Correlation Analysis Notes For MBA 1st Year Semester Short Question Answer Notes Study Material Notes Sample Model Practise Notes Rank Method And Kari Pearson’s Coefficient Of Correlation And Properties Of Correlation Regression And Properties Of Correlation. Regression Analysis Fitting Of A Regression Line And Interpretation Of Results, Properties Of Regression Coefficients And Relationship Between Regression And Correlation.
Short Question Answer
Q.1. Explain the various types of correlation.
Ans. Types of Correlation: In a bivariate distribution, the correlation may be:
- Positive and Negative Correlation: As a forst case, the correlation may be classified according to the direction of change in the variables. In this regard, the correlation may be either positive or negative.
Possitive or direct correlation refers to the movement of variable in the same direction. The correlation is said to be positive when the increase in the value of one variable is accompanied by an increase in the value of other variables. In short, two variables covarying in the same direction are positively correlated. For example, height and weight, etc.
Negative or inverse correlation refers to the movement of the variables in opposite direction. Correlation is said to be negative if and increase in the value of one variable is followed by a decrease in the value of the others. For example, price and demand.
- Linear and Non-Linear Correlation: The distinction between linear and non-linear correlation is based upon the ratio of change between the two variables. In perfect linear correlation, the amount of change in one variable bears a constant ratio to the amount of change in the other. On the other hand, in non-linear, the amount of change in one variable does not bear a constant ratio to amount of change in the other variable.
Q.2. Write a short note on Spearman’s coefficient of rank correlation.
Or What is coefficient of rank correlation? How it is interpreted?
Ans. Spearman’s Coefficient of Rank Correlation: Karl pearson coefficient of correlation discussed the degree of convertability of linear relationship between two quantitative variables. But often we come across situation when definite measurement on the variable are not possible, i.e. the factor under sudy cannot be measured in quantitative terms. For instance , the evaluation of a group of students on the basis of leadership ability, the ordering of women in a beauty contest, the pictures ranked according to their aesthetic values, and so on. In all such cases, objects or individual may be ranked and arranged in order of them, we measure the degree of covariation or relationship by coefficient of rank correlation. Spearman’s coefficient of rank correlation is denoted by Greek letter p (rho).
Q.10. Write short notes on the following:
1. Partial correlation,
2. Multiple correlation.
Ans. 1. Partial Correlation: Correlation is defined as partial on the basis of the number of variables studied. Partial correlation is a correlation between two variables when the effects of one or more of the related variables are removed. For example, the study of relationship between ledge R amount of rainfall, temperature and yield of wheat under constant temperature is a type of partial correlation.
2. Multiple Correlation: This correlation is also defined on the correlation measures correlation between the
basis of the number of variables studied. By multiple correlation, it is meant that there is measurement of the effect of several variables on one variable. For example, if we study the relationship between rainfall, temperature and yield of wheat, then it is a case of multiple correlation.
Q.11. What are the properties of regression coefficients?
Ans. Properties of regression coefficients are as follows:
1. The geometric mean between regression coefficients is the coefficient of correlation, i.e.
R = +bxy X byx
(a) ‘r’ will be positive if both regression coefficients are positive.
(b) ‘r’ will be negative if both regression coefficients are negative.
(c) The values of both regression coefficients cannot be more than one.
2. Regression coefficients are independent of origin but not of scale.
3. If one of the regression coefficients is greater than unity, the other must be less than unity.
4. Both the regression coefficients will have the same sign.
5. The average value of the two regression coefficients would be greater than the value coefficient of correlation.