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)