Question

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

y = β₀ + β₁x + ε

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
1,227	30
1,336	45
1,349	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 =

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.  

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

(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:

From above output:

a) ŷ = 426 + 37.88 x - 0.389 x²

b) Test statistic = 71.12

c) Predicted value = 1275.06