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.)
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 31EQ
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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
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