The American Association of Individual Investors (AAII) On-Line Discount Broker Survey polls members on their experiences with discount brokers. As part of the survey, members were asked to rate the quality of the speed of execution with their broker as well as provide an overall satisfaction rating for electronic trades. Possible responses (scores) were no opinion (0), unsatisfied (1), somewhat satisfied (2), satisfied (3), and very satisfied (4). For each broker summary scores were computed by calculating a weighted average of the scores provided by each respondent. A portion of the survey results follow (AAII website, February 7, 2012). Satisfaction a. Select a scatter diagram for these data with the speed of execution as the independent variable. A. B. 4.5 3.5- 3- 2.5 2.5 3 4 3.5 Speed of Execution 4.5 Satisfaction 4.5- 3.5- 3- Brokerage Scottrade, Inc. Charles Schwab Fidelity Brokerage Services TD Ameritrade 2.5 E*Trade Financial Vanguard Brokerage Services USAA Brokerage Services Thinkorswim Wells Fargo Investments Interactive Brokers Zecco.com 2.5 3 3.5 4 Speed of Execution Speed 2.4 2.8 3.9 3.3 4.0 2.5 3.3 3.8 3.8 2.6 4.0 4.5 Satisfaction 2.4 3.3 3.9 3.0 3.7 2.4 2.9 3.9 3.3 2.2 3.8

MATLAB: An Introduction with Applications
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Chapter1: Starting With Matlab
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### Graphs and Analysis

#### Graphs C and D:
These scatter plots illustrate the relationship between two variables: the speed of execution rating (x-axis) and the overall satisfaction rating for electronic trades (y-axis).

- **Graph C** shows a distribution of points with varying satisfaction levels for different execution speeds.
- **Graph D** appears to have a different distribution pattern, possibly indicating a stronger relationship between speed of execution and satisfaction.

### Questions and Instructions

**b. Analysis of Scatter Diagrams:**
- What does the scatter diagram developed in part (a) indicate about the relationship between the two variables?
- The scatter diagram indicates a [dropdown menu] linear relationship between \( x = \) speed of execution rating and \( y = \) overall satisfaction rating for electronic trades.

**c. Regression Equation:**
- Develop the least squares estimated regression equation. Enter negative values as negative numbers.
  
  **Satisfaction =** \[ \text{____} \] + \[ \text{____} \] \(\times\) Speed (to 4 decimals)

**d. Interpretation of Slope:**
- Provide an interpretation for the slope of the estimated regression equation.
- The slope of the estimated regression line is approximately \[ \text{____} \] (to 4 decimals). So, a one-unit [dropdown menu] in the speed of execution rating will increase the overall satisfaction rating by approximately [dropdown menu] points (to 1 decimal).

**e. Prediction:**
- Suppose Scottrade, Inc. developed new software to increase their speed of execution rating. If the new software is able to increase their speed of execution rating from the current value of 2.4 to the average speed of execution rating for the other 10 brokerage firms that were surveyed, what value would you predict for the overall satisfaction rating?
  
  **Prediction:** \[ \text{____} \] (to 3 decimals) 

These activities are intended to help understand the statistical relationships and the interpretation of regression analysis in practical scenarios.
Transcribed Image Text:### Graphs and Analysis #### Graphs C and D: These scatter plots illustrate the relationship between two variables: the speed of execution rating (x-axis) and the overall satisfaction rating for electronic trades (y-axis). - **Graph C** shows a distribution of points with varying satisfaction levels for different execution speeds. - **Graph D** appears to have a different distribution pattern, possibly indicating a stronger relationship between speed of execution and satisfaction. ### Questions and Instructions **b. Analysis of Scatter Diagrams:** - What does the scatter diagram developed in part (a) indicate about the relationship between the two variables? - The scatter diagram indicates a [dropdown menu] linear relationship between \( x = \) speed of execution rating and \( y = \) overall satisfaction rating for electronic trades. **c. Regression Equation:** - Develop the least squares estimated regression equation. Enter negative values as negative numbers. **Satisfaction =** \[ \text{____} \] + \[ \text{____} \] \(\times\) Speed (to 4 decimals) **d. Interpretation of Slope:** - Provide an interpretation for the slope of the estimated regression equation. - The slope of the estimated regression line is approximately \[ \text{____} \] (to 4 decimals). So, a one-unit [dropdown menu] in the speed of execution rating will increase the overall satisfaction rating by approximately [dropdown menu] points (to 1 decimal). **e. Prediction:** - Suppose Scottrade, Inc. developed new software to increase their speed of execution rating. If the new software is able to increase their speed of execution rating from the current value of 2.4 to the average speed of execution rating for the other 10 brokerage firms that were surveyed, what value would you predict for the overall satisfaction rating? **Prediction:** \[ \text{____} \] (to 3 decimals) These activities are intended to help understand the statistical relationships and the interpretation of regression analysis in practical scenarios.
### On-Line Discount Broker Survey Results

