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satisfaction with BRT (y), safety on bus (x₁), seat ability (₂), dependability (x3), travel time (x4), cost (xs), information/maps (x6), convenience of routes (x), traffic signals (x8), safety at bus stops (x9), hours of service (10), and frequency of service (x1). CUTR analysts used stepwise regression to model overall satisfaction (y). a. How many models are fit at step 1 of the regression? stepwise b. How many models are fit at step 2 of the stepwise regression? c. How many models are fit at step 11 of the stepwise regression? d. The stepwise regression selected the following eight variables to include in the model (in order of selec- tion): X11, X4, X2, X7, X10, X₁, X, and x3. Write the equa- tion for E(y) that results from stepwise regression. e. The model, part d, resulted in R2 = .677. Interpret this value. f. Explain why the CUTR analysts should be cautious in concluding that the best model for E(y) has been found.

satisfaction with BRT (y), safety on bus (x₁), seat ability (₂), dependability (x3), travel time (x4), cost (xs), information/maps (x6), convenience of routes (x), traffic signals (x8), safety at bus stops (x9), hours of service (10), and frequency of service (x1). CUTR analysts used stepwise regression to model overall satisfaction (y). a. How many models are fit at step 1 of the regression? stepwise b. How many models are fit at step 2 of the stepwise regression? c. How many models are fit at step 11 of the stepwise regression? d. The stepwise regression selected the following eight variables to include in the model (in order of selec- tion): X11, X4, X2, X7, X10, X₁, X, and x3. Write the equa- tion for E(y) that results from stepwise regression. e. The model, part d, resulted in R2 = .677. Interpret this value. f. Explain why the CUTR analysts should be cautious in concluding that the best model for E(y) has been found.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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12.117 explain the answers to the steps for a,b,c,d

**Satisfaction with BRT Analysis** ### Overview The analysis involves examining overall satisfaction with Bus Rapid Transit (BRT) using several variables: - **x₁**: Safety on bus - **x₂**: Seat availability - **x₃**: Dependability - **x₄**: Travel time - **x₅**: Cost - **x₆**: Information/maps - **x₇**: Convenience of routes - **x₈**: Traffic signals - **x₉**: Safety at bus stops - **x₁₀**: Hours of service - **x₁₁**: Frequency of service **CUTR analysts** used **stepwise regression** to model overall satisfaction (y). ### Stepwise Regression Analysis **a. Number of Models at Step 1** - One model is fit at step 1 of the stepwise regression. **b. Number of Models at Step 2** - Another model is fit at step 2 of the stepwise regression. **c. Number of Models at Step 11** - A total of 11 models are fit by step 11 of the stepwise regression. **d. Selected Variables for Final Model** - The stepwise regression selected eight variables: x₁₁, x₄, x₂, x₇, x₁₀, x₁₅, and x₃. - These variables were included in the model to predict E(y). **e. Interpretation of R² = 0.677** - The R² value of 0.677 indicates that 67.7% of the variability in overall satisfaction is explained by the model. **f. Caution in Model Conclusion** - Caution is advised when concluding that the best model for E(y) has been found. This could be due to overfitting, missing variables, or data limitations that affect model reliability.
Transcribed Image Text:**Satisfaction with BRT Analysis** ### Overview The analysis involves examining overall satisfaction with Bus Rapid Transit (BRT) using several variables: - **x₁**: Safety on bus - **x₂**: Seat availability - **x₃**: Dependability - **x₄**: Travel time - **x₅**: Cost - **x₆**: Information/maps - **x₇**: Convenience of routes - **x₈**: Traffic signals - **x₉**: Safety at bus stops - **x₁₀**: Hours of service - **x₁₁**: Frequency of service **CUTR analysts** used **stepwise regression** to model overall satisfaction (y). ### Stepwise Regression Analysis **a. Number of Models at Step 1** - One model is fit at step 1 of the stepwise regression. **b. Number of Models at Step 2** - Another model is fit at step 2 of the stepwise regression. **c. Number of Models at Step 11** - A total of 11 models are fit by step 11 of the stepwise regression. **d. Selected Variables for Final Model** - The stepwise regression selected eight variables: x₁₁, x₄, x₂, x₇, x₁₀, x₁₅, and x₃. - These variables were included in the model to predict E(y). **e. Interpretation of R² = 0.677** - The R² value of 0.677 indicates that 67.7% of the variability in overall satisfaction is explained by the model. **f. Caution in Model Conclusion** - Caution is advised when concluding that the best model for E(y) has been found. This could be due to overfitting, missing variables, or data limitations that affect model reliability.
**Bus Rapid Transit Study** Bus Rapid Transit (BRT) is a rapidly growing trend in the provision of public transportation in America. The Center for Urban Transportation Research (CUTR) at the University of South Florida conducted a survey of BRT customers in Miami (Transportation Research Board Annual Meeting, Jan. 2003). Data on the following variables (all measured on a 5-point scale, where 1 = very unsatisfied and 5 = very satisfied) were collected for a sample of over 500 bus riders.
Transcribed Image Text:**Bus Rapid Transit Study** Bus Rapid Transit (BRT) is a rapidly growing trend in the provision of public transportation in America. The Center for Urban Transportation Research (CUTR) at the University of South Florida conducted a survey of BRT customers in Miami (Transportation Research Board Annual Meeting, Jan. 2003). Data on the following variables (all measured on a 5-point scale, where 1 = very unsatisfied and 5 = very satisfied) were collected for a sample of over 500 bus riders.
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Step 1: Given Information

The CUTR analysts used stepwise regression to model satisfaction with the Bus Rapid Transit (BRT) system.

There are 11 independent variables are included in this regression model.

Let Xi be the ith independent variable  where i=1,2,3,...,11

Stepwise regression: is a method used to construct a regression model by iteratively selecting independent variables to be included in the final model. It involves adding or removing potential explanatory variables in succession and testing for their statistical significance after each iteration.


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