Question

# A statistical program is recommended. A highway department is studying the relationship between traffic flow and...

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
1,328 40
1,225 30
1,333 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 = 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: One or more of the parameters is not equal to zero.
Ha: b0 = b1 = b2 = 0

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

H0: b0 = b1 = b2 = 0

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 = 0

Find the value of the test statistic. (Round your answer to two decimal places.)

p-value =

Reject H0. We conclude that the relationship is significant.

Do not 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.

(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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