L1 Flashcards
What is a model?
Explanation of the world in an easy way with variables
How are y and x related?
Linearly
What does u capture?
Everything that determines y, that is not x
Name observable, and non-observable: y, x, u.
y and x observable. u unnobservable.
What are Betas?
Unobservable parameters -> we want to estimate
What is B1 in y = B0 + B1 x + B2 x2 + u?
CAUSAL effect of x on y, ceteris paribus.
What is spurious correlation?
Correlation without causation.
What is the key assumption for causality?
Zero Conditional Mean Assumption -> E[u|x] = E[u] = 0
Divide the systematic part from the idiosyncratic part.
Starting with E[y|x] = B0 + B1 x
y = E[y|x] (systematic) + u (idiosyncratic)
For the population sample, yi equals?
yi = E[y|xi] + ui
Symbol to represent estimated error:
ûi
ûi equals:
yi - ^yi
(Estimated error = real value - estimated value)
What is the goal of choosing ^B0 and ^B1?
Minimizing ûi (squared)
^B1 equals:
^B1 = cov(x,y) / var(x)
^B0 equals:
Intercept -> avg(y) - ^B1 avg(x)
Do the properties of OLS estimators always hold true?
Yes
Explain the difference between errors and residuals
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
Difference between PRF and Estimated RF?
The first one is for the population (almost theoretical -> the real one), the other is the one we estimate.
What does SST measure?
Total sample variation in the yi
What does SSE measure?
Sample variation in the ^yi
What does SSR measure?
Sample variation in the ^ui
What is R-squared?
How much of the total variation can be explained by the model.
R-squared formulas:
SSE / SST
1 - SSR / SST
Formula Sheet
What does an higher R-squared mean?
Higher proportion of variation in yi is explained by variation in xi (as long as they are not correlated)
Types of Scaling variables:
Scaling y
Scaling x
Shifting y
Shifting x
Describe Scaling y:
all coefficients are scaled
y = B0 + B1 x + u
c y = c B0 + c B1 x + c u
Describe Scaling x:
Slope coefficient is scaled
y = B0 + B1 x + u
y = B0 + B1/c x + u
Decribe Scaling both dependent and independent variables:
y = B0 + B1 x + u
c y = c B0 + c B1/d x + c u
Describe shifting the dependent variable:
Intercept shifts, slope is unchanged.
y = B0 + B1 x + u
(y + c) = (B0 + c) + B1 x + u
Describe shifting the independent variable:
Intercept shifts, slope unchanged
y = B0 + B1 x + u
y = (B0 - B1 c) + B1 (x + c) + u
Do changes in scaling of shifting have any effect on significance or interpretation?
No
Usefulness of logs?
If y > 0, can mitigate skewness and heteroskedacity by reducing the influence of outliers
When not to take logs?
Variables measured in years, months, etc
Proportions (rates)
Limitations of logs
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)
log(y)=x
y = e^x
What to do if log isn’t working?
Quadratic terms
log(wage) = B0 + B1 educ + B2 (educ^2) + u
What is B1?
No longer the ceteris paribus effect of educ on log(wage)
