Some association 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 (l), 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 is contained in the Excel Online file below. ### Understanding Scatter Diagrams and Regression Analysis#### Scatter Diagram Analysis**Scatter Diagram Description:**The scatter diagram provided in this example plots the relationship between two variables: the speed of execution rating (on the x-axis) and the overall satisfaction rating for electronic trades (on the y-axis).**Analysis (Part b):**The scatter diagram developed in part (a) indicates that there is a **positive linear relationship** between the two variables. That is, as the speed of execution rating increases, the overall satisfaction rating for electronic trades also tends to increase.#### Linear Regression Development**Equation Development (Part c):**To quantify this relationship, we can develop a least squares estimated regression equation. The general form of this equation is:\[ \text{Satisfaction} = \text{intercept} + \text{slope} \times \text{Speed} \]where "intercept" and "slope" are constants that you need to calculate from the data.#### Interpretation of Slope**Slope Interpretation (Part d):**The slope in the regression equation represents the change in the satisfaction rating for each one-unit increase in the speed of execution rating. This value is approximately **(fill in the blank)**. Therefore, an increase in the speed of execution rating by one unit will increase the overall satisfaction rating by approximately **(fill in the blank)** points.#### Practical Application**Prediction Example (Part e):**Suppose Wells Fargo Investments 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 2.3 to the average speed of execution rating of 4.0 for the other 10 brokerage firms that were surveyed, you would use the regression equation to predict the resulting overall satisfaction rating. Fill in the regression equation and calculate the predicted satisfaction rating to three decimal places.#### SummaryUnderstanding the relationship between variables through scatter diagrams and regression analysis can provide valuable insights. The positive linear relationship observed here suggests that improvements in speed of execution can lead to greater customer satisfaction in electronic trades.For practice, students can now use the given data points to calculate the regression equation and interpret the slope. Following this, students can make predictions about satisfaction ratings based on different speed of execution ratings.#### Graphical Explanation**Graph/Diagram Details:**The scatter diagram features several data points that show the relationship between speed of execution on the x-axis (ranging from ### Brokerage Speed and Satisfaction Analysis#### Data SummaryThe table below summarizes the speed and satisfaction ratings for various brokerages:| Brokerage | Speed | Satisfaction ||---------------------|-------|--------------|| Inc. | 3.4 | 3.5 || Schwab | 3.5 | 3.2 || Brokerage Services | 3.9 | 3.2 || Trade Financial | 3.6 | 3.7 || Zynga | 2.9 | 3.1 || JP Brokerage Services | 2.7 | 3.6 || EXG Brokerage Services | 3.6 | 3.6 || VI Investments | 2.6 | 2.8 || Sogo Investments | 2.3 | 2.7 || Top Brokers | 3.8 | 4.1 || M Brokerage | 2.5 | 2.4 |#### Scatter DiagramA scatter diagram should be drawn in the area specified in the chart. This scatter plot will help visualize the relationship between the speed of execution and overall satisfaction for each brokerage. Each data point on the graph will represent one brokerage.#### Regression Analysis (Part c)- **Slope**: The slope of the regression line that quantifies the average change in satisfaction for a unit change in execution speed.- **Intercept**: The intercept of the regression line that represents the expected satisfaction rating when the speed of execution is zero.#### Estimated Values (Part e)- **Speed of Brokerage Discussed**: 2.3- **Average Speed of Execution**: N/A (to be calculated)- **Estimation of the Overall Satisfaction Rating**: N/A (to be calculated by regression formula)---This data visualization and analysis can provide insights into how the speed of broker services influences customer satisfaction. Students and researchers can create regression models, analyze correlations, and evaluate the efficiency of brokerage services based on the provided dataset.

The scatter plot is used to visualize the numerical data. It examines the degree of relationship…

Answered: Some association On-Line Discount…

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter1: Equations And Graphs

Section1.FOM: Focus On Modeling: Fitting Lines To Data

Problem 8P