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Correlation Introduction

The document defines and describes the coefficient of correlation, a statistic that measures the strength and direction of the linear relationship between two variables on a scale of -1 to +1. It provides examples of different types of correlation: perfect positive correlation (+1), perfect negative correlation (-1), moderately positive (0<r<1) and moderate negative (-1<r<1) correlation, and absolute no correlation (r close to 0). Methods for computing correlation coefficients include Karl Pearson's and Spearman's rank correlation coefficients.

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Shabbir Hussain
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51 views17 pages

Correlation Introduction

The document defines and describes the coefficient of correlation, a statistic that measures the strength and direction of the linear relationship between two variables on a scale of -1 to +1. It provides examples of different types of correlation: perfect positive correlation (+1), perfect negative correlation (-1), moderately positive (0<r<1) and moderate negative (-1<r<1) correlation, and absolute no correlation (r close to 0). Methods for computing correlation coefficients include Karl Pearson's and Spearman's rank correlation coefficients.

Uploaded by

Shabbir Hussain
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Coefficient of correlation

A statistic representing how closely two


variables co-vary; it can vary from -1
(perfect negative correlation) through 0
(no correlation) to +1 (perfect positive
correlation).
• The correlation coefficient, denoted by r, is a
measure of the strength of the straight-line or
linear relationship between two variables. The
correlation coefficient takes on values ranging
between +1 and -1.
• The quantity r, called the linear correlation
coefficient, measures the strength and the
direction of a linear relationship between two
variables
Type of correlation coefficient

1. Perfect Positive correlation

2. Perfect negative correlation

3. Moderately Positive correlation

4. Moderate negative correlation

5. Absolute no correlation
Perfect Positive correlation
• If x and y have a strong positive linear correlation,
r is close to +1. An r value of exactly +1
indicates a perfect positive fit. Positive values
indicate a relationship between x and y variables
such that as values for x increases, values for y
also increase.
Perfect negative correlation
• If x and y have a strong negative linear
correlation, r is close to -1. An r value of exactly
-1 indicates a perfect negative fit. Negative
values indicate a relationship between x and y
such that as values for x increase, values for y
decrease.
Moderately Positive correlation
• 0<r<1

Moderate negative correlation


-1<r<1
Absolute no correlation
• If there is no linear correlation or a weak
linear correlation, r is close to 0. A value near
zero means that there is a random, nonlinear
relationship between the two variables
Methods of computing the
correlation

• karl pearson’s correlation coefficient

• spearman’s rank correlation coefficient


karl pearson’s correlation
coefficient
Spearman’s rank correlation
coefficient

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