Thursday, April 19, 2012

Multiple Linear Regression - Investment Analysis


Example of a multi-variable model


Rit = ai + bitRmt + bi2MPt + bi3DEIt + bi4UIt + bi5UPRt + bi6UTSt + eit




Rit = Return on a security i in period t

Rm = Return on valued weighted index of NYSE listed stocks


MPt = monthly growth rate in industrial production

DEIt = change in inflation

UIt = difference between actual and expected levels of inflation

UPRt = unanticipated change in the bond credit spread

UTSt = unanticipated term structure shift



Estimates for the period 1978-84

constant = 15.45

Rmt = -3.68

MPt = 8.40

DEIt = -0.12

UIt = -0.74

UPRt = 6.06

UTSt = -5.93


(Source: Nai-fu chen, Richard roll, andStephen A. Ross, “Economic Forces and the Stock Market,” Journal of Business, 59, No. 3(April 1986).


Linear multi-variable models are estimated by using multiple regression methods.


The topics for discussing multiple regression.


A.   Assumptions

B.   Statistical Software

C.   Writing The Multiple Regression Equation

D.   Using the Regression Equation to Estimate what the Value of the Dependent Variable will be for a Specified set of values of the Independent  Variables

E.   Testing the Overall Validity of the Regression (Whether all the Population Regression Coefficients are Equal to Zero)

F.    Testing for the Significance f the Intercept and the Regression Coefficients

G.  Determining Whether a regression Coefficient is Significantly Different from a Specified Value

H.   Determining confidence Intervals for Regression Parameters

I.      Determining the Standard Error or Estimate of a Multiple Regression Model

J.     Determining the Coefficient of Determination and the Correlation Coefficient of a Multiple Regression

K.   Heterdoskedasticity in Regression Residuals

1.     Unconditional Heteroskedasticity

2.     Conditional Heteroskedasticity

3.     Testing for Heteroskedasticity in Regression Residuals

4.     Correcting for Conditional Heteroskedasticity in regression Residuals

L.    Serial Correlation in regression Residuals (Autocorrelation)

1.     testing for Serial Correlation in regression residuals

2.     Correcting for Serial Correlation in Regression residuals

M.  Multicollinearity among the Independent Variables of a Regression

1.     Testing for Multicollinearity among a Regression Model’s Independent Variables

2.     Correcting for Multicollinearity among a Regression Model’s Independent Variables

Original Knol - 486

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