DESGLOSE DE LOS COSTOS INDIRECTOS

Explanatory variables are called external or exogenous variables. If x a considered t be the cause of y, then x is the explanatory variable (or) causal or independent variables.

2. Criterion Variable

These are called endogenous variables. In the above stated case y is called as criterion (or) dependent resultant variable.

3. Observable & Latent variable

When explanatory variable are directly observable variable, they are termed observable variable. However some unobservable variable may influence criterion variable in which case they are called latent variables.

4. Discrete variable & Continuous Variable

Discrete variables are those that lake only the integer value when measured. Continuous variables are those that when measured, can assume any real volume.

5. Dummy Variable

This term is used in a technical sense and is useful in algebraic manipulations in the context of multivariate analysis

TECHNIQUES

I. MULTIPLE REGRESSION

When there are two or more than two independent variables, the equation describing such a relationship is the multiple regression equation. In this situation the results are interpreted as

Y= a + b1 x1+ b2 x2

X1, x2 = independent variable y = dependent variable

a, b1, b2 = constant

• The no of normal equation would depend upon the number of independent variable. If there are two independent variables, then three equations, if there are three independent variable then four equations and so on are used.

• In multiple regression analysis the regression co-efficient (b1,b2) become less reliable as the degree of correlation between the independent variable (x1,x2).

• If there is high degree of correlation between independent variables. We have what is commonly described as the problem of multicollinearity. In such a situation we should use only one set of the independent variable to make our estimate.

• Adding a second variable say x2 _{which is correlated with the first variable say x} 1

distorts the values of the regression co-efficient.

• The main objective in using this technique is to predict the variability the dependent variable based on its covariance with all the independent variables.

• One can predict the level of the dependant variable through the multiple regression analysis model given the levels of independent variables.

• When multiple independent variables are measured with different scales, it is not possible to make relative comparisons between regressions co-efficient to see which independent variables have the most influence on the dependent variable.

• To solve this problem, we calculate the standardized regression co-efficient. It is called beta co-efficient and it is calculated from the normal regression co- efficient.

• The beta co-efficient allows direct comparison between independent variables to determine which variables have the most influence on the dependant measure.

• When using multiple regression analysis, it is important to examine the overall statistical significance of the regression model. The amount of variation in the dependant variable that you have been able to explain with the independent measures is compared with total variation in the dependant measure. This comparison result in a statistic allied a mode F Statistic

Application:

 Used to predict the dependent variable, given knowledge of independent variable.

 To understand the relationship between the dependent variable and independent

variable. Inputs:

Variable value for dependent and the independent variable. Output:

It will output the regression coefficients and their associated beta coefficient and t- Values which can be used to evaluate the strength of the relationship between the respective independent variable and the dependent variable.

Statistical Test:

The hypothesis that a regression parameter obtained from the sample evidence is zero or not is based on the t-value.

Limitation

 The knowledge of a regression coeffient and it’s t-value can suggest the extent of association or influence that an independent variable has on the dependent variable.

 The regression coeffient will reflect the impact of the omitted variable on the dependent variable.

 The model is based on collected data that represent certain environmental conditions.

 The model is limited by the methodology associated with the data collection including the sample size and measures used.

II. MULTIPLE DISCRIMINATE ANALYSIS

• It is a multivariate technique used for predicting group membership on the basis of two or more independent variables. A discriminate function is a regression equation with a dependant variable that represents group membership. This

function maximally discriminate between members of the group. It tells us to which group each member probably belong.

• It can be used to assign individual to groups on the basis of their scores on two or measure. From those scores the best composite score based on least squares is calculated. Then the higher R2 _{is the better predictor of the group membership.}

• One can use discriminate analysis to classify objects into two groups (ie.,) success, failure, default, non-default.

• In discriminate analysis a scoring system is used on the basis of which an individual is classified as category.

• Suppose an individual is 25 years of age earns an annual income of Rs.60000/- and has undergone formal education for a period of 17years. Each of three variables is given a weight indicating its relative importance.

Y=dependant variable.

• A certain limit is fixed of the value of y below which all values will be classified in Group I and the others in Group II. The values of b1,b2 and b3 indicae their importance. The numerical value of y can be transformed into t probability of the individual being credit worthy.

• It may be noted that in the linear discriminate, the “b” co-efficient are similar to the regression co-efficient. However the main differences is that while the regression co-efficient are used to predict the value of the dependant variable. The discriminate co-efficient are used to classify correctly as many individual or object as possible.

• One major advantage of linear discriminate analysis is that it enables the researcher to know, by a simple device whether an individual is likely to belong to one or the other category on the basis of his overall score. In this context, it is not only the values of the discriminate coefficient but also their positive or negative signs that are equally relevant.

• Given a certain minimum vale of Z and credit worthiness, it should be clear that the higher the values of the independent variable provided the discriminate

coefficient are positive, the more chances there are for the individual to be classified under this category.

Application:

Used to identify variables that contribute to differences in the a priori defined groups with the use of discriminate functions. It classify objects into one or more groups that are already defined.

Inputs:

Variables values for the independent variable and dependent variable. Output:

It provide the characteristics of the discriminate fuction., such as the variables that contribute to each discriminate fuction. The significance of the fuction is also given. Statistical Tests:

The significance of the discriminant fuction and the variables are evaluated through through an F-statistic.

Limitation :

 It is similar to regression analysis such as intervariable correlations in the model, correlation of variables with the omitted variables,and change of environment condition.

 The assumption of the discriminant analysis has to be tested and it is often possible that the assumption of equal variance –covariance matrices of the Independent variable in each group is not met.

III. FACTOR ANALYSIS

It is a multivariate statistical technique that is used to summarize the information contained in a large number of variables into smaller number of subsets or factors. The purpose of factor analysis is to simplify the data with factory analysis there is no distinction between dependent and independent variables rather all variables under investigation are analyzed together to identify underlying factor.

1. It simplifies the data by reducing a large number of variable to a set of a small number of variables.

2. It analyses the interdependence of interrelationship among a total set of variables.

Factor analysis is an appropriate technique in case where the variables have a high degree of Interco relation.

METHODS OF FACTOR ANALYSIS: