ANALYSIS

Statistical Analysis

Statistical Analysis

Section A

2001

 

LEV

PROFMARG

MTBV

SIZE

LIQ

CF%S

CATAR

CLTAR

EBITDA

LEV

1

 

 

 

 

 

 

 

 

PROFMARG

-0.00956

1

 

 

 

 

 

 

 

MTBV

0.18542

-0.04295

1

 

 

 

 

 

 

SIZE

0.097874

-0.03914

-0.08842

1

 

 

 

 

 

LIQ

-0.11195

0.073327

0.087411

-0.27792

1

 

 

 

 

CF%S

0.032996

0.719486

-0.03143

0.016617

0.199246

1

 

 

 

CATAR

-0.04937

-0.09102

0.105817

-0.33237

0.180877

-0.29298

1

 

 

CLTAR

0.102351

-0.09874

0.046814

-0.05053

-0.36328

-0.29197

0.477456

1

 

EBITDA

0.032109

0.003876

-0.0341

0.550992

-0.09014

0.04502

-0.17285

-0.04044

1

Similarly, all other correlations matrix table are given in the appendix.

There should be no multicollinearity among the explanatory or independent variables. Multicollinearity originally implied the existence of a linear relationship "perfect or accurate" between some or all of the independent variables in a regression model. Today the term multicollinearity is used in a broader sense to include the case of perfect multicollinearity, as well as a situation in which the variables X are intercorrelated, but not perfectly. Multicollinearity, includes only the linear relationships between independent variables and eliminates the nonlinear interactions between them. For example consider the following regression model:

Y = + 1 X + 2 X 2 + 3 X 3 + e

Where Y is the total cost of production and X is production. The variables X 2 (production squared) and X 3 (production cubed) are functionally related to X, but the relationship is not linear. So similar to the previous models do not violate the assumption of no multicollinearity. If multicollinearity is perfect, the regression coefficients are indeterminate and their standard deviations or errors are infinite. If multicollinearity is less than perfect, although the regression coefficients determined or finite, have standard errors too large, which implies that the coefficients can not be estimated with great precision or accuracy. In cases of high multicollinearity, the regression coefficients continue to be unbiased and consistent but no longer efficient or minimum variance.

Time-series analysis (TSA) is a statistical methodology appropriate for longitudinal research designs that involve single subjects or research units that are measured repeatedly at regular intervals over time. TSA can be viewed as the exemplar of all longitudinal designs. TSA can provide an understanding of the underlying naturalistic process and the pattern of change over time, or it can evaluate the effects of either a planned or unplanned intervention. The advances in information systems technology are making time-series designs an increasingly feasible method for studying important psychological phenomena.

Modern TSA and related research methods represent a sophisticated leap forward in the ability to analyze longitudinal data. Early time-series designs, especially within psychology, relied heavily on graphical analysis to describe and interpret the results. Although graphical methods are useful and provide important ancillary information, the ability to bring a sophisticated statistical methodology to bear has revolutionized the area of single-subject research.

TSA was developed more extensively in areas such as engineering and economics before it came into widespread use within social science research. The prevalent methodology that has developed and been adapted in psychology is the class of models known as Autoregressive Integrated Moving Average (ARIMA) models. TSA requires the use of high-speed computers; the estimation of the basic parameters cannot be performed by precomputer methods.

Section B

A major characteristic of time-series data is the dependency that results from repeated measurements over time on a single subject or unit. All longitudinal designs must take dependency into account. Dependency precludes the use of traditional statistical tests because they assume the independence of the error. ARIMA models have proven especially useful because they ...