Question

A statistical program is recommended.

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)
1,256	35
1,328	40
1,228	30
1,337	45
1,349	50
1,122	25

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 hou

question 2-

A statistical program is recommended.

Car manufacturers produced a variety of classic cars that continue to increase in value. Suppose the following data is based upon the Martin Rating System for Collectible Cars, and shows the rarity rating (1–20) and the high price ($1,000) for 15 classic cars.

Model	Rating	Price ($1,000)
A	16	225.0
B	16	375.0
C	19	1,325.0
D	18	1,625.0
E	19	4,025.0
F	17	400.0
G	15	102.5
H	14	87.0
I	17	450.0
J	17	140.0
K	19	2,675.0
L	18	1,000.0
M	18	350.0
N	16	100.0
O	13	95.0

Develop an estimated multiple regression equation with x = rarity rating and

x²

as the two independent variables. (Round b₀ and b₁ to the nearest integer and b₂ to one decimal place.)

ŷ =

Consider the nonlinear relationship shown by equation (16.7):

E(y) = β₀β₁^x

Use logarithms to develop an estimated regression equation for this model. (Round b₀ to three decimal places and b₁ to four decimal places.)

log(ŷ) =

Answer 1

1)

Excel > Data > Data Analysis > Regression

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.989505956
R Square	0.979122037
Adjusted R Square	0.965203395
Standard Error	16.25305832
Observations	6
ANOVA
	df	SS	MS	F	Significance F
Regression	2	37165.51429	18582.75714	70.34609006	0.0030167
Residual	3	792.4857143	264.1619048
Total	5	37958
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	421.2857143	144.9818614	2.905782214	0.062209261	-40.11127487	882.6827034	-40.11127487	882.6827034
Vehicle Speed(x)	38.01571429	8.017835518	4.741393634	0.017792499	12.49938326	63.53204531	12.49938326	63.53204531
X^2	-0.39	0.106401243	-3.665370717	0.035113239	-0.728616242	-0.051383758	-0.728616242	-0.051383758

Regression equation:

Y = 421+38.02*X-0.390*X^2

Fstat = 70.35

P value = 0.003

If X = 38 miles per hour

Y = 421+38.02*X-0.390*X^2

Y = 421+38.02*38-0.390*38^2 = 1302.60 vehicles per hour

2)

a) Quadratic regression:

Y = 34745-4683*X+157.0*X^2

Exponential regression:

Price ($1,000)(Y)	Ln(y)	Rating(X)
225	5.4161	16
375	5.926926	16
1325	7.189168	19
1625	7.393263	18
4025	8.30028	19
400	5.991465	17
102.5	4.629863	15
87	4.465908	14
450	6.109248	17
140	4.941642	17
2675	7.891705	19
1000	6.907755	18
350	5.857933	18
100	4.60517	16
95	4.553877	13

Log(Y) = -4.175+0.6064*X

Y = e^(-4.175+0.6064*X)

Y = 0.0154*1.8338^X