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)
1,257	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 =

(b)

Use α = 0.01 to test for a significant relationship.

State the null and alternative hypotheses.

H₀: b₀ = b₁ = b₂ = 0
H_a: One or more of the parameters is not equal to zero.H₀: b₁ = b₂ = 0
H_a: One or more of the parameters is not equal to zero.    H₀: One or more of the parameters is not equal to zero.
H_a: b₀ = b₁ = b₂ = 0H₀: One or more of the parameters is not equal to zero.
H_a: b₁ = b₂ = 0

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 =

What is your conclusion?

Reject H₀. We conclude that the relationship is significant.Reject H₀. We cannot conclude that the relationship is significant.    Do not reject H₀. We cannot conclude that the relationship is significant.Do not reject H₀. We conclude that the relationship is significant.

(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

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
X²	-0.38214	0.102137	-3.74148	0.033311	-0.70719	-0.0571	-0.70719	-0.0571

a)

ŷ = 432 + 37.41x -0.382x².

b)

H₀: b₁ = b₂ = 0
H_a: One or more of the parameters is not equal to zero.

test stat=75.78

p value=0.003

p value >α=0.01, do not reject Ho

Do not reject H₀. We cannot conclude that the relationship is significant

c)

ŷ = 432 + 37.41x -0.382x².

x=38

ŷ = 432 + 37.41*38 -0.382*38²= 1301.31(answer)
.