1. Statistics in Data Mining on Finance by Jian Chen
Linear Regression
Two-variables
Y=f(x)+e f(x)=polynomial
Observations: (x1,y1) … (xn,yn)
f(x)=a+b x
The line of “best” fit:
minimize the sum of the squared residuals.
(It is convenient in that it permits statistical testing)
Minimize the sum of the absolute residuals (least absolute value)
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Statistics in Data Mining on Finance by Jian Chen
o:\tem\regression.ppt

2. Linear (Least Squres) Regression
See it work: Another
How to estimate the “goodness of fit”?
Error: Total variation of squares
Standard deviation of the residuals
Se= (95 %)
The sample correlation coefficient
r2: R-squared of the regression equations r:
11/11/2018
Statistics in Data Mining on Finance by Jian Chen

3. Statistics in Data Mining on Finance by Jian Chen
Linear Regression
Ei: Error
Y=a+bX
Predicted value
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Statistics in Data Mining on Finance by Jian Chen
o:\tem\regression.ppt

4. Statistics in Data Mining on Finance by Jian Chen
Linear Regression
Test of Regression Coefficients:
b=0? (p-value)
Multiple Regression:
Model selection? Backward, forward
Multiple correlation R2 (The Corrected R2)
Se (95 %)
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Statistics in Data Mining on Finance by Jian Chen

5. Statistics in Data Mining on Finance by Jian Chen
Linear Regression (2)
Multicollinearity: Y, xi, axi+b
Effects:
Identification
Correctness
Other issues in linear model
Use of Dummy variables
Transformations:
(logYi, logXi), Nonlinear, Probit, Logit etc.
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Statistics in Data Mining on Finance by Jian Chen

6. Statistics in Data Mining on Finance by Jian Chen
Section 2
Heteroscedasticity pp145
Test ?
Serial Correlation? => Time Series
Regression Diagnostics: Outliers
Forecasting
At x=xp, what is the Y? What is the average of Y predicted?
Point estimates, confidence intervals.
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Statistics in Data Mining on Finance by Jian Chen

7. Statistics in Data Mining on Finance by Jian Chen
Linear Regression
Regression tools
SAS
SPSS
SPLUS
11/11/2018
Statistics in Data Mining on Finance by Jian Chen