Multivariate Statistical Techniques

Technique

Multiple Regression Analysis(MRA)

• It deals with the study of relationship between one metric dependent variable and more than one metric independent variables.

Relevance and Uses

• One could assess the individual impact of the independent variables on the dependent variable
• Given the values of the independent variables, one could forecast the value of the dependent variable.

Example

• The sale of a product depends on expenditures on advertisements as well as on R&D. Given the values of these two variables, one could establish a relationship among these variables and the dependent variable, say, profit. Subsequently, if the relationship is found appropriate, it could be used to predict the profit with the knowledge of the two types of expenditure.

Discriminant Analysis

• It is a statistical technique for classification or determining a linear function, of the variables which helps in discriminant between two groups of entities or individuals.

• The basic objective of discriminant analysis is to perform a classification function.
• From the analysis of past data, it can classify a given group of entities or individuals into categories—one those which would turn out to be successful and others which would not be so.
• With the help of financial parameters, a firm could be classified as worthy of extending credit or not.
• With the help of financial and personal parameters, an individual could be classified as eligible for loan or not or whether he would be a buyer of a particular product/service or not.
• Salesmen could be classified according to their age, health, sales aptitude score, communication ability score, etc.,

• It can predict whether a company or an individual would turn out to be a good borrower.

Logistic Regression

• It is a technique that assumes the errors are drawn from a binomial distribution.
• In logistic regression, the dependent variable is the probability that an event will occur, hence it is constrained between 0 and 1.
• All of the predictors can be binary, a mixture of categorical and continuous or just continuous.

• Logistic regression is highly useful in biometrics and health sciences. It is used frequently by epidemiologists for the probability (sometimes interpreted as risk) that an individual will acquire a disease during some specified period of vulnerability.
• Credit Card Scoring:Various demographic and credit history variables could be used to predict if an individual will turn out to be ‘good’ or ‘bad’ customers.
• Market segmentation: Various demographic and purchasing information could be used to predict if an individual will purchase an item or not.

• Individual stock rates of return, Payout ratio, and Market rates of return.
• Determination of price per share.

Multivariate Analysis of Variance (MANOVA)

• It simultaneously explores the relationship between several non-metric independent variables (Treatments, say Fertilisers) and two or more metric dependant variables (say, yield and Harvest Time). If there is only one dependent variable, MANOVA is the same as ANOVA.

• Determine whether statistically significant difference of means of several variables occur simultaneously between two levels of a variable.

Assessing whether

• A change in the compensation system has brought about changes in sales, profit and job satisfaction.
• Geographic region (North, South, East, West) has any impact on consumers’ preferences, purchase intentions or attitudes towards specified products or services.
• A number of fertilisers have equal impact on the yield of rice as also on the harvest time of the crop.

Principal Component Analysis (PCA)

• Technique for forming set of new variables that are linear combinations of the original set of variables, and are uncorrelated. The new variables are called Principal Components.
• These variables are fewer in number as compared to the original variables, but they extract most of the informant provided by the original variables.

• One could identify several financial parameters and ratios exceeding ten for determining the financial health of a company. Obviously, it would be extremely taxing to interpret all such pieces of information for assessing the financial health of a company. However, the task could be much simpler if these parameters and ratios could be reduced to a few indices, say two or there, which are linear combinations of the original parameters and ratios.
• A multiple regression model may be derived to forecast parameters like sales, profit, price, etc. However, the variables under consideration could be correlated among themselves indicating multicollinearity in the data. This could lead to misleading interpretation of regression coefficients as also increase in the standard errors of the estimates of parameters. It would be very useful, if the new uncorrelated variables could be formed which are linear combinations of the original variables. These new variables could then be used for developing the regression model, for appropriate interpretation and better forecast

• Financial parameters/ ratios for predicting health of a company.
• This is highly useful in marketing and financial applications involving forecasting, sales, profits, price, etc...

Common Factor Analysis (CFA)

• It is a statistical approach that is used to analyse interrelationships among a large number of variables (indicators) and to explain these variables (indicators) in terms of a few unobservable constructs (factors). In fact, these factors impact the variables, and are reflective indicators of the factors. The Statistical approach involves finding a way of condensing the information contained in a number of original variables into a smaller set of constructs (factors) mostly one or two –with a minimum loss of information
• Identifies the smallest number of common factors that best explain or account for most of the correlation among the indicators.

Helps in assessing

• The image of a company / enterprise
• Attitudes of sales personnel and customers
• Preference or priority for the characteristics of different products.

• A product like television , mobile phone , etc.
• A service like TV Program, air travel etc
• Intelligence quotient of a student might explain most of the marks obtained in Mathematics, Physics, Statistics, etc. Yet another example, when two variables x and y are highly correlated, only one of them could be used to represent the entire data.

Canonical Correlation Analysis (CRA)

• An extension of multiple regression analysis ( MRA involving one dependant variable and several metric independent variables). It is used for situations wherein there are several dependent variables and several independent variables.
• Involves developing linear combinations of the sets of variables (both dependant and independent variables) and studies the relationship between the two sets. The weights in the linear combination are derived based on the criterion that maximizes the correlation between the two sets of variables.

• Used in studying relationship between types of products purchased and consumer life styles and personal traits. Also, for assessing impact of life styles and eating habits on health as measured by number of health –related parameters.
• Given assets and liabilities of a set of banks / financial institutions, helps in examining interrelationship of variables on the asset and liability sides.
• HRD department might like to study the relationship between set of behavioural, technological and social skills of a salesman with the set of variables representing sales performance, discipline and cordial relations with staff.
• The Central Bank of a country might like to study the relationship between sets of variables representing several risk factors and the financial indicators arising out of a bank’s operations. Similar analysis could be carried out for any organisation.

• A medical research could be interested in determining if individuals’ lifestyle and personal habits have an impact on their health as measured by a number of heath related variable such as hypertension, weight, blood sugar, etc..
• The marketing manager of a consumer goods firm could be interested in determining if there is a relationship between types of products purchased and consumers’ income and profession.

Cluster Analysis

• It is an analytical technique that is used to develop meaningful subgroups of entities which are homogeneous or compact with respect to certain characteristics. Thus, observations in each group would be similar to each other. Further, each group should be different from each other with respect to the same characteristics, and therefore, observations of one group would be different from the observations of the other groups.

• It helps in classifying a given set of entities into a smaller set of distinct entities by analysing similarities among the given set of entities.
• An investment bank could identify groups of firms that are vulnerable for takeover.
• A marketing department could identify similar markets where products or services could be tested or used for target marketing.

• Investment in commodity markets
• Investment in stock markets
• Investment in Fixed deposits
• Investment in Mutual funds

Conjoint Analysis

• Involves determining the contribution of variables (each of several levels) to the choice preference over combinations of variables that represent realistic choice sets (products, concepts, services, companies, etc...)

• Useful for analyzing consumer responses, and use the same for designing of product and services.
• Helps in determining the contributions of the predictor variables and their respective levels to the desirability of the combinations of variables.

• How much does the quality of food contribute to continued loyalty of a traveller to an airline? Which type of food is liked most?

Multidimensional Scaling

• It is a set of procedures, for drawing pictures of data so as to visualise and clarify relationship described by the data more clearly.
• The requisite data is typically collected by having respondents give simple one-dimensional responses.
• Transforms consumer judgments / perceptions of similarity or preferences in usually a two-dimensional space

• Useful for designing of products and services
• Understanding the criteria used by people while judging objects (products, services, companies, advertisement).
• Identifying the products and services that are more competitive with each other.

• Illustrating market segments based on indicated preferences.