Concept explainers
(a)
To explain: Whether the value of the
(a)
Answer to Problem 20P
Solution: The
Explanation of Solution
Given: The formula for the correlation coefficient is given in the question as:
The numerator of the above formula is
In this part, the values are squared; so, ultimately, they will show a positive result and hence, it will not make any difference to the resultant value of r.
(b)
To explain: Whether the value of the correlation coefficient will change if the values of x and y are exchanged.
(b)
Answer to Problem 20P
Solution: The correlation coefficient remains the same if the corresponding values of x and y are exchanged.
Explanation of Solution
Given: A hypothetical set of x and y data values are given in the question. The formula for correlation coefficient is also provided in it as:
The numerator of the above formula is
In this part, the values are squared; so, ultimately, they will show a positive result and hence, it will not make any difference to the resultant value of r.
(c)
To find: The value of the correlation coefficient of the two samples, and to show that the computed value of r is the same for both samples.
(c)
Answer to Problem 20P
Solution: The computed value of the correlation coefficient of both data sets is 0.618.
Explanation of Solution
Given: Consider the first data set:
x | 1 | 3 | 4 |
y | 2 | 1 | 6 |
The second data set is provided below:
x | 2 | 1 | 6 |
y | 1 | 3 | 4 |
Calculation: The value of the correlation coefficient of data set 1 can be computed by using the formula given below:
To compute
x | y | |||
1 | 2 | 1 | 4 | 2 |
3 | 1 | 9 | 1 | 3 |
4 | 6 | 16 | 36 | 24 |
Substitute the values of
Now, the correlation coefficient of data set 2 can be calculated as:
x | y | |||
2 | 1 | 4 | 1 | 2 |
1 | 3 | 1 | 9 | 3 |
6 | 4 | 36 | 16 | 24 |
Substitute the values of
Interpretation: For the data set 1, the value of r is 0.618 and for the data set 2, the value of r is also 0.618. This means that the value of the correlation coefficient remains the same if the values of x and y are exchanged.
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Chapter 4 Solutions
Understanding Basic Statistics
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