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{Exercise 16.5} a. Use the data to compute the b1 coefficient of this estimated

ID: 3172244 • Letter: #

Question

{Exercise 16.5}

a. Use the data to compute the b1 coefficient of this estimated regression equation (to 4 decimals).

b1 =  

(Create the xSquare variable first using Data/Transform Data/Square.)

b. Using = .01, test for a significant relationship.

F =   (to 2 decimals)
p-value =  

The relationship - Select your answer -isis notItem 4  significant.

c. Estimate the traffic flow in vehicles per hour at a speed of 38 miles per hour (to 2 decimals).

95% Prediction interval =   (n1,n2)

Traffic Flow 1256 1329 1226 1335 1349 1124 Vehicle Speed (x) 30 45 25

Explanation / Answer

Result:

Using the data above, statisticians suggested the use of the following curvilinear estimated regression equation.

a. Use the data to compute the b1 coefficient of this estimated regression equation (to 4 decimals).

b0 = 432.5714

b1 = 37.4286

b2 = -0.3829

(Create the xSquare variable first using Data/Transform Data/Square.)

b. Using = .01, test for a significant relationship.

F =  73.15 (to 2 decimals)
p-value =  0.0028

The relationship - Select your answer   is   significant.

c. Estimate the traffic flow in vehicles per hour at a speed of 38 miles per hour (to 2 decimals).

95% Prediction interval =   (1242.55, 1361.47)

Regression Analysis

0.980

Adjusted R²

0.967

n

6

R

0.990

k

2

Std. Error

15.826

Dep. Var.

y

ANOVA table

Source

SS

df

MS

F

p-value

Regression

36,643.4048

2  

18,321.7024

73.15

.0028

Residual

751.4286

3  

250.4762

Total

37,394.8333

5  

Regression output

confidence interval

variables

coefficients

std. error

   t (df=3)

p-value

95% lower

95% upper

Intercept

432.5714

141.1763

3.064

.0548

-16.7146

881.8574

x

37.4286

7.8074

4.794

.0173

12.5820

62.2751

x*x

-0.3829

0.1036

-3.695

.0344

-0.7126

-0.0531

Predicted values for: y

95% Confidence Interval

95% Prediction Interval

x

x*x

Predicted

lower

upper

lower

upper

Leverage

38

1,444

1,302.011

1,270.415

1,333.608

1,242.554

1,361.469

0.394

Regression Analysis

0.980

Adjusted R²

0.967

n

6

R

0.990

k

2

Std. Error

15.826

Dep. Var.

y

ANOVA table

Source

SS

df

MS

F

p-value

Regression

36,643.4048

2  

18,321.7024

73.15

.0028

Residual

751.4286

3  

250.4762

Total

37,394.8333

5  

Regression output

confidence interval

variables

coefficients

std. error

   t (df=3)

p-value

95% lower

95% upper

Intercept

432.5714

141.1763

3.064

.0548

-16.7146

881.8574

x

37.4286

7.8074

4.794

.0173

12.5820

62.2751

x*x

-0.3829

0.1036

-3.695

.0344

-0.7126

-0.0531

Predicted values for: y

95% Confidence Interval

95% Prediction Interval

x

x*x

Predicted

lower

upper

lower

upper

Leverage

38

1,444

1,302.011

1,270.415

1,333.608

1,242.554

1,361.469

0.394