Practical no. 4 Karl Pearson's correlation coefficient
Correlation
In previous blog we discussed about the measure central tendency and Dispersion to use to study the variable. the correlation is a statistical concept that allows us to measure and understand the relationship between two or more variables. it provided a valuable information about that variables. e.g. price and demand of commodity, income and expenditure of family, height and weight of group of persons. their we use the relation between this two variables. in above examples we see the one variable increases other variable is also changes in same or opposite direction.
definition: Correlation is statistical tool which study the relationship between two or more variables. for analysis of correlation various method and techniques are used.
example: i. Demand and supply of product ii. price and demand iii. Income and expenditure
Use Of Correlation:
the correlation analysis is widely used in economic, business and other fields.
i. To Predict: if we know the relation between two variables, we can estimate the value of them when value of other is known. e.g. we know the correlation between height and weight then we calculate the weight for known value of height.
ii. To control: The correlation also enables us to control our activity. e.g. we know the correlation between fertilizer and crop, then we control the yield and life of the crop, (use of more fertilizer is hazard to crop.
iii. To Plan: the knowledge of correlation help to planning. e.g. if we know the relation between the rainfall and yield of crop, then we know the rainfall we calculate the yield of crop, depend on the yield of crop we plan for import and export.
Types of Correlation:
i. Positive and Negative Correlation
ii. Linear and non-liner Correlation.
iii, simple, Multiple and Partial Correlation.
Positive correlation: If both the variables changes in same direction i.e. if one variable increases other variable also increases or if the one variable decreases then other variable also decreases, the correlation is said to be positive correlation. e.g. i. height and weight mean height is increases weight also increases.
Negative Correlation: if the both variables are changes in opposite direction i.e. if one variable increases other variable decreases or if the one variable decreases then other variable also increases. e.g. price and demand mean the price increases demand is decreases.
the difference between the positive and negative correlation depends on the direction of change of two variables.
when change in one variable is not affected on other variable it is no correlation between two variables.
Linear Correlation: this type of correlation is based on the nature of the graph of two variables. if the graph is straight line the correlation is Linear correlation.
if the graph is not a straight line but is curve is called Non-Linear Correlation.
Simple Correlation: we study only two variable say price and demand it is simple correlation.
Multiple Correlation: we study more than two variables is called multiple correlation.
Partial Correlation: we study the more than two variables but correlation is studied between two variables only, and the effect of the other variable is assumed as constant.
Methods of studying Correlation:
II. Mathematical Method:
i. Karl Pearson Coefficient of correlation 'r'
Karl Pearson's Coefficient of correlation:
Karl Pearson's gives the mathematical method to measure the correlation between two variables. based on following assumptions.
i. there is linear relationship between two variables.
ii. there is cause and effect relationship between two variables.
definition: Karl Pearson's Coefficient of correlation between two variables X and Y, denoted as corr(X,Y) or "r" and it is given as
To calculating correlation coefficient:
There are three methods of calculating r.
i. Actual Mean method.
ii. Step Deviation Method.
iii. Assumed Mean Method.
We see the one by one methods
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