L1

Question 1

What is a model?

Answer 1

Explanation of the world in an easy way with variables

Question 2

How are y and x related?

Answer 2

Linearly

Question 3

What does u capture?

Answer 3

Everything that determines y, that is not x

Question 4

Name observable, and non-observable: y, x, u.

Answer 4

y and x observable. u unnobservable.

Question 5

What are Betas?

Answer 5

Unobservable parameters -> we want to estimate

Question 6

What is B1 in y = B0 + B1 x + B2 x2 + u?

Answer 6

CAUSAL effect of x on y, ceteris paribus.

Question 7

What is spurious correlation?

Answer 7

Correlation without causation.

Question 8

What is the key assumption for causality?

Answer 8

Zero Conditional Mean Assumption -> E[u|x] = E[u] = 0

Question 9

Divide the systematic part from the idiosyncratic part.

Answer 9

Starting with E[y|x] = B0 + B1 x

y = E[y|x] (systematic) + u (idiosyncratic)

Question 10

For the population sample, yi equals?

Answer 10

yi = E[y|xi] + ui

Question 11

Symbol to represent estimated error:

Answer 11

ûi

Question 12

ûi equals:

Answer 12

yi - ^yi

(Estimated error = real value - estimated value)

Question 13

What is the goal of choosing ^B0 and ^B1?

Answer 13

Minimizing ûi (squared)

Question 14

^B1 equals:

Answer 14

^B1 = cov(x,y) / var(x)

Question 15

^B0 equals:

Answer 15

Intercept -> avg(y) - ^B1 avg(x)

Question 16

Do the properties of OLS estimators always hold true?

Answer 16

Yes

Question 17

Explain the difference between errors and residuals

Answer 17

Errors (u) are never observed -> distance between the observations and the PRF

Residuals (û) are captured from data -> distance between observations and estimated regression function

Question 18

Difference between PRF and Estimated RF?

Answer 18

The first one is for the population (almost theoretical -> the real one), the other is the one we estimate.

Question 19

What does SST measure?

Answer 19

Total sample variation in the yi

Question 20

What does SSE measure?

Answer 20

Sample variation in the ^yi

Question 21

What does SSR measure?

Answer 21

Sample variation in the ^ui

Question 22

What is R-squared?

Answer 22

How much of the total variation can be explained by the model.

Question 23

R-squared formulas:

Answer 23

SSE / SST

1 - SSR / SST

Formula Sheet

Question 24

What does an higher R-squared mean?

Answer 24

Higher proportion of variation in yi is explained by variation in xi (as long as they are not correlated)

Question 25

Types of Scaling variables:

Answer 25

Scaling y
Scaling x
Shifting y
Shifting x

Question 26

Describe Scaling y:

Answer 26

all coefficients are scaled

y = B0 + B1 x + u

c y = c B0 + c B1 x + c u

Question 27

Describe Scaling x:

Answer 27

Slope coefficient is scaled

y = B0 + B1 x + u

y = B0 + B1/c x + u

Question 28

Decribe Scaling both dependent and independent variables:

Answer 28

y = B0 + B1 x + u

c y = c B0 + c B1/d x + c u

Question 29

Describe shifting the dependent variable:

Answer 29

Intercept shifts, slope is unchanged.

y = B0 + B1 x + u

(y + c) = (B0 + c) + B1 x + u

Question 30

Describe shifting the independent variable:

Answer 30

Intercept shifts, slope unchanged

y = B0 + B1 x + u

y = (B0 - B1 c) + B1 (x + c) + u

Question 31

Do changes in scaling of shifting have any effect on significance or interpretation?

Answer 31

No

Question 32

Usefulness of logs?

Answer 32

If y > 0, can mitigate skewness and heteroskedacity by reducing the influence of outliers

Question 33

When not to take logs?

Answer 33

Variables measured in years, months, etc
Proportions (rates)

Question 34

Limitations of logs

Answer 34

Can’t be used if variables takes 0 or negative values (function log is undefined there)

If y is non-negative but may be equal to zero: log (1+y) may be a solution (assuming few zeros)

Question 35

log(y)=x

Answer 35

y = e^x

Question 36

What to do if log isn’t working?

Answer 36

Quadratic terms

Question 37

log(wage) = B0 + B1 educ + B2 (educ^2) + u

What is B1?

Answer 37

No longer the ceteris paribus effect of educ on log(wage)