Question

In: Statistics and Probability

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

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
1,327 40
1,226 30
1,333 45
1,350 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 =

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

Find the p-value. (Round your answer to three decimal places.)

p-value =

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

Solutions

Expert Solution

using excel data analysis tool for regression,steps are: write data>menu>data>data analysis>regression>enter required labels>ok> and following o/p is obtained

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.990248
R Square 0.980591
Adjusted R Square 0.967651
Standard Error 15.60166
Observations 6
ANOVA
df SS MS F Significance F
Regression 2 36892.6 18446.3 75.78224 0.002704
Residual 3 730.2357 243.4119
Total 5 37622.83
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 431.5714 139.1712 3.10101 0.053254 -11.3336 874.4764 -11.3336 874.4764
(x) 37.40929 7.696494 4.860562 0.01663 12.91561 61.90297 12.91561 61.90297
-0.38214 0.102137 -3.74148 0.033311 -0.70719 -0.0571 -0.70719 -0.0571

Y^ = 432 + 37.41*X - 0.382*X²

test stat=75.78

P value=0.003

----------------

Y^ = 432 + 37.41*X - 0.382*X²

X=38

Y^ = 432 + 37.41*38 - 0.382*38² = 1301.31(answer)


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