Correlation and OLS Flashcards
(21 cards)
inference
Given that ….
Probability
Likelihood
descriptive inference
the prevalence of a feature or the correlation between two features
predictive inference
the value of a feature for a unit we do not observe
causal inference
the causal effect of a treatment on an outcome in the population
correlation
The correlation between two features of the world is the extent to which they occur together
When can we talk about correlation
- There has to be a comparison and 2. Both features of the world have to have some variation
Covariance
To what extent does X and Y vary together?
cov (X,Y)
E[(X - E[X]) (E-E[Y])]
What does that equation mean
It is the expectation of X - its mean and the expectation of Y minus its mean. If X is greater than its mean, we expect a positive covariance. Cannot tell us how great a relationship is - how much they vary from the mean, indicates the value - how much variance exists between the two variables
correlation
corr (X,Y) = cov (X, Y)/ square root var(x) var(Y)
Correlation scale
-1 to 1 - closer the correlation to a variable the stronger the relationship is ie. if close to 1 stronger than like 0.1. Correlation is standardised on the scale
Best Linear Predictor
Is the linear function of X (Y = a + bX) that best predicts Y
What does the BLP do?
Minimises the sum of squared prediction errors
b0
intercept
b1
slope
What does the BLP do?
Minimises the sum of squared prediction errors ie the difference between X and E[X] - they are squared to make everything positive
What is the b in BLP - X(Y= a+bX)
The sign, it tells us the correlation
Positive b
Positive correlation
Equations
b =
σX,Y
/σ2X
