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CHAPTER
7
Studying this chapter should enable you to:
• understand the meaning of the term correlation;
• understand the nature of relationship between two variables; • calculate the different measures of correlation;
• analyse the degree and direction of the relationships.
1. INTRODUCTION
In previous chapters you have learnt how to construct summary measures out of a mass of data and changes among similar variables. Now you will learn how to examine the relationship between two variables.
Correlation
As the summer heat rises, hill stations, are crowded with more and more visitors. Ice-cream sales become more brisk. Thus, the temperature is related to number of visitors and sale of ice-creams. Similarly, as the supply of tomatoes increases in your local mandi, its price drops. When the local harvest starts reaching the market, the price of tomatoes drops from a princely Rs 40 per kg to Rs 4 per kg or even less. Thus supply is related to price. Correlation analysis is a means for examining such relationships systematically. It deals with questions such as:
• Is there any relationship between two variables?
92
STATISTICS FOR ECONOMICS
•
If the value of one variable changes, does the value of the other also change?
•
Do both the variables move in the same direction?
•
How strong is the relationship?
2. TYPES
OF
RELATIONSHIP
Let us look at various types of relationship. The relation between movements in quantity demanded and the price of a commodity is an
integral part of the theory of demand, which you will read in class XII. Low rainfall is related to low agricultural productivity. Such examples of relationship may be given a cause and effect interpretation. Others may be just coincidence. The relation between the arrival of migratory birds in a sanctuary and the birth rates in the locality can not be given any cause and ef fect interpretation. The
relationships
7
Studying this chapter should enable you to:
• understand the meaning of the term correlation;
• understand the nature of relationship between two variables; • calculate the different measures of correlation;
• analyse the degree and direction of the relationships.
1. INTRODUCTION
In previous chapters you have learnt how to construct summary measures out of a mass of data and changes among similar variables. Now you will learn how to examine the relationship between two variables.
Correlation
As the summer heat rises, hill stations, are crowded with more and more visitors. Ice-cream sales become more brisk. Thus, the temperature is related to number of visitors and sale of ice-creams. Similarly, as the supply of tomatoes increases in your local mandi, its price drops. When the local harvest starts reaching the market, the price of tomatoes drops from a princely Rs 40 per kg to Rs 4 per kg or even less. Thus supply is related to price. Correlation analysis is a means for examining such relationships systematically. It deals with questions such as:
• Is there any relationship between two variables?
92
STATISTICS FOR ECONOMICS
•
If the value of one variable changes, does the value of the other also change?
•
Do both the variables move in the same direction?
•
How strong is the relationship?
2. TYPES
OF
RELATIONSHIP
Let us look at various types of relationship. The relation between movements in quantity demanded and the price of a commodity is an
integral part of the theory of demand, which you will read in class XII. Low rainfall is related to low agricultural productivity. Such examples of relationship may be given a cause and effect interpretation. Others may be just coincidence. The relation between the arrival of migratory birds in a sanctuary and the birth rates in the locality can not be given any cause and ef fect interpretation. The
relationships