Question

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

where y=b0+b1x+b2x2

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 ()		Vehicle Speed ()
1257		36
1329		45
1226		35
1335		45
1349		55
1125		25

a. Use the data to compute the coefficients of this estimated regression equation (to 4 decimals). (Enter negative value as negative number).

b0=

b1=

b2=

  

  

(Create the x2 variable first using Data/Transform Data/Square.)

b. Using a=.01, test for a significant relationship.

f= (to 4 decimals)

p-value    (to 4 decimals)

The relationship - Select your answer -is notisItem 6  significant.

c. Estimate the traffic flow in vehicles per hour at a speed of 39 miles per hour (to 2 decimals).

99%The estimated value is    (to 2 decimals)

99% Confidence interval         (to 2 decimals)

Prediction interval         (to 2 decimals)

Answer 1

This is done in Minitab.

[IF YOU ARE REQUIRED TO SOLVE THIS BY ANY OTHER SOFTWARE OR BY HAND, LET ME KNOW IN THE COMMENTS SECTION. I SHALL SOLVE THE PROBLEM BY THAT METHOD]

Enter the data properly in the worksheet with indexes as y and x. Go to stat, click on regression, click on fitted line plot. Click on the checkbox of quadratic, enter the response as y, enter the predictor as x. Click on options, select the checkbox of display confidence interval and display prediction interval. Give the confidence level as 99.0;  Click on OK. Click on Storage, select the checkbox of co-efficients and click on OK; Click on OK. From the output thus obtained the following questions are answered.

a.

b0=597.658

b1=26.778

b2=-0.2366

b.

F value=92.17

p-value=0.002

The relationship is not significant.

c.

When x=39, the estimated value is

y=597.658+(26.778*39)-(0.2366*392)

y=597.658+1044.342+359.8686

y=2001.8686

y=2001.87

99% confidence interval for x is given by

(29.3,51.1)

99% confidence interval for y is given by

(1179.7,1360.7)

The prediction interval is given by

(1110.90,1411.09)

Hopefully this will help you. In case of any query, do comment. If you are satisfied with the answer, give it a like. Thanks.