Assumptions Flashcards
1
Q
What are some assumptions/rules for SIMPLE linear regression?
A
- SR1: Yt = α + βXt + εt
- SR2: E(εt) = 0
- SR3: Var(εt) = σ²
- SR4: Cov (εt, εt+1) = 0
- SR5: Xt is given, and must take at least 2 values
- SR6: εt ~ N (0, σ²)
2
Q
What are some assumptions/rules for MULTIPLE linear regression?
A
- MR1: Yt = α +ΣβiXit + εt
- MR2: E(εt) = 0
- MR3: Var(εt) = σ²
- MR4: Cov (εi, εj) = 0
- MR5: Xs are given, and are linearly independant
- MR6: εt ~ N (0, σ²)
3
Q
What are some assumptions/rules for Summation?
A
- S1: ΣXi= X1+X2+…..+Xn, where i is the number of observation [start] and n is the last observations
- S2: If ΣaXi, then this is aΣXi + na
- S3: If Σ(Xi + Yi), then = ΣXi + ΣYi
- S4: If ΣΣ(Xi+Yi), do the first Σ [inside], BUT ΣΣ are interchangeable
- S5: ΣXi = Tx̄
4
Q
What are some assumptions/rules for Expected Values?
A
- E1: Expectation of Sum = Sum of expectation [E(X+Y) = E(X) + E(Y)]
- E2: Expectation of a constant is a constant [E(C) = C]
- E3: Constant can be taken common [E(cX) = cE(X)]
- E4: Expectations of expected values do not change [E(E(X)) = E(X)]
- E5: E(XY) = E(X)E(Y) + Cov(X,Y)
5
Q
What are some assumptions/rules for Variance?
A
- V1: Variance of a Constant is 0
- V2: Variance of constant can get taken out [Var(cX) = c²(Var(X))]
- V3: Var(X+Y) = Var(X) + Var(Y) + 2Cov(X,Y)
- V4: Var(X-Y) = Var(X) + Var(Y) - 2Cov(X,Y)
6
Q
What are some Probability rules?
A
- JOINT: Probability with multiple variables; f(X,Y) = P(A∩B)
- MARGINAL: Finding outcome for one variable with joint probability; f(X) = Σf(X,Y) [only Y]
- CONDITIONAL: Outcome given a differnet outcome; F(A|B) = P(A∩B) / P(B)
7
Q
How can you calculate Covariance?
A
- Cov(X,Y) = E(X-x̄)(Y-ȳ)
- Cov(X,Y) = ρX,Y *σXσY
8
Q
What happens if variables are log-linear [mathematical intuition]?
A
- If relationships are not log-linear (i.e. y=ax), increasing x by one unit increases y by a units
- If relationships are log-linear (i.e. y=alnx), increasing x by 1% will increase y by a units
