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Quantitative by Mind Map: Quantitative

1. Correlation

1.1. Cov(无穷)

1.2. Correlation

1.2.1. 取值

1.2.2. linear correlation

1.2.3. limitation outlier no linear relation

1.2.4. Sig Test 2 tailed T-test df=n-2

2. regression

2.1. simple linear regression

2.1.1. assumption E(e)=0,Var(e)-C Eeiej)=0 e is normal distribution

2.1.2. estimated coefficent intercept slope Cov(x,y))/Var(x)

2.1.3. Sig Test H0:b1=0 2 tailed T-test t=b1/sb1 df=n-2

2.2. ANOVA table

2.2.1. Regression df=k=1 RSS MSR=RSS/k=RSS

2.2.2. error df=n-2 SSE MSE=SSE/(n-2)

2.2.3. Total df=n-1 TSS=RSS+SSE

2.2.4. Analysis Analysis:SEE=sqrt(MSE) R2 =RSS/TSS

2.2.5. Limitation assumption violated change overtime useless when others are aware

3. multi-linear regression

3.1. assumption

3.1.1. xi xj are independent

3.1.2. violation heteroskdasticity type detect correct autocorrelation(serial) type Detect correct multicollinearity Xi Xj correlation <>0 Detect Correct misspecification wrong pooling data

3.2. ANOVA:same as simpel LR

3.2.1. Analysis Analysis:SEE=sqrt(MSE) R2 =RSS/TSS adjust R2

3.3. Sig Test

3.3.1. Sig Test:every X is linear relation to Y? 2 tailed t-test df=n-k-1 ti=bi/sbi

3.3.2. Sig Test: more than zero X is linear 1 tailed F-test F=MSR/MSE

3.4. Special Example

3.4.1. Dummy variable(X) Y:EPS,Xi:Qi

3.4.2. Dummy variable(Y) Probit and Logit model Discriminant model

4. Time serial

4.1. linear trend model

4.1.1. log linear trend model autocorrelation detect

4.2. Autoregressive AR(p)

4.2.1. autocorrelation Detect kth order

4.2.2. seasonality

4.2.3. mean reversion AR(1)=b0/(1-b1)

4.2.4. Compare performance for forecast model in sample out of sample RMSE smaller ,it better disadvantage dymatic stable in short time

4.3. Random walk

4.3.1. type with drift simle

4.3.2. cov stationary undefined mean reverting correct first differencing detect unit root test

4.3.3. heteroskedasticity detect e~N(0,a0+a1e2)