 # Correlation

## IntroductionCorrelation measures the relationship between two variables so that changes in the value of one variable are accompanied with the changes in the value of other variable. When there are two variables A and B and they change in such a way that with the change of one variable the other variable will also change then they are said to be correlated. Correlation analysis is highly significant and has vast utility. By knowing one variable other variables can be ascertained.The properties of correlation includes:    Correlation has no unit of measurement,    The value of correlation(r) lies between –1 to +1,    High value of ‘r’ shows strong linear relationship,    In case of Perfect correlation, r is equal to +1 or – 1,    Value of correlation is unaffected by the change of origin and change of scale, etc.On the basis of these properties, the degree of correlation can be expressed as perfect correlation, absence of correlation, limited degree or imperfect correlation.Correlation is commonly classified on the basis of direction of change as positive correlation and negative correlation, on the basis of change in proportion as linear correlation and non-linear correlation and on the basis of number of variables as simple correlation, partial correlation and multiple correlations.

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• Q1

In case of no correlation, the value of r is

Marks:1

0

##### Explanation:

The higher value of r shows strong correlation. The lower value of r, shows the weak correlation.

• Q2

The unit of correlation coefficient between height in feet and weight in kgs is

Marks:1

non-existent.

##### Explanation:
Coefficient of correlation being a relative measure and being a pure number, has no unit.
• Q3

Sale of woolen garments and day temperature indicates

Marks:1

negative correlation.

##### Explanation:

As temperature increases the sale of woolen garments decreases. This indiates negative correlation as both the variables are moving in the opposite directions.

• Q4

The value of correlation is unaffected by

Marks:1

the change of origin and change of scale.

##### Explanation:

The value of correlation is unaffected by the change of origin and change of scale.

rxy= ruv

Where

rxy = correlation between X and Y variables

ruv = correlation between U and V variables

u = (X-A)/h

v = (Y-B)/k