Annual high temperatures in a certain location have been tracked for several years. Let X represent the year and Y the high temperature. Based on the data shown below, calculate the correlation coefficient (to three decimal places) between X and Y. Use your calculator! T= X 4 5 6 y 15.02 15.5 18.88 7 17.76 8 18.24 9 20.02 10 24.6 11 22.58 12 26.06 13 27.54 14 29.92 27.2 28.58 15 16
Annual high temperatures in a certain location have been tracked for several years. Let X represent the year and Y the high temperature. Based on the data shown below, calculate the correlation coefficient (to three decimal places) between X and Y. Use your calculator! T= X 4 5 6 y 15.02 15.5 18.88 7 17.76 8 18.24 9 20.02 10 24.6 11 22.58 12 26.06 13 27.54 14 29.92 27.2 28.58 15 16
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![### Question 16
Annual high temperatures in a certain location have been tracked for several years. Let \( X \) represent the year and \( Y \) the high temperature. Based on the data shown below, calculate the correlation coefficient (to three decimal places) between \( X \) and \( Y \). Use your calculator!
| \( x \) | \( y \) |
|--------|----------|
| 4 | 15.02 |
| 5 | 15.5 |
| 6 | 18.88 |
| 7 | 17.76 |
| 8 | 18.24 |
| 9 | 20.02 |
| 10 | 24.6 |
| 11 | 22.58 |
| 12 | 26.06 |
| 13 | 27.54 |
| 14 | 29.92 |
| 15 | 27.2 |
| 16 | 28.58 |
Fill in the box with the calculated correlation coefficient.
\[ r = \]
---
#### Explanation of Data Table
The table above lists the yearly high temperatures (in an unspecified unit) over several years. Each pair of values \((X, Y)\) consists of:
- \( X \), which represents the year (starting from 4 to 16)
- \( Y \), which represents the corresponding high temperature recorded for that year.
The objective is to find the correlation coefficient \( r \), which measures the strength and direction of the linear relationship between the two variables \( X \) (year) and \( Y \) (high temperature).
**How to Calculate the Correlation Coefficient:**
1. Calculate the mean of both \( X \) and \( Y \).
2. Find the deviations from the mean for both \( X \) and \( Y \).
3. Calculate the product of the deviations for each pair of \( X \) and \( Y \).
4. Sum up the products of the deviations.
5. Find the square root of the sum of squares of the deviations for \( X \) and \( Y \).
6. Use the correlation coefficient formula:
\[ r = \frac{n \sum (XY) - (\sum X)(\sum Y)}{\sqrt{[n \sum X^2 - (\](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbed7ab37-3726-4b83-a741-6ed60a3ee8a9%2Fc2769449-27bf-4549-bc3c-286dd862c480%2F4wyexg_processed.png&w=3840&q=75)
Transcribed Image Text:### Question 16
Annual high temperatures in a certain location have been tracked for several years. Let \( X \) represent the year and \( Y \) the high temperature. Based on the data shown below, calculate the correlation coefficient (to three decimal places) between \( X \) and \( Y \). Use your calculator!
| \( x \) | \( y \) |
|--------|----------|
| 4 | 15.02 |
| 5 | 15.5 |
| 6 | 18.88 |
| 7 | 17.76 |
| 8 | 18.24 |
| 9 | 20.02 |
| 10 | 24.6 |
| 11 | 22.58 |
| 12 | 26.06 |
| 13 | 27.54 |
| 14 | 29.92 |
| 15 | 27.2 |
| 16 | 28.58 |
Fill in the box with the calculated correlation coefficient.
\[ r = \]
---
#### Explanation of Data Table
The table above lists the yearly high temperatures (in an unspecified unit) over several years. Each pair of values \((X, Y)\) consists of:
- \( X \), which represents the year (starting from 4 to 16)
- \( Y \), which represents the corresponding high temperature recorded for that year.
The objective is to find the correlation coefficient \( r \), which measures the strength and direction of the linear relationship between the two variables \( X \) (year) and \( Y \) (high temperature).
**How to Calculate the Correlation Coefficient:**
1. Calculate the mean of both \( X \) and \( Y \).
2. Find the deviations from the mean for both \( X \) and \( Y \).
3. Calculate the product of the deviations for each pair of \( X \) and \( Y \).
4. Sum up the products of the deviations.
5. Find the square root of the sum of squares of the deviations for \( X \) and \( Y \).
6. Use the correlation coefficient formula:
\[ r = \frac{n \sum (XY) - (\sum X)(\sum Y)}{\sqrt{[n \sum X^2 - (\
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