Correlation Analysis Notes For MBA 1st Year Semester Long Question Answer Notes
Correlation Analysis Notes For MBA 1st Year Semester Long Question Answer Notes:- In this Post, you will see about Correlation Analysis Notes For MBA 1st Year Semester Long Question Answer Notes and 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.
Q.1. Discuss the meaning of correlation and distinguish between positive and negative correlation.
Ans. Meaning of Correlation: Correlation is the study of the linear relationship between two variables. When there is a relationship of quantitative measure between two sets of variables, the appropriate statistical tool for measuring the relationship and expressing each in a precise way is known as correlation. For example, there is a relationship between the heights and weights of persons, demand and prices of commodities, etc.
‘Correlation means that between two series or groups of data, there exist some casual connections.’
‘The coefficient of correlation measures the degree of relationship between two sets of figures. As the reliability of estimates depends upon the closeness of the relationship, it is imperative that utmost care must be taken while interpreting the value of the coefficient of correlation, otherwise, a fallacious conclusion can be drawn.
The distinction between positive and Negative Correlation
Positive Correlation: When the values of two variables move in the same direction, i.e. when an increase in the value of one variable is associated with an increase in the value of another variable and a decrease in the value of one variable is associated with the decrease in the value of the other variable correlation is considered to be positive. For example, heights and weights, income and expenditure of a group of individuals, price, and supply of commodities.
Negative Correlation: The values of two variables move in opposite directions so that with an increase In the values of one variable, the values of the other variable decrease, and with a decrease in the values of one variable, the values of the other variable increase, correlation is said to be negative. For example, when prices increase, demand goes down, Thus there is a negative correlation between two variables, i.e. demand and supply.
|S.No.||Direction||The value of two variables moves in the same direction.||The values of the two variables move in opposite directions.|
|2.||Type of relation||Price and supply are positively correlated.||The correlation between price and demand is positive.|
|3.||Degree||The positive correlation will be 1.0||The positive correlation between price and demand is positive.|
|4.||Moving trend||The trend of a point is upward moving from the lower left-hand corner to the upper right-hand corner.||The trend of the point is downward moving from the upper left-hand corner to the lower right-hand corner.|
Q.2. Write the mathematical properties of the coefficient of correlation. Define Karl Pearson’s coefficient of correlation. How would you interpret the sign and magnitude of the correlation coefficient?
Ans. Karl Pearson’s Coefficient of Correlation: Karl Pearson, a great biometrician and statistician, suggested a mathematical method for measuring the magnitude of a linear relationship between two variables. Karl Pearson’s method is the most widely used method in practice and is known as the pearsonian coefficient of correlation. It correlation. It is denoted by the symbol ‘r’; the formula for calculating pearsonian r is:
The mathematical properties of Karl Pearson’s coefficient of correlation are as follows:
1. It is an ideal measure of correlation and is independent of the units of X and Y.
2. It is independent of change of origin and scale.
3. It is based on all the observations.
4. It varies between – 1 and +1:
- r=-1, when there is a perfect negative correlation,
- r=0 when there is no correlation,
- r = +1 when there is a perfect positive correlation.
5. It does not tell anything about the cause and effect relationship. 6. It is somehow difficult to calculate.
7. It requires some interpretation.
Interpretation of Sign and Magnitude of R
Karl Pearson has given a formula for measuring correlation. The result of this formula (r) varies between 1. In the case of a perfect positive correlation, the result will be r = +1 and in the case of a perfect negative correlation, the result will be r=-1 If the result is ‘O’, there is the absence of correlation. The following chart will show approximate degrees of correlation according to Karl Pearson formula:
Q.3. Define regression. Give important uses and applications of regression analysis. (2011-12)
What is regression? Why are there, in general, two regression lines?
Ans. Regression: Regression analysis is concerned with the formulation and determination of algebraic expression for the relationship between the two variables. We use the general regression lines for those expressions. By regression, we mean the average relationship between the two or more variables which is useful for estimating the value of one variable from the given values of one or more variables.
Utility of Regression Analysis (Uses)
The regression analysis has great practical utility in almost all scientific disciplines. Its applications are extended to all the natural, physical and social sciences. To be specific, some of its uses may be listed as under:
- It helps in the formulation and determination of functional relationships.
- It helps in establishing a cause-and-effect relationship.
- It helps in prediction and estimation.
Lines of Regression
In a bivariate study, we have two lines of regression namely:
- Regression of Y on X
- Regression of X on Y