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.)
