiased, consistent, and have a sampling distribution with a variance that is inversely proportional to the sample size n. OR, OLS estimators as unbiased, consistent, & normally distributed when the sample is large.

Question 7

binary variable is also called ___ or ____

Answer 7

indicator or dummy variable example: male or female, urban or rural

Question 8

The two conditions for OVB are:

Answer 8

The two conditions for OVB are: 1. X2 (or priGPA) is a determinant of Y 2. X2 (priGPA) and X1 (attend) are correlated

Question 9

The formula for bias

Answer 9

The formula for bias α1-1 = γ1 * β2

Question 10

A high R2 means that the regressors…… A high R2 does not mean that you have eliminated …. A high R2 does not mean that you have an unbiased… A high R2 does not mean that the included variables are ….

Answer 10

A high R2 means that the regressors explain the variation in Y. A high R2 does not mean that you have eliminated omitted variable bias. A high R2 does not mean that you have an unbiased estimator of a causal effect (1). A high R2 does not mean that the included variables are statistically significant – this must be determined using hypotheses tests.

Question 11

linear log log linear log log

Answer 11

Linear Log: A 1% change in X is associated with a change in Y of 0.01β1 Log Linear: A change in X by 1 unit is associated with a 100β1% change in Y Log log:A 1% change in X is associated with a β1% change in Y (β1 is the elasticity with respect to X)

Question 12

OLS Assumptions

Answer 12

1. E(u|X = x) = 0. The conditional distribution of u given X has mean zero.
2. (Xi,Yi), i =1,…,n, are i.i.d.
3. X and u have four finite moments.

Question 13

Answer 13

1. Assumption 1 is violated. for any slice, the average of residuals = 0
2. Assumption 2 is violated. you can see predictive cycles, there’s a cyclical pattern, likely seasonal data

Question 14

Answer 14

• Assumption 1 is violated.
• Assumption 2 is violated - some trending happening

Question 15

Answer 15

• Assumption 1 is violated.

Correction: Likely large outlier, could take log transformation on x or y axis. and bring down effect of outlier.

Question 16

r² is the….

Answer 16

percentage of variance explained by the model

Question 17

key assumptions in multiple linear regression

Answer 17

1. the conditional distribution of u given the X’s has mean zero, that is, E(u|X₁ = x₁ …. X_k = x_k) = 0
2. X_1i ….. X_ki, Y_i), i=1….n, are independent and identically distributed
3. X₁…X_k and u have four finite moments
4. There is no strong multicollinearity

Question 18

linear log interpretation

Y_i = B₀ + B₁ln(X_i) + u_i

Answer 18

A 1% change in X is associated with a change in Y of 0.01β1

Question 19

log linear interpretation

ln(Y_i) = B_o + B₁X^_i + u_i

Answer 19

A change in X by 1 unit is associated with a 100β1% change in Y

Question 20

log-log interpretation

ln(Y_i) = B₀ + B₁ln(X_i) + u_i

Answer 20

A 1% change in X is associated with a β1% change in Y (β1 is the elasticity with respect to X)

Question 21

interaction term interpretations

Answer 21