Question

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)
1,254	35
1,331	40
1,224	30
1,335	45
1,348	50
1,123	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 =

(b) Use α = 0.01 to test for a significant relationship.

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

Test statistic=?

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

p-value = ?

(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

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.989108
R Square	0.978335
Adjusted R Square	0.963891
Standard Error	16.56732
Observations	6
ANOVA
	df	SS	MS	F	Significance F
Regression	2	37183.4	18591.7	67.73521	0.003189
Residual	3	823.4286	274.4762
Total	5	38006.83
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	422.1429	147.7852	2.856463	0.064765	-48.1756	892.4613	-48.1756	892.4613
x	37.91429	8.172866	4.639044	0.018876	11.90458	63.92399	11.90458	63.92399
x²	-0.38857	0.108459	-3.58267	0.037216	-0.73374	-0.04341	-0.73374	-0.04341

a) Y^ = 422 + 37.91*x - 0.389*x²

b) test stat=67.74
p value=0.003

c)

Y^ = 422 + 37.91*38 - 0.389*38² = 1301.79