A highway department is studying the relationship between traffic flow and speed. The following model has been hypothesized: y = Bo + B;x + e 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. Vehicle Speed (x) Traffic Flow (y) 1,254 35 1,327 40 1,227 30 1,335 45 1,348 50 1,122 25 In working further with this problem, statisticians suggested the use of the following curvilinear estimated regression equation. ŷ = Bo + B,x + B,x2 (a) Develop an estimated regression equation for the data of the form ý = B, + B,x + B,x². (Round B, to the nearest integer and B, to two decimal places and B, to three decimal places.) (b) Use a = 0.01 to test for a significant relationship. State the null and alternative hypotheses. O H,: One or more of the parameters is not equal to zero. H3: Bo = B1 = B2 = 0 O Họ: B1 = B2 = 0 H: One or more of the parameters is not equal to zero. O Ho: One or more of the parameters is not equal to zero.
A highway department is studying the relationship between traffic flow and speed. The following model has been hypothesized: y = Bo + B;x + e 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. Vehicle Speed (x) Traffic Flow (y) 1,254 35 1,327 40 1,227 30 1,335 45 1,348 50 1,122 25 In working further with this problem, statisticians suggested the use of the following curvilinear estimated regression equation. ŷ = Bo + B,x + B,x2 (a) Develop an estimated regression equation for the data of the form ý = B, + B,x + B,x². (Round B, to the nearest integer and B, to two decimal places and B, to three decimal places.) (b) Use a = 0.01 to test for a significant relationship. State the null and alternative hypotheses. O H,: One or more of the parameters is not equal to zero. H3: Bo = B1 = B2 = 0 O Họ: B1 = B2 = 0 H: One or more of the parameters is not equal to zero. O Ho: One or more of the parameters is not equal to zero.
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 examining the relationship between traffic flow and speed. They have proposed the following model:
\[ y = \beta_0 + \beta_1 x + \varepsilon \]
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) |
|-------------------|-------------------|
| 1,254 | 35 |
| 1,327 | 40 |
| 1,227 | 30 |
| 1,335 | 45 |
| 1,348 | 50 |
| 1,122 | 25 |
Statisticians suggested using the following curvilinear estimated regression equation for further analysis:
\[ \hat{y} = \beta_0 + \beta_1 x + \beta_2 x^2 \]
**(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.
- \( H_0 \): One or more of the parameters is not equal to zero.
- \( H_3 \): \(\beta_0 = \beta_1 = \beta_2 = 0\)
- \( H_0 \): \(\beta_1 = \beta_2 = 0\)
- \( H_3 \): One or more of the parameters is not equal to zero.
- \( H_0 \): One or more of the parameters is not equal to zero.
- \( H_3 \): \(\beta_1 = \beta_2 = 0\)
- \( H_0 \): \(\beta_0 = \beta_1 = \beta_2 = 0\)
- \( H_3 \): One or](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F358923dd-976b-4983-a367-bafd3b4b55c1%2F054dc41b-c4cd-45f9-8308-7880aed30c97%2F43s7meo_processed.png&w=3840&q=75)
Transcribed Image Text:A highway department is examining the relationship between traffic flow and speed. They have proposed the following model:
\[ y = \beta_0 + \beta_1 x + \varepsilon \]
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) |
|-------------------|-------------------|
| 1,254 | 35 |
| 1,327 | 40 |
| 1,227 | 30 |
| 1,335 | 45 |
| 1,348 | 50 |
| 1,122 | 25 |
Statisticians suggested using the following curvilinear estimated regression equation for further analysis:
\[ \hat{y} = \beta_0 + \beta_1 x + \beta_2 x^2 \]
**(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.
- \( H_0 \): One or more of the parameters is not equal to zero.
- \( H_3 \): \(\beta_0 = \beta_1 = \beta_2 = 0\)
- \( H_0 \): \(\beta_1 = \beta_2 = 0\)
- \( H_3 \): One or more of the parameters is not equal to zero.
- \( H_0 \): One or more of the parameters is not equal to zero.
- \( H_3 \): \(\beta_1 = \beta_2 = 0\)
- \( H_0 \): \(\beta_0 = \beta_1 = \beta_2 = 0\)
- \( H_3 \): One or
![Find the p-value. (Round your answer to three decimal places.)
p-value = [Text Box]
What is your conclusion?
- ○ Reject \( H_0 \). We cannot conclude that the relationship is significant.
- ○ Reject \( H_0 \). We 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.)
[Text Box] vehicles per hour](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F358923dd-976b-4983-a367-bafd3b4b55c1%2F054dc41b-c4cd-45f9-8308-7880aed30c97%2Fh0lzzcw_processed.png&w=3840&q=75)
Transcribed Image Text:Find the p-value. (Round your answer to three decimal places.)
p-value = [Text Box]
What is your conclusion?
- ○ Reject \( H_0 \). We cannot conclude that the relationship is significant.
- ○ Reject \( H_0 \). We 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.)
[Text Box] vehicles per hour
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