Legal Case Study 3: Lawsuit Regression (Part Four)

Continued from Lawsuit Regression Part Three

LAWSUIT - White Heteroskedasticity-Consistent Standard Errors & Covariance #2

This regression includes all the available explanatory variables, and now provides a coefficient for BIG5 that is negative, which implies that having a Big 5 auditor reduces the probability of a lawsuit by a small fraction.  The primary concern is the extremely large p-value for the BIG5 coefficient, which implies that this variable is no longer relevant to the regression model.  By conducting a Wald Test on this coefficient, we failed to reject the null hypothesis that the coefficient of BIG5 is zero.

Wald Test:
Equation: Untitled
Null Hypothesis: C(2)=0
F-statistic 4.67E-05 Probability 0.994548

Removing the BIG5 variable from the regression, provides the following model:

 

Dependent Variable: LAWSUIT
Method: Least Squares
Date: 01/17/02   Time: 15:06
Sample: 1 1988
Included observations: 1988
White Heteroskedasticity-Consistent Standard Errors & Covariance
Variable Coefficient Std. Error t-Statistic Prob.
C -0.073815 0.014354 -5.142396 0.0000
LOGSALES 0.012882 0.002756 4.673628 0.0000
CHEMDUM 0.025029 0.016572 1.510333 0.1311
COMPDUM 0.035772 0.013900 2.573440 0.0101
ELECDUM 0.016708 0.013951 1.197599 0.2312
BETA 0.061541 0.009101 6.762179 0.0000
CUMRET -0.012170 0.003944 -3.085824 0.0021
SIGMARET 0.118635 0.074700 1.588162 0.1124
R-squared 0.073388    Mean dependent var 0.055835
Adjusted R-squared 0.070112    S.D. dependent var 0.229661
S.E. of regression 0.221463    Akaike info criterion -0.173104
Sum squared resid 97.11108    Schwarz criterion -0.150589
Log likelihood 180.0650    F-statistic 22.40241
Durbin-Watson stat 0.103945    Prob(F-statistic) 0.000000

Excluding BIG5 from the regression had no affect on the adjusted R-squared, and it did not change the probability of a lawsuit, on average, and with a small change to the 95% confidence interval of (-0.50,0.50).

4. Refining the Regression Model

Using variables that are statistically significant gives the regression:

Halden Zimmermann Least Squares Regression
Least Squares Model

Variable Significance:

C: If you are not is any of the listed industries and have a 0 Beta, 0 sales and 0 cumulative returns you have a 0 increase in probability that you will get sued

 

Beta: 1 beta higher increases probability by .06 that your company get sued

Logsales: 1% increase in log sales increases probability by .012

Cumret: Cannot have a negative probability, removal reduced adjusted R-squared. (Low occurrence of suits)

Dummy Significance:

Chemdum: If in Chemical industry increases probability of getting sued by .023

Compdum: If in Computer industry increases probability of getting sued by .035

Electdum: If in Electrical industry increases probability of getting sued by .016

It seems that if you are in business in the computer industry this increases the probability of being sued by .035. This is significantly more than the other industries.

2. Probability of having a Lawsuit

Already established is that using a Big5 firm does not increase a firms potential of being involved in litigation. The regressions presented shows that there is no statistical significance sowing that there is a relationship

Wald test?

P-value rule

Adjusted R-squared

However it would be interesting to understand the probability of getting sued by using equation # 3

Probability of Getting Sued in Computer Industry Given average Cumret, Beta and logsales

Lawsuit Probability Computer Industry
Lawsuit Probability Computer Industry

.07 probability of getting sued in the computer industry with average cumret, log sales and beta

95% confidence that probability will fall between .51 and -.037

Probability of getting sued in the electrical industry given average variables

Lawsuit Probability Electrical Industry
Lawsuit Probability Electrical Industry

.05 probability of getting sued in the Electrical industry

95% confidence between .49 and -.39

Probability of getting sued in the Chemical industry

Probability of Being Sued in the Computer Industry
Probability of Being Sued in the Computer Industry
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