oooooooo O A highway department is studying the relationship between traffic flow and speed. The following model has been hypothesized. ŷbo+b₁x + b₂x² O O O O where The following data were collected during rush hour for six highways leading out of the city. bo= b₁ = b₂ = X b. Using a = 0.01, test for a significant relationship. F= (to 4 decimals) y = traffic flow in vehicles per hour x= vehicle speed in miles per hour Traffic Flow (3) 1257 1330 1226 1335 1350 1125 a. Use the data to compute the coefficients of this estimated regression equation (to 4 decimals). Enter negative value as negative number. (Create the ² variable first using Data/Transform Data/Square.) p-value = (to 4 decimals) Vehicle Speed (2) 36 M The relationship is significant. c. Estimate the traffic flow in vehicles per hour at a speed of 38 miles per hour (to 2 decimals). vehicles per hour 40 35 45 55 30

MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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## Chapter 16 Assignment

**3.** A highway department is studying the relationship between traffic flow and speed. The following model has been hypothesized:
\[ \hat{y} = b_0 + b_1 x + b_2 x^2 \]
where:
- \( y \) = traffic flow in vehicles per hour
- \( x \) = vehicle speed in miles per hour

**7.** The following data were collected during rush hour for six highways leading out of the city:

|  | **Traffic Flow (y)** | **Vehicle Speed (x)** |
|---|---|---|
|  | vehicles per hour | miles per hour |
| 1 | 1257 | 36 |
| 2 | 1330 | 40 |
| 3 | 1226 | 35 |
| 4 | 1335 | 45 |
| 5 | 1350 | 55 |
| 6 | 1125 | 30 |

**14.**
**a.** Use the data to compute the coefficients of this estimated regression equation (to 4 decimals). Enter negative value as negative number. (Create the \( x^2 \) variable first using Data/Transform Data/Square.)

\[
\begin{aligned}
b_0 & = \_\_\_\_ \\
b_1 & = \_\_\_\_ \\
b_2 & = \_\_\_\_ \\
\end{aligned}
\]

**b.** Using \( \alpha = 0.01 \), test for a significant relationship.

\[
\begin{aligned}
F & = \_\_\_\_ \text{ (to 4 decimals)} \\
p\text{-value} & = \_\_\_\_ \text{ (to 4 decimals)} \\
\end{aligned}
\]

The relationship \_\_\_\_\_\_ significant.

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

\[
\text{vehicles per hour } = \_\_\_\_
\]
Transcribed Image Text:## Chapter 16 Assignment **3.** A highway department is studying the relationship between traffic flow and speed. The following model has been hypothesized: \[ \hat{y} = b_0 + b_1 x + b_2 x^2 \] where: - \( y \) = traffic flow in vehicles per hour - \( x \) = vehicle speed in miles per hour **7.** The following data were collected during rush hour for six highways leading out of the city: | | **Traffic Flow (y)** | **Vehicle Speed (x)** | |---|---|---| | | vehicles per hour | miles per hour | | 1 | 1257 | 36 | | 2 | 1330 | 40 | | 3 | 1226 | 35 | | 4 | 1335 | 45 | | 5 | 1350 | 55 | | 6 | 1125 | 30 | **14.** **a.** Use the data to compute the coefficients of this estimated regression equation (to 4 decimals). Enter negative value as negative number. (Create the \( x^2 \) variable first using Data/Transform Data/Square.) \[ \begin{aligned} b_0 & = \_\_\_\_ \\ b_1 & = \_\_\_\_ \\ b_2 & = \_\_\_\_ \\ \end{aligned} \] **b.** Using \( \alpha = 0.01 \), test for a significant relationship. \[ \begin{aligned} F & = \_\_\_\_ \text{ (to 4 decimals)} \\ p\text{-value} & = \_\_\_\_ \text{ (to 4 decimals)} \\ \end{aligned} \] The relationship \_\_\_\_\_\_ significant. **c.** Estimate the traffic flow in vehicles per hour at a speed of 38 miles per hour (to 2 decimals). \[ \text{vehicles per hour } = \_\_\_\_ \]
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