# What is Multivariate Analysis of Data

Hello Researchers, today we will discuss about the “Multivariate Analysis of Data” . It is very much important topic for research methodology.

For management, the questions regarding conflict, satisfaction, and employee turnover are often key dependent variables of interest. Question can be a complex one, with many different work and family independent variables affecting work-family conflict.

In marketing, sales volume is often the dependent variable managers want to predict. Independent variables including marketing mix elements such as price, number of sales people, amount of advertising related to sales volume. Uncontrollable variables including population, economic conditions, and competitive intensity also affect sales.

The mathematical symbol X is commonly used for an independent variable, and Y typically denotes a dependent variable.

X= Independent Variable

Y= Dependent Variable

Y = X      (means Y depend on the function of X)

Regression can accommodate either less-than interval independent variables, but the dependent variable must be continuous. Regression analysis finds out the degree or relationship between dependable variable and a set of independent variables by fitting a statistical equation. Generally speaking, regression refers to the prediction of one variable from our knowledge of another variable.

Correlation analysis is most appropriate for interval or ratio variables. Correlations estimate relationships between continuous variables. The most popular technique for indicating the relationship of one variable to another is correlation. .

♦ A correlation coefficient is a statistical measure of co-variation, or association between two variables. Co-variance is the extent to which a change in one variable corresponds systematically to a change in another. Correlation can be thought of as a standardized co-variance.

Correlation coefficient, r, ranges from –1.0 to 1.0. If the value of r equals 1.0, a perfect positive relationship exists.

Perhaps the two variables are one and the same!

1. Correlation coefficient, r, ranges from -1.0 to +1.0.
2. If the value of r equals +1.0 a perfect positive relationship
3. If the value of r equals –1.0 ⇒ perfect negative relationship implies one variable is a mirror image of the other. As one goes up, the other goes down in proportion and vice versa.
4. r = 0 ⇒ No correlation relationship exists

A correlation coefficient indicates both the magnitude of the linear relationship and the direction of that relationship.

For example, if we find that r = –0.92, we know we have a very strong inverse relationship—that is, the greater the value measured by variable X, the lower the value measured by variable Y.

Regression refers to prediction, degree of relationship measure is correlation, measure of correlation called the correlation coefficient ( degree of relationship is expressed by coefficient)