Concept explainers
In Exercises 17-20, compute the
To calculate: To compute the correlation coefficient.
Answer to Problem 19E
The correlation coefficient is
Explanation of Solution
Given information:
The data is,
5.5 | 4.2 | 4.7 | 5.6 | 6.0 | 3.9 | 6.3 | 5.7 | |
4.9 | 4.8 | 4.8 | 4.7 | 5.5 | 5.1 | 5.8 | 6.5 |
Formula used:
The correlation coefficient of a data is given by:
Where,
The standard deviations are given by:
Calculation:
The mean of x is given by:
The mean of y is given by:
The data can be represented in tabular form as:
x | y | ||||
5.5 | 4.9 | 0.2625 | 0.06891 | -0.3625 | 0.13141 |
4.2 | 4.8 | -1.0375 | 1.07641 | -0.4625 | 0.21391 |
4.7 | 4.8 | -0.5375 | 0.28891 | -0.4625 | 0.21391 |
5.6 | 4.7 | 0.3625 | 0.13141 | -0.5625 | 0.31641 |
6 | 5.5 | 0.7625 | 0.58141 | 0.2375 | 0.05641 |
3.9 | 5.1 | -1.3375 | 1.78891 | -0.1625 | 0.02641 |
6.3 | 5.8 | 1.0625 | 1.12891 | 0.5375 | 0.28891 |
5.7 | 6.5 | 0.4625 | 0.21391 | 1.2375 | 1.53141 |
Hence, the standard deviation is given by:
And,
Hence, the table for calculating coefficient of correlation is given by:
x | y | |||
5.5 | 4.9 | 0.2625 | -0.3625 | -0.09516 |
4.2 | 4.8 | -1.0375 | -0.4625 | 0.47984 |
4.7 | 4.8 | -0.5375 | -0.4625 | 0.24859 |
5.6 | 4.7 | 0.3625 | -0.5625 | -0.20391 |
6 | 5.5 | 0.7625 | 0.2375 | 0.18109 |
3.9 | 5.1 | -1.3375 | -0.1625 | 0.21734 |
6.3 | 5.8 | 1.0625 | 0.5375 | 0.57109 |
5.7 | 6.5 | 0.4625 | 1.2375 | 0.57234 |
The correlation coefficient of a data is given by:
Plugging the values in the formula,
Therefore, the correlation coefficient for the given data is 0.515
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Chapter 4 Solutions
Elementary Statistics ( 3rd International Edition ) Isbn:9781260092561
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw HillBig Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt