Question

A statistical program is recommended.

A highway department is studying the relationship between traffic flow and speed. The following model has been hypothesized:

y = β₀ + β₁x + 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 (y)	Vehicle Speed (x)
1,257	35
1,331	40
1,225	30
1,337	45
1,349	50
1,126	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 α = 0.01 to test for a significant relationship.

State the null and alternative hypotheses.

H₀: b₁ = b₂ = 0
H_a: One or more of the parameters is not equal to zero.H₀: b₀ = b₁ = b₂ = 0
H_a: One or more of the parameters is not equal to zero.    H₀: One or more of the parameters is not equal to zero.
H_a: b₀ = b₁ = b₂ = 0H₀: One or more of the parameters is not equal to zero.
H_a: 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?

Reject H₀. We conclude that the relationship is significant.Do not reject H₀. We cannot conclude that the relationship is significant.    Reject H₀. We cannot conclude that the relationship is significant.Do not reject H₀. 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

Answer 1

The statistical software output for this problem is:

Hence,

a) The regression equation will be:

= 431 + 37.59 x - 0.385 x²

b) Hypotheses:

H₀: b₁ = b₂ = 0
H_a: One or more of the parameters is not equal to zero. Option A is correct.

Test statistic = 79.17

p - value = 0.003

Conclusion: Reject H₀. We conclude that the relationship is significant. Option A is correct.

c) Predicted value = 1303.17 vehicles per hour