where y =B₁ + B₂x + 8 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 Vehicle Speed (y) (x) 1,256 1,331 1,224 1,334 1,350 1,124 35 40 30 45 50 25 n working further with this problem, statisticians suggested the use of the following curvilinear estimated regression equation. ŷ =B₁ + B₂x + B₂x² (a) Develop an estimated regression equation for the data of the form ý = B₁ + B₁x + ₂x². (Round 3 to the nearest integer and to two decimal places and ₂ to three decimal places.)
where y =B₁ + B₂x + 8 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 Vehicle Speed (y) (x) 1,256 1,331 1,224 1,334 1,350 1,124 35 40 30 45 50 25 n working further with this problem, statisticians suggested the use of the following curvilinear estimated regression equation. ŷ =B₁ + B₂x + B₂x² (a) Develop an estimated regression equation for the data of the form ý = B₁ + B₁x + ₂x². (Round 3 to the nearest integer and to two decimal places and ₂ to three decimal places.)
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
Transcribed Image Text:A highway department is studying the relationship between traffic flow and speed. The following model has been hypothesized:
y = B₁ + B₁x + ε
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 Vehicle Speed
(y)
(x)
1,256
1,331
1,224
1,334
1,350
1,124
35
40
30
45
50
25
In working further with this problem, statisticians suggested the use of the following curvilinear estimated regression equation.
ŷ =B₁ + B₁₂x + ₂x²
(a) Develop an estimated regression equation for the data of the form ŷ = B + B₁x + ₂x². (Round Bo to the nearest integer and to two decimal places and ₂ to three decimal places.)
0
0
ŷ =
Transcribed Image Text:(b) Use a = 0.01 to test for a significant relationship.
State the null and alternative hypotheses.
O Ho: B1 = B2 = 0
H₂: One or more of the parameters is not equal to zero.
o Hoi Bo = Bi = B2 = 0
H₂: One or more of the parameters is not equal to zero.
O Ho: One or more of the parameters is not equal to zero.
Hai Bo = B = B2 = 0
O Ho: One or more of the parameters is not equal to zero.
H₂: B₁ = B₂ = 0
Find the value of the test statistic. (Round your answer to two decimal places.)
Find the p-value. (Round your answer to three decimal places.)
p-value =
What is your conclusion?
O Reject Ho. We cannot conclude that the relationship is significant.
O Do not reject Ho. We conclude that the relationship is significant.
O Do not reject Ho. We cannot conclude that the relationship is significant.
O Reject Ho. We conclude that the relationship is significant.
(c) Base 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
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 5 steps with 3 images
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