Legal Case Study 3: Lawsuit Regression (Part Two)

continued from previous post

Probability of Being Sued
Probability of Being Sued

6% probability of getting sued if you are represented by big 5 firm.

It appears from the regression estimate above that BIG5 is statistically significant; however, only 0.5% of the variation is explained with this independent dummy variable.

Our desire is to determine whether or not having a Big 5 auditor is the sole reason for this phenomenon, i.e. are there other factors in addition to or instead of having a Big 5 auditor that explains the likelihood for a lawsuit.

The descriptive statistics for each of the variables compiled above is presented below to enable a further understanding of the other factors that may come to bear upon our regression

Descriptive Statistics Regression - Halden Zimmermann
Descriptive Statistics Regression

The Mean of each of the explanatory variables will be used throughout this report for probability estimation of the dependent dummy variable LAWSUIT.

2. Developing a Better Model for Predicting LAWSUIT

Starting with the regression above, we initially included the variable SALES, but this only slightly improved the regression and the residuals of the regression did not vary consistently about zero.  We noted that SALES is not normally distributed, see the histogram below, so we then considered LOGSALES as a potentially better explanatory variable.

LOGSALES Variable - Halden Zimmermann
LOGSALES Variable

The variable of LOGSALES has a more normal distribution.  See the histogram of LOGSALES below.

LOGSALES Histogram Normal Distribution - Halden Zimmermann
LOGSALES Histogram Normal Distribution

LogSales is a measure of a firm’s size: the larger the Sales, the larger the firm (HAOVC).

The E-Views regression is given below, including a correction for heteroskedasticty because the inherent inconstant variation of the residuals that occurs with a dependent dummy variable.

E-Views Regression
E-Views Regression

This regression improves the adjusted R-squared of the model to 3.3%.  From this regression model, we forecasted the probability of a lawsuit, given that LOGSALES = 3.944636 (mean of LOGSALES) and BIG5 = 1.  The result of this forecast was a probability of 5.6% with a 95% confidence interval of (-0.39, 0.51). This implies that a lawsuit will occur nearly 6% of the time for an average size firm that has hired a BIG5 firm, and only 4% if they do not hire a BIG5 firm.  Additionally, the regression shows that an increase in LOGSALES by 1% will result in a 1.6 increase in the probability that a lawsuit will occur.

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