# 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.