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! 1 7.64 6.68 10.92 4 9.46 14.1 15.74 15.68 8 15.32 9. 17.76 10 17.7
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! 1 7.64 6.68 10.92 4 9.46 14.1 15.74 15.68 8 15.32 9. 17.76 10 17.7
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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![Title: Analyzing Annual High Temperatures Over Time
**Description:**
In this exercise, we analyze the annual high temperatures in a specific location over several years. The data consists of two variables:
- \( X \): The year
- \( Y \): The high temperature
**Data Table:**
\[
\begin{array}{|c|c|}
\hline
X & Y \\
\hline
1 & 7.64 \\
2 & 6.68 \\
3 & 10.92 \\
4 & 9.46 \\
5 & 14.1 \\
6 & 15.74 \\
7 & 15.68 \\
8 & 15.32 \\
9 & 17.76 \\
10 & 17.7 \\
\hline
\end{array}
\]
**Task:**
Based on the data shown in the table, calculate the correlation coefficient to three decimal places between \( X \) (the year) and \( Y \) (the high temperature). Use your calculator to determine the extent to which temperature changes can be associated with changes in time.
**Purpose:**
Understanding the correlation between these variables can help in predicting future temperature trends and examining the potential impact of climate factors over time.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0f725b05-6985-474e-a031-937034e54c0f%2F40b0fb4a-3c00-4e91-af93-66d2205cfd8b%2F62a3xpn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Title: Analyzing Annual High Temperatures Over Time
**Description:**
In this exercise, we analyze the annual high temperatures in a specific location over several years. The data consists of two variables:
- \( X \): The year
- \( Y \): The high temperature
**Data Table:**
\[
\begin{array}{|c|c|}
\hline
X & Y \\
\hline
1 & 7.64 \\
2 & 6.68 \\
3 & 10.92 \\
4 & 9.46 \\
5 & 14.1 \\
6 & 15.74 \\
7 & 15.68 \\
8 & 15.32 \\
9 & 17.76 \\
10 & 17.7 \\
\hline
\end{array}
\]
**Task:**
Based on the data shown in the table, calculate the correlation coefficient to three decimal places between \( X \) (the year) and \( Y \) (the high temperature). Use your calculator to determine the extent to which temperature changes can be associated with changes in time.
**Purpose:**
Understanding the correlation between these variables can help in predicting future temperature trends and examining the potential impact of climate factors over time.
![**Linear Regression Application, Interpolation and Extrapolation**
Use the data and story to answer the following questions.
The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states.
- \( x = \) Thousands of automatic weapons
- \( y = \) Murders per 100,000 residents
| \( y \) | \( x \) |
|--------|--------|
| 11.6 | 8.6 |
| 13.7 | 11.6 |
| 11.6 | 9.4 |
| 7.3 | 6.7 |
| 6.1 | 3.6 |
| 6.1 | 2.6 |
| 5.5 | 2.1 |
| 4.7 | 0.5 |
Use your calculator to determine the equation of the regression line. Determine the regression equation in \( y = ax + b \) form and write it below. (Round to 2 decimal places)
Answer:
**A) How many murders per 100,000 residents can be expected in a state with 1.9 thousand automatic weapons?**
- Round to 3 decimal places.
- Answer:
**B) How many murders per 100,000 residents can be expected in a state with 4.8 thousand automatic weapons?**
- Round to 3 decimal places.
- Answer:
Question Help: [Video] [Message instructor]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0f725b05-6985-474e-a031-937034e54c0f%2F40b0fb4a-3c00-4e91-af93-66d2205cfd8b%2Fblfn06i_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Linear Regression Application, Interpolation and Extrapolation**
Use the data and story to answer the following questions.
The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states.
- \( x = \) Thousands of automatic weapons
- \( y = \) Murders per 100,000 residents
| \( y \) | \( x \) |
|--------|--------|
| 11.6 | 8.6 |
| 13.7 | 11.6 |
| 11.6 | 9.4 |
| 7.3 | 6.7 |
| 6.1 | 3.6 |
| 6.1 | 2.6 |
| 5.5 | 2.1 |
| 4.7 | 0.5 |
Use your calculator to determine the equation of the regression line. Determine the regression equation in \( y = ax + b \) form and write it below. (Round to 2 decimal places)
Answer:
**A) How many murders per 100,000 residents can be expected in a state with 1.9 thousand automatic weapons?**
- Round to 3 decimal places.
- Answer:
**B) How many murders per 100,000 residents can be expected in a state with 4.8 thousand automatic weapons?**
- Round to 3 decimal places.
- Answer:
Question Help: [Video] [Message instructor]
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