Question

Consider the following data for two variables, x and y.

x	9	32	18	15	26
y	10	19	21	17	23

(a)Develop an estimated regression equation for the data of the form ŷ = b₀ + b₁x. (Round b₀ to two decimal places and b₁ to three decimal places.)

ŷ =____

(b)Develop an estimated regression equation for the data of the form ŷ = b₀ + b₁x + b₂x². (Round b₀ to two decimal places and b₁ to three decimal places and b₂ to four decimal places.)

ŷ =____

(c)Use the model from part (b) to predict the value of y when x = 20. (Round your answer to two decimal places.)____

**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)
1,258	35
1,330	40
1,226	30
1,336	45
1,349	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 =_____

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 = ______

(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

usig minitab>stat>Regression

we have

Regression Analysis: y versus x

The regression equation is
y = 10.18 + 0.3909 x

S = 4.06500 R-Sq = 50.4% R-Sq(adj) = 33.9%

Analysis of Variance

Source DF SS MS F P
Regression 1 50.427 50.4273 3.05 0.179
Error 3 49.573 16.5242
Total 4 100.000

Fitted Line: y versus x

Polynomial Regression Analysis: y versus x

The regression equation is
y = - 10.49 + 2.751 x - 0.05693 x^2

S = 0.861884 R-Sq = 98.5% R-Sq(adj) = 97.0%

Analysis of Variance

Source DF SS MS F P
Regression 2 98.514 49.2572 66.31 0.015
Error 2 1.486 0.7428
Total 4 100.000

a) estimated regression equation for the data of the form ŷ = b0 + b1x is

ŷ =10.18 + 0.3909 x

(b)an estimated regression equation for the data of the form ŷ = b0 + b1x + b2x2

ŷ =- 10.49 + 2.751 x - 0.05693 x^2

(c) the value of y when x = 20

ŷ =-10.49 + 2.751*20 - 0.05693*20*20 = 20.81

Ans 2 ) using minitab>stat>Regression

'we have

Polynomial Regression Analysis: y versus x

The regression equation is
y = 414.4 + 38.43 x - 0.3957 x^2

S = 15.3042 R-Sq = 98.1% R-Sq(adj) = 96.9%

Analysis of Variance

Source DF SS MS F P
Regression 2 37182.7 18591.3 79.38 0.003
Error 3 702.7 234.2
Total 5 37885.3

(a)ŷ =414.4 + 38.43 x - 0.3957 x^2

the value of the test statistic is 79.38

p-value =0.003

(c)the model predict the traffic flow in vehicles per hour at a speed of 38 miles per hour is

ŷ =414.4 + 38.43*38 - 0.3957*38*38

1303.35vehicles per hour