Linear Regression: Correlation, Bivariate Regression; OLS Assumptions, Robust Standard Errors Flashcards
Correlation
2 variables vary together: there can be positive correlation or negative correlation. Correlation is always between -1 and 1.
POSITIVE: (moves from bottom left to top right) DV increases as the IV also increases.
NEGATIVE: (moves from top left to bottom right) as the DV decreases the IV increases.
Perfect Correlation
r=1 means perfect correlation
r=-1 means imperfect correlation
r=0 means no correlation between variables
The closest to 0 the less relationship there is between variables
Covariance
Cov(X,Y) = Σ E((X – μ) E(Y – ν)) / n-1
X is a random variable
E(X) = μ is the expected value (the mean) of the random variable X and
E(Y) = ν is the expected value (the mean) of the random variable Y
n = the number of items in the data set.
Σ summation notation
Bivariate Regression
Finds the best fit for a line through data - the line of best fit is the one who minimizes the y distance from each observation to the line.
Correlation vs Regression
Correlation tells us how strongly associated two variables are;
Regression tells on average how much a one unit increases or decreases the predicted value of the variable.
Regression gives more precise information on the strength of a relationship
Vertical Deviations
Explain the DV (y) and why it is on the vertical axis, therefore vertical distance.
Ordinary Least Squares (OLS)
Coefficient
Hypothesis Testing for Regression
S.E. for Regression Root Mean
Null Hypothesis (H0)
Build t-value
Estimators
Estimators (Bias)
Estimators (Efficiency)