Correlation Analysis Notes For MBA 1st Year Semester Long 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.
Long Questions Answer
Q.1. Discuss the meaning of correlation and distinguish between positive and negative correlation.
Ans. Meaning of Correlation: Correlation is the study of 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 exists 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 coefficient of correlation, otherwise fallacious conclusion can be drawn.
Distinction between positive and Negative Correlation
Positive Correlation: When the values of two variables move in the same direction, i.e. when and increase in the value of one variable is associated with and increase in the value of other variable an 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 postitive. 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 two variables moves in opposite direction.|
|2.||Type of relation||Price and supply are positively correlated.||The correlation between price and demand is positive.|
|3.||Degree||Positive correlation will be 1.0||Positive correlation between price and demand is positive.|
|4.||Moving trend||The trend of point is upward moving from lower left hand corner to upper right hand corner.||The trend of point is downward moving from upper left hand corner to lower right hand corner.|
Q.2. Write the mathemactical properties of coefficient of correlation.
Or Define karl Pearson’s coefficient of correlation. How would you interpret the sign and magnitude of 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 linear relationship between two variables. Karl Pearson’s method is the most widely used method in practice and is known as pearsonian coefficient of correlation. It correlation. It is denoted by the symbol ‘r’; the formula for calculating pearsonian r is:
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:
(a) r=-1, when there is a perfect negative correlation,
(b) r=0, when there is no correlation,
(c) r = +1, when there is a perfect positive correlation.
5. It does not tell anything about 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 case of perfect positive correlation, the result will be r = +1 and in case of perfect negative correlation, the result will be r=-1 If result is ‘O’, there is 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)
Or 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)
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:
1. It helps in the formulation and determination of function relationship.
2. It helps in establishing a cause and effect relationship.
3. It helps in prediction and estimation.
Lines of Regression
In a bivariate study, we have two lines of regression namely:
1. Regression of Yon X.
2. Regression of X on Y.
Differences between Correlation and Regression
|S.No.||Basis of difference||Correlation||Regression|
|1.||Relationship||Correlation is the relationship between two or more variables, which vary in sympathy with the other in the same or the opposite direction.||Regression means going back and it is a mathematicwcal measure showing the average relationship between two|
|2.||Types of variables||Both the variables X and Y are random variables.||Here, X is a random variable and Y is fixed variable. Sometimes, both the variables may be random variables.|
|3.||It finds out the degree of relationship between two variables and not the cause effect of the variable.||It indicates the cause and effect relationship between variables and and establishes a function relationship.|
|4.||It is used for testing and verifying the relation between two variables and gives limited information.||Besides verification, it is used for the prediction of one value, in relationship to the other given value.|
|5.||The coefficient of correlation is a relative measure. The range of relationship lies between 1.||Regression coefficient is an absolute figure. If we know the value of the independent variable, we can find the value of the dependent variable.|
|6.||There may be non-sense correlation between two variables.||In regression, there is no such non-sense regression.|
|7.||It has limited application because it is confined only \to linear relationship between the variables.||It has wider application, as it studies linear and non-linear relationship between the variables.|