y = X y 1 705 y= 2 681 3 4 749 760 Use exponential regression to find an exponential equation that best fits this data. Give both a and b rounded to at least 4 decimal places. 5 735 6 731 Use linear regression to find an linear equation that best fits this data. Give both m and b rounded to at least two decimal places. O Exponential O Linear Of these two, which equation best fits the data!
y = X y 1 705 y= 2 681 3 4 749 760 Use exponential regression to find an exponential equation that best fits this data. Give both a and b rounded to at least 4 decimal places. 5 735 6 731 Use linear regression to find an linear equation that best fits this data. Give both m and b rounded to at least two decimal places. O Exponential O Linear Of these two, which equation best fits the data!
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![### Question 25
The table below provides a set of data points:
| x | 1 | 2 | 3 | 4 | 5 | 6 |
|---|-----|-----|-----|-----|-----|-----|
| y | 705 | 681 | 749 | 760 | 735 | 731 |
**Tasks:**
1. **Exponential Regression:**
- Use exponential regression to find an equation that best fits the data.
- Provide the equation in the form \(y = a \cdot b^x\).
- Round both \(a\) and \(b\) to at least 4 decimal places.
\[
y = \_\_\_\_\_\_\_
\]
2. **Linear Regression:**
- Use linear regression to find an equation that best fits the data.
- Provide the equation in the form \(y = mx + b\).
- Round both \(m\) and \(b\) to at least 2 decimal places.
\[
y = \_\_\_\_\_\_\_
\]
3. **Choose the Best Fit:**
- Based on the fits from exponential and linear regression, select which model best fits the data.
- [ ] Exponential
- [ ] Linear
**Instructions:**
Evaluate both models and determine which provides the most accurate representation of the given data set.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F282a3a3f-59f1-4615-b9ef-ee283c9e8b4d%2F453719e3-73c3-4dc4-b5f2-989a93cae3f9%2F16ee1e4_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Question 25
The table below provides a set of data points:
| x | 1 | 2 | 3 | 4 | 5 | 6 |
|---|-----|-----|-----|-----|-----|-----|
| y | 705 | 681 | 749 | 760 | 735 | 731 |
**Tasks:**
1. **Exponential Regression:**
- Use exponential regression to find an equation that best fits the data.
- Provide the equation in the form \(y = a \cdot b^x\).
- Round both \(a\) and \(b\) to at least 4 decimal places.
\[
y = \_\_\_\_\_\_\_
\]
2. **Linear Regression:**
- Use linear regression to find an equation that best fits the data.
- Provide the equation in the form \(y = mx + b\).
- Round both \(m\) and \(b\) to at least 2 decimal places.
\[
y = \_\_\_\_\_\_\_
\]
3. **Choose the Best Fit:**
- Based on the fits from exponential and linear regression, select which model best fits the data.
- [ ] Exponential
- [ ] Linear
**Instructions:**
Evaluate both models and determine which provides the most accurate representation of the given data set.
Expert Solution
Step 1
Given,
| X | 1 | 2 | 3 | 4 | 5 | 6 |
| Y | 705 | 681 | 749 | 760 | 735 | 731 |
To find :
Exponential Regression, (Exponential Equation).
Linear Regression, (Linear Equation).
Step by step
Solved in 5 steps with 2 images
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