Chapter 6: Correlation

Economics - Statistics • Class 11

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Chapter Analysis

Intermediate15 pages • English

Quick Summary

The chapter on correlation in Class 11 Economics explores the relationship between two variables. It covers the concept of correlation, types of correlation (positive and negative), and various techniques for measuring correlation such as scatter diagrams, Karl Pearson's coefficient, and Spearman's rank correlation. The chapter emphasizes that correlation measures the direction and strength of a relationship but does not imply causation.

Key Topics

  • Concept of correlation
  • Positive and negative correlation
  • Scatter diagram
  • Karl Pearson's coefficient
  • Spearman's rank correlation
  • Properties of correlation
  • Misinterpretations of correlation

Learning Objectives

  • Understand the meaning and concept of correlation
  • Differentiate between various types of correlations
  • Calculate and interpret correlation coefficients
  • Use scatter diagrams to assess relationships
  • Discern the limitations of correlation analysis
  • Recognize when to apply rank vs. Pearson's correlation

Questions in Chapter

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

Answer: (iii) non-existent

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The range of simple correlation coefficient is

Answer: (ii) minus one to plus one

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If rxy is positive the relation between X and Y is of the type

Answer: (i) When Y increases X increases

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If rxy = 0 the variable X and Y are

Answer: (ii) not linearly related

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Of the following three measures which can measure any type of relationship

Answer: (iii) Scatter diagram

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Additional Practice Questions

Explain how a scatter diagram is used to determine the nature of relationship between two variables.

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Answer: A scatter diagram is a graph that plots the values of two variables as points on the Cartesian plane. By examining the pattern of the points, one can infer the nature of the relationship. If the points pattern near a line, the relationship is linear; if they are scattered widely, the relationship is weak. A positive slope suggests a positive correlation, negative slope indicates negative correlation, and no discernible pattern suggests no correlation.

Differentiate between correlation and causation with examples.

hard

Answer: Correlation implies a mutual relationship between two variables, where changes in one variable are associated with changes in another. However, causation indicates that one variable directly affects the change in another. For example, ice cream sales and drowning incidents might be correlated because both increase in summer, but one does not cause the other. A causation example is smoking causing lung cancer.

Why is Pearson's coefficient of correlation preferred over covariance as a measure of association?

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Answer: Pearson's coefficient of correlation is preferred over covariance because it provides a normalized measure of the degree of linear relationship between variables on a scale from -1 to +1. Covariance, on the other hand, is not normalized and depends on the units of measurement, making it difficult to compare across contexts.

How does the rank correlation coefficient differ from Pearson's correlation coefficient?

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Answer: The rank correlation coefficient, such as Spearman's, is used when the data are ordinal or not suitable for Pearson's due to non-linear relationships or outliers. It measures the association between ranked variables. Pearson's correlation, however, requires interval data and assumes a linear relationship between the variables.

What are the advantages and limitations of using a scatter diagram?

easy

Answer: Advantages of scatter diagrams include easy visual determination of relationships and the ability to indicate correlations intuitively. Limitations include lack of precise numeric data and difficulty in determining correlations in non-linear relationships. It's also challenging to quantify the strength of the relationship.