# 302 Chapter 2

P-Value
Prob of getting a test statistic value that is equally or more extreme than the one actually observed
If p-value < α, reject H_0 adn accept H_α
If p-value > α, do not reject H_0
Smaller p-value: Less likely H_0 is true
p-value < 0.01: Strong evidence against H_0
p-value < 0.05: Moderate evidence against H_0
p-value < 0.1: Weak evidence against H_0
p-value > 0.1: No evidence against H_0
Interpretation of b_0 and b_1
b_0 is intercept
b_1 is slope
Prediction Interval
Wider than confidence intervals
Confidence Band
Confidence intervals are just for a single X_h while confidence bands are for entire regression line.
Gauss-Markov Theorem
Says that OLS estimates have lowest variance among all unbiased linear estimators (BLUE).
There could be non-linear estimates w/ lower vaiance
There could also be biased estimates w/ lower MSE.
Mean Squares (MS)
MS = SS/df
Correlation
Vales close to ±1.00: Strong correlation
Values close to 0.00: weak correlation
Positive values: Direct relationship
Negative values: inverse relationship
Proofs:
See notes.