Linear Regression: Correlation, Bivariate Regression; OLS Assumptions, Robust Standard Errors

Question 1

Correlation

Answer 1

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.

Question 2

Perfect Correlation

Answer 2

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

Question 3

Covariance

Answer 3

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

Question 4

Bivariate Regression

Answer 4

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.

Question 5

Correlation vs Regression

Answer 5

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

Question 6

Vertical Deviations

Answer 6

Explain the DV (y) and why it is on the vertical axis, therefore vertical distance.

Question 7

Ordinary Least Squares (OLS)

Question 8

Coefficient

Question 9

Hypothesis Testing for Regression

Question 10

S.E. for Regression Root Mean

Question 11

Null Hypothesis (H0)

Question 12

Build t-value

Question 13

Estimators

Question 14

Estimators (Bias)

Question 15

Estimators (Efficiency)

Question 16

Estimators (Consistency)

Question 17

OLS Assumptions

Answer 17

1. Linearity
2. Mean Independence
3. Homocedasticity
4. Uncorrelated Distributions
5. Normal Distributions

Question 18

Linearity (OLS)

Question 19

Mean Independence (OLS)

Question 20

Homocedasticity (OLS)

Question 21

Uncorrelated Distributions (OLS)

Question 22

Normal Distributions (OLS)