Correlation Analysis

Correlation analysis is an analysis of the relationship of two or more variables.

Types of correlation:

1. Positive or Negative Correlation2. Simple, partial and multiple correlation3. Linear and non linear correlation

Methods of correlation Analysis :1. Graphic methoda. Scatter Diagram method b. Graphic plot2. Statistical methoda. Karl Pearsons Coefficient of Correlationb. Rank Methodc. Concurrent Deviation Methodd. Method of Least Squares

Problem 1:Draw a correlation graph from the following data:MonthsJanFebMarchAprilMayJuneJuly

Income1000120014001800190020002200

Expenses900120013001600170019002000

Inference : There exists a very close positive correlation between income and expenses

Statistical Method1. Karl Pearsons coefficient of Correlation:a. Arithmetic Mean Method

r = xy/ where x=X - and y=Y- Problem2 :Compute coefficient of correlation for the following data through Karl Pearsons coefficient method

X2535455220334030

Y2015101423182230

Find mean = X / N = Y /N

x=X - y=Y- Use formula above to calculate

Problem 3 : Assumed Mean method

Calculate Karl Pearsons coefficient of correlation Income230560490360270480580600

Expenses200440350250240300420550

d=x-A

r=

Karl Pearsons coefficient for Grouped data

r=

Problem 4: Calculate coefficient of correlation for the following data Weekly IncomeWeekly Expenses

100-120120-140140-160160-180180-200200- 220Total

125-15023331112

150-1754419

175-2002222311

200-22512238

225-250132410

5912106850

Rank Correlation Co-efficient:

When ranks are given1. Find out the difference of the two ranks( i.e., D) for the two variables2. Take the squares of these differences ( i.e, D2) and find D23. Substitute the values in the formula

rR = 1 - 6D2/ N3 N

Problem : 5

Calculate rank co-efficient of correlation for 12 students in 2 different subjects

StudentsNo.123456789101112

SubjectI871014536911122

SubjectII24931211817652

Regression Analysis:

Regression is a statistical technique, through which estimation of unknown variable from the known can be done.