Quantatitive

 

CFA_LV2_Quant_F.hwp

 

 

 

 

Quant

 

○ Correlation

- rXY = covXY / (sX) (sY)

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○ T-test vs. F-test

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○ Assumption

- 독립변수와 종속변수는 선형

- 독립변수는 random이 아니며, 독립변수간 선형관계가 없다 → multicolinearity

- 독립변수와 잔차는 uncorrelated

- 잔차의 기댓값은 0

- 잔차의 분산은 일정하다 → heteroskedasticity

- 잔차는 uncorrelated → serial correlation

- 잔차는 normally distributed

 

○ Violation of assumption

	heteroskedasticity	serial correlation	multicolinearity
definition	residuals are not constant	residuals are correlated	independent variables are correlated
detection	Breush-Pagan n×R2resid 60×0.08=4.8 4.8>3.841(one-tailed critical value 5%) = heteroskedasticity	Durbin-Watson 2(1-r) 2 no serial correlation 0 positive, 4 negative	conflict in t & f test
correction	White-corrected standard t = coefficient / white-corrected standard error	Hansen method to adjust standard error	drop one of the correlated variables

 

 

 

 

○ Example

Regression Statistics
Multiple R	0.753840729
R-squared	0.568275844
Adjusted R-squared	0.553127628
Standard error of estimate	0.054691883
Durbin-Watson(DW)	2.02
Observations	60
ANOVA	Degree of Freedom	Sum of Squares	Mean Square
Regression	2	0.224426149	0.112213075
Residual (Error)	57	0.170498519	0.002991202
Total	59	0.394924669
	Coefficients	Standard Error	t-Statistic	p-value
Intercept	0.000214	0.007127649	0.030025	0.976152
NASDAQ return	1.122096	0.130216256	8.617173	0.000000
JPY/USD change	0.286426	0.291700144	0.981919	0.330289

 

- R-squared = RSS / SST = 0.224426149/0.394924669 = 0.568275844 = 0.8 이상이 좋음

- standard error of estimate = SSE / n-k-1 = (0.170498519 / 57)(0.5) = 0.054691883

- Adjusted R-squared = n을 증가시키면 올라가는 R2를 조정

- Durbin-Watson = 2(1-r) = 2.02 = 2에 가까움으로 non-correlation → no serial correlation,

0에 가까우면 positive correlation, 4에 가가우면 negative correlation

- F-test = = MSR / MSE = 0.112213075/0.002991202 = 37.51438

- Standard error = coefficients / t-statistic = 1.122096 / 8.617173 = 0.130216256 (b1=0)

- t-test = = coefficients - b1 / standard error = 1.1222096 - 0 / 0.130216256

= 8.617173으로 유의미, no multicolinearity

- confidence intervals = 1.122096 ± 1.96 × 0.130216256 = 0.866872 ~ 1.377319

- p-value = 0.00000 = 5% significance level, 0.05보다 작음으로 유의미 (reject null)