A highway department is studying the relationship betweentraffic flow and speed. The following model has beenhypothesized:

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 sixhighways leading out of the city.

Traffic Flow (y)	Vehicle Speed (x)
1,256	35
1,329	40
1,226	30
1,333	45
1,347	50
1,122	25

In working further with this problem, statisticians suggestedthe use of the following curvilinear estimated regressionequation.

Å· = b₀ +b₁x +b₂x²

(a) Develop an estimated regression equation for the data of theform Å· = b₀ + b₁x +b₂x² (Round b₀ to thenearest integer and b₁ to two decimal placesand b₂ to three decimal places.)

Å· =

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

Base on the model predict the traffic flow in vehicles per hourat a speed of 38 miles per hour. (Round your answer to two decimalplaces.)

vehicles per hour

A study of emergency service facilities investigated therelationship between the number of facilities and the averagedistance traveled to provide the emergency service. The followingtable gives the data collected.

Number of Facilities	Average Distance (miles)
9	1.67
11	1.12
16	0.82
21	0.63
27	0.50
30	0.47

Develop an estimated regression equation for the datacorresponding to a second-order model with one predictor variable.(Round your numerical values to four decimal places.)