y = Bo + Bqx + 8 here y = traffic flow in vehicles per hour x = vehicle speed in miles per hour. he following data were collected during rush hour for six highways leading out of the city. Vehicle Speed (x) Traffic Flow (y) 1,257 35 1,329 40 1,225 30 1,333 45 1,351 50 1,126 25 n working further with this problem, statisticians suggested the use of the following curvilinear estimated regression equation.
y = Bo + Bqx + 8 here y = traffic flow in vehicles per hour x = vehicle speed in miles per hour. he following data were collected during rush hour for six highways leading out of the city. Vehicle Speed (x) Traffic Flow (y) 1,257 35 1,329 40 1,225 30 1,333 45 1,351 50 1,126 25 n working further with this problem, statisticians suggested the use of the following curvilinear estimated regression equation.
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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![**A highway department is studying the relationship between traffic flow and speed. The following model has been hypothesized:**
\[ y = \beta_0 + \beta_1 x + \varepsilon \]
where:
- \( y = \) traffic flow in vehicles per hour
- \( x = \) vehicle speed in miles per hour
**The following data were collected during rush hour for six highways leading out of the city:**
| Traffic Flow (y) | Vehicle Speed (x) |
|------------------|-------------------|
| 1,257 | 35 |
| 1,329 | 40 |
| 1,225 | 30 |
| 1,333 | 45 |
| 1,351 | 50 |
| 1,126 | 25 |
**In working further with this problem, statisticians suggested the use of the following curvilinear estimated regression equation:**
\[ \hat{y} = \beta_0 + \beta_1 x + \beta_2 x^2 \]
(a) **Develop an estimated regression equation for the data of the form** \(\hat{y} = \beta_0 + \beta_1 x + \beta_2 x^2\). (Round \(\beta_0\) to the nearest integer, \(\beta_1\) to two decimal places, and \(\beta_2\) to three decimal places.)
\[ \hat{y} = \]
(b) **Use \(\alpha = 0.01\) to test for a significant relationship.**
**State the null and alternative hypotheses.**
- \( H_0: \beta_0 = \beta_1 = \beta_2 = 0 \)
\( H_a: \) One or more of the parameters is not equal to zero.
- \( H_0: \) One or more of the parameters is not equal to zero.
\( H_a: \beta_1 = \beta_2 = 0 \)
- \( H_0: \beta_1 = \beta_2 = 0 \)
\( H_a: \) One or more of the parameters is not equal to zero.
- \( H_0: \) One or more of the parameters is not equal to zero.
\( H_a: \beta_0 = \](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F358923dd-976b-4983-a367-bafd3b4b55c1%2F16766b4d-6ac9-4131-b855-0bca87cdd0b3%2Fsi274fk_processed.png&w=3840&q=75)
Transcribed Image Text:**A highway department is studying the relationship between traffic flow and speed. The following model has been hypothesized:**
\[ y = \beta_0 + \beta_1 x + \varepsilon \]
where:
- \( y = \) traffic flow in vehicles per hour
- \( x = \) vehicle speed in miles per hour
**The following data were collected during rush hour for six highways leading out of the city:**
| Traffic Flow (y) | Vehicle Speed (x) |
|------------------|-------------------|
| 1,257 | 35 |
| 1,329 | 40 |
| 1,225 | 30 |
| 1,333 | 45 |
| 1,351 | 50 |
| 1,126 | 25 |
**In working further with this problem, statisticians suggested the use of the following curvilinear estimated regression equation:**
\[ \hat{y} = \beta_0 + \beta_1 x + \beta_2 x^2 \]
(a) **Develop an estimated regression equation for the data of the form** \(\hat{y} = \beta_0 + \beta_1 x + \beta_2 x^2\). (Round \(\beta_0\) to the nearest integer, \(\beta_1\) to two decimal places, and \(\beta_2\) to three decimal places.)
\[ \hat{y} = \]
(b) **Use \(\alpha = 0.01\) to test for a significant relationship.**
**State the null and alternative hypotheses.**
- \( H_0: \beta_0 = \beta_1 = \beta_2 = 0 \)
\( H_a: \) One or more of the parameters is not equal to zero.
- \( H_0: \) One or more of the parameters is not equal to zero.
\( H_a: \beta_1 = \beta_2 = 0 \)
- \( H_0: \beta_1 = \beta_2 = 0 \)
\( H_a: \) One or more of the parameters is not equal to zero.
- \( H_0: \) One or more of the parameters is not equal to zero.
\( H_a: \beta_0 = \
![**Statistical Analysis and Traffic Flow Prediction**
**Find the p-value. (Round your answer to three decimal places.)**
p-value = [______]
**What is your conclusion?**
- ○ Reject \( H_0 \). We conclude that the relationship is significant.
- ○ Reject \( H_0 \). We cannot conclude that the relationship is significant.
- ○ Do not reject \( H_0 \). We cannot conclude that the relationship is significant.
- ○ Do not reject \( H_0 \). We conclude that the relationship is significant.
**(c) Based on the model, predict the traffic flow in vehicles per hour at a speed of 38 miles per hour. (Round your answer to two decimal places.)**
[______] vehicles per hour](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F358923dd-976b-4983-a367-bafd3b4b55c1%2F16766b4d-6ac9-4131-b855-0bca87cdd0b3%2Fy14h07_processed.png&w=3840&q=75)
Transcribed Image Text:**Statistical Analysis and Traffic Flow Prediction**
**Find the p-value. (Round your answer to three decimal places.)**
p-value = [______]
**What is your conclusion?**
- ○ Reject \( H_0 \). We conclude that the relationship is significant.
- ○ Reject \( H_0 \). We cannot conclude that the relationship is significant.
- ○ Do not reject \( H_0 \). We cannot conclude that the relationship is significant.
- ○ Do not reject \( H_0 \). We conclude that the relationship is significant.
**(c) Based on the model, predict the traffic flow in vehicles per hour at a speed of 38 miles per hour. (Round your answer to two decimal places.)**
[______] vehicles per hour
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