A highway department is studying the relationship between traffic flow and speed. The following model has been hypothesized: y = ?0 + ?1x + ? 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) 1,258 35 1,329 40 1,227 30 1,336 45 1,348 50 1,125 25
A highway department is studying the relationship between traffic flow and speed. The following model has been hypothesized: y = ?0 + ?1x + ? 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) 1,258 35 1,329 40 1,227 30 1,336 45 1,348 50 1,125 25
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 = ?0 + ?1x + ?
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) |
|---|---|
| 1,258 | 35 |
| 1,329 | 40 |
| 1,227 | 30 |
| 1,336 | 45 |
| 1,348 | 50 |
| 1,125 | 25 |
In working further with this problem, statisticians suggested the use of the following curvilinear estimated regression equation.
ŷ = b0 + b1x + b2x2
(a)
Develop an estimated regression equation for the data of the form ŷ = b0 + b1x + b2x2.(Round b0 to the nearest integer and b1 to two decimal places and b2 to three decimal places.)
ŷ = ??
(b) Use ? = 0.01 to test for a significant relationship.
State the null and alternative hypotheses.
-H0: One or more of the parameters is not equal to zero.
Ha: b0 = b1 = b2 = 0
Ha: b0 = b1 = b2 = 0
-H0: b0 = b1 = b2 = 0
Ha: One or more of the parameters is not equal to zero.
Ha: One or more of the parameters is not equal to zero.
-H0: One or more of the parameters is not equal to zero.
Ha: b1 = b2 = 00:
Ha: b1 = b2 = 00:
-H0b1 = b2 = 0
Ha: One or more of the parameters is not equal to zero.
Ha: One or more of the parameters is not equal to zero.
Find the value of the test statistic. (Round your answer to two decimal places.)
Statistic=??
Find the p-value. (Round your answer to three decimal places.)
p-value = ??
What is your conclusion?
-Reject H0. We conclude that the relationship is significant.
-Do not reject H0. We cannot conclude that the relationship is significant.
- Do not reject H0. We conclude that the relationship is significant.
-Reject H0. We cannot 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
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