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

Free

50.1K

Verified Solution

Question

Statistics

A highway department is studying the relationship betweentraffic flow and speed. The following model has beenhypothesized:
y = Î²₀ +Î²₁x + Îµ
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)
1,257 35
1,327 40
1,226 30
1,333 45
1,350 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 the nearest integer andb₁ to two decimal places andb₂ to three decimal places.)Å· =
Find the value of the test statistic. (Round your answer to twodecimal places.)
Find the p-value. (Round your answer to three decimalplaces.)
p-value =
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

Traffic Flow (y)	Vehicle Speed (x)
1,257	35
1,327	40
1,226	30
1,333	45
1,350	50
1,122	25

Answer & Explanation Solved by verified expert

4.0 Ratings (722 Votes)

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
XÂ²	-0.38214	0.102137	-3.74148	0.033311	-0.70719	-0.0571	-0.70719	-0.0571

Y^ = 432 + 37.41*X - 0.382*XÂ²

test stat=75.78

P value=0.003

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

Y^ = 432 + 37.41*X - 0.382*XÂ²

X=38

Y^ = 432 + 37.41*38 - 0.382*38Â² = 1301.31(answer)

Get Answers to Unlimited Questions

Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!

Membership Benefits:

Unlimited Question Access with detailed Answers
Zin AI - 3 Million Words
10 Dall-E 3 Images
20 Plot Generations
Conversation with Dialogue Memory
No Ads, Ever!
Access to Our Best AI Platform: Flex AI - Your personal assistant for all your inquiries!

Become a Member