The following are sample data provided by a moving company on the weights of six shipments, the distances they are moved, and the damage that that was incurred: Weight Distance (1,000 pounds) (1,000 miles) X1 4.0 3.0 1.6 1.2 3.4 4.8 X2 1.5 2.2 1.0 2.0 0.8 1.6 Damage (dollars) y 160 112 69 90 123 186 a) Fit an equation of the form y = bo + b1 x1 + b2 x2 b) Use the equation obtained in part (a) to estimate the damage when a shipment weighting 2400 pounds is moved 1200 miles. Hint: Use the given equation to solve for bo, bi and b2 and then put it back in y = bo + b₁ xl + b2 X2
The following are sample data provided by a moving company on the weights of six shipments, the distances they are moved, and the damage that that was incurred: Weight Distance (1,000 pounds) (1,000 miles) X1 4.0 3.0 1.6 1.2 3.4 4.8 X2 1.5 2.2 1.0 2.0 0.8 1.6 Damage (dollars) y 160 112 69 90 123 186 a) Fit an equation of the form y = bo + b1 x1 + b2 x2 b) Use the equation obtained in part (a) to estimate the damage when a shipment weighting 2400 pounds is moved 1200 miles. Hint: Use the given equation to solve for bo, bi and b2 and then put it back in y = bo + b₁ xl + b2 X2
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
Please write legible
![### Data Analysis on Shipment Weight, Distance, and Damage
The table below presents sample data from a moving company, which shows the relationship between the weights of six shipments, the distances they are moved, and the damage costs incurred:
| Weight (1,000 pounds) \(x_1\) | Distance (1,000 miles) \(x_2\) | Damage (dollars) \(y\) |
|-------------------------------|--------------------------------|----------------------|
| 4.0 | 1.5 | 160 |
| 3.0 | 2.2 | 112 |
| 1.6 | 1.0 | 69 |
| 1.2 | 2.0 | 90 |
| 3.4 | 0.8 | 123 |
| 4.8 | 1.6 | 186 |
### Tasks
a) **Equation Formation:** Fit an equation of the form \( y = b_0 + b_1 x_1 + b_2 x_2 \).
b) **Damage Estimation:** Using the equation derived in part (a), estimate the damage when a shipment weighing 2400 pounds is moved 1200 miles.
### Hint for Equation Derivation
To derive the coefficients \( b_0 \), \( b_1 \), and \( b_2 \), use the given system of equations:
\[
\sum y = nb_0 + b_1 \sum x_1 + b_2 \sum x_2
\]
\[
\sum x_1 y = b_0 \sum x_1 + b_1 \sum x_1^2 + b_2 \sum x_1 x_2
\]
\[
\sum x_2 y = b_0 \sum x_2 + b_1 \sum x_1 x_2 + b_2 \sum x_2^2
\]
These equations help solve for \( b_0 \), \( b_1 \), and \( b_2 \), allowing you to substitute back into the original equation \( y = b_0 + b_1 x_1 + b_2 x_2 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9cb769e4-ba9f-4168-862a-bb68b5e0d9ff%2F55988d12-43d3-47be-9c04-a8883dc0d9ff%2Fs5x7gx_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Data Analysis on Shipment Weight, Distance, and Damage
The table below presents sample data from a moving company, which shows the relationship between the weights of six shipments, the distances they are moved, and the damage costs incurred:
| Weight (1,000 pounds) \(x_1\) | Distance (1,000 miles) \(x_2\) | Damage (dollars) \(y\) |
|-------------------------------|--------------------------------|----------------------|
| 4.0 | 1.5 | 160 |
| 3.0 | 2.2 | 112 |
| 1.6 | 1.0 | 69 |
| 1.2 | 2.0 | 90 |
| 3.4 | 0.8 | 123 |
| 4.8 | 1.6 | 186 |
### Tasks
a) **Equation Formation:** Fit an equation of the form \( y = b_0 + b_1 x_1 + b_2 x_2 \).
b) **Damage Estimation:** Using the equation derived in part (a), estimate the damage when a shipment weighing 2400 pounds is moved 1200 miles.
### Hint for Equation Derivation
To derive the coefficients \( b_0 \), \( b_1 \), and \( b_2 \), use the given system of equations:
\[
\sum y = nb_0 + b_1 \sum x_1 + b_2 \sum x_2
\]
\[
\sum x_1 y = b_0 \sum x_1 + b_1 \sum x_1^2 + b_2 \sum x_1 x_2
\]
\[
\sum x_2 y = b_0 \sum x_2 + b_1 \sum x_1 x_2 + b_2 \sum x_2^2
\]
These equations help solve for \( b_0 \), \( b_1 \), and \( b_2 \), allowing you to substitute back into the original equation \( y = b_0 + b_1 x_1 + b_2 x_2 \).
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman