RBSE Class 11 Economics Notes Chapter 7 Correlation

These comprehensive RBSE Class 11 Economics Notes Chapter 7 Correlation will give a brief overview of all the concepts.

RBSE Class 11 Economics Chapter 7 Notes Correlation

Correlation and its Types:
Correlation is a statistical measure that shows the degree to which two or more variables fluctuate in relation to one another, Correlation does not imply causation.

Techniques of Measuring Correlation

• Scatter diagram
• Karl Pearson’s Coefficient of Correlation
• Spearman’s Rank Correlation

Types of Correlation

• Positive correlation - variables move in same direction
• Negative correlation - variables move in opposite direction
• Linear correlation - represented by straight line
• Non-linear correlation - represented by a smooth curve

Scatter Diagram:
Scatter diagram graphically shows the direction and degree of correlation between variables. Relationship between Variables
(i) Perfect correlation - all the points lie on a line

(ii) Low linear correlation - points are widely dispersed around the line

(iii) High linear correlation - points lie near a line or on a line

(iv) No correlation - points do not follow any pattern

Kari Pearson’s Coefficient of Correlation:

• Karl Pearson’s coefficient of correlation gives the numerical value of the degree of correlation between two variables.
• Karl Pearson has given a quantitative method of calculating correlation.
• Karl Pearson’s measure of correlation (r) is given by:
  r = \(\frac{\sum x y}{N \sigma_x \sigma_y}\)
  where; x = X - X̄ and y = Y - Ȳ
• The value of r lies between -1 and +1, that is, -1 ≤ r ≤ +1.

Type of Correlation for Different Values of r

• r = 0 No Correlation
• r = +1 Perfect Positive Correlation
• r = -1 Perfect Negative Correlation

The value of r indicates high linear relation when it is close to +1 or -1 while it indicates a weak relation when close to zero.

Formula to calculate Karl Pearson’s coefficient of correlation for continuous series:

where; A and B are assumed means, h and k are common factors for variable X and Y respectively.

Spearman’s Rank Correlation

• Spearman’s rank correlation measures the linear relation between ranks assigned to individual items according to their attributes.
• It was developed by British psychologist C.E. Spearman.
• Attributes are the variables that cannot be measured numerically.

Spearman’s rank correlation (r_k) is given by:
r_k = l - \(\frac{6 \sum D^2}{N^3-N}\)
When the ranks are repeated, Spearman’s rank correlation (r_k) is given by:
r_k = l - \(\frac{6\left[\sum D^2+\frac{\left(m_1^3-m_1\right)}{12}+\frac{\left(m_2^3-m_2\right)}{12}+\ldots\right]}{N^3-N}\)
where; m₁, m₂, ........... are the number of repetitions of ranks.
The value of rk lies between -1 and +1, that is, -1 ≤ r_k ≤ +1.