The American Association of Individual Investors (AAII) conducts an On-Line Discount Broker Survey to collect members' experiences with discount brokers. Participants rated the quality of the speed of execution and overall satisfaction for electronic trades. Ratings were given on a scale from 1 (unsatisfied) to 4 (very satisfied), with an average summary score calculated for each broker.

#### Survey Data:

| Brokerage                        | Speed | Satisfaction |
|----------------------------------|-------|--------------|
| Scottrade, Inc.                  | 2.4   | 2.4          |
| Charles Schwab                   | 2.8   | 3.3          |
| Fidelity Brokerage Services      | 3.9   | 3.9          |
| TD Ameritrade                    | 3.3   | 3.0          |
| E*Trade Financial                | 4.0   | 3.7          |
| Vanguard Brokerage Services      | 2.5   | 2.4          |
| USAA Brokerage Services          | 2.9   | 2.9          |
| Thinkorswim                      | 3.8   | 3.9          |
| Wells Fargo Investments          | 3.8   | 3.3          |
| Interactive Brokers              | 2.6   | 2.2          |
| Zecco.com                        | 4.0   | 3.8          |

### Scatter Diagram Selection

#### Explanation:

Two scatter diagrams (A and B) are provided for visual comparison of "Speed of Execution" vs. "Satisfaction" ratings for the brokers, with "Speed of Execution" as the independent variable (x-axis).

- **Scatter Diagram A:** Displays various data points where x-axis represents speed (ranging from 2.0 to 4.5) and y-axis represents satisfaction (ranging from 2.0 to 4.5). The points are scattered with no apparent trend line.

- **Scatter Diagram B:** Similar layout with the x-axis for speed and y-axis for satisfaction. Shows more structured dispersion with potential indication of relationship between higher speed ratings and higher satisfaction ratings.

Choosing the appropriate scatter diagram involves determining which best represents the data correlation based on the axes alignment and point dispersion.
Transcribed Image Text:### On-Line Discount Broker Survey Results The American Association of Individual Investors (AAII) conducts an On-Line Discount Broker Survey to collect members' experiences with discount brokers. Participants rated the quality of the speed of execution and overall satisfaction for electronic trades. Ratings were given on a scale from 1 (unsatisfied) to 4 (very satisfied), with an average summary score calculated for each broker. #### Survey Data: | Brokerage | Speed | Satisfaction | |----------------------------------|-------|--------------| | Scottrade, Inc. | 2.4 | 2.4 | | Charles Schwab | 2.8 | 3.3 | | Fidelity Brokerage Services | 3.9 | 3.9 | | TD Ameritrade | 3.3 | 3.0 | | E*Trade Financial | 4.0 | 3.7 | | Vanguard Brokerage Services | 2.5 | 2.4 | | USAA Brokerage Services | 2.9 | 2.9 | | Thinkorswim | 3.8 | 3.9 | | Wells Fargo Investments | 3.8 | 3.3 | | Interactive Brokers | 2.6 | 2.2 | | Zecco.com | 4.0 | 3.8 | ### Scatter Diagram Selection #### Explanation: Two scatter diagrams (A and B) are provided for visual comparison of "Speed of Execution" vs. "Satisfaction" ratings for the brokers, with "Speed of Execution" as the independent variable (x-axis). - **Scatter Diagram A:** Displays various data points where x-axis represents speed (ranging from 2.0 to 4.5) and y-axis represents satisfaction (ranging from 2.0 to 4.5). The points are scattered with no apparent trend line. - **Scatter Diagram B:** Similar layout with the x-axis for speed and y-axis for satisfaction. Shows more structured dispersion with potential indication of relationship between higher speed ratings and higher satisfaction ratings. Choosing the appropriate scatter diagram involves determining which best represents the data correlation based on the axes alignment and point dispersion.
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