Questions: The American Association of Individual Investors (AAII) Online 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 (0), 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). Develop a scatter diagram for these data with the speed of execution as the independent variable.

a) Develop a scatter diagram for these data with the speed of execution as the independent variable. Create a scatter plot The scatter plot is already provided in the image. The x-axis represents the speed of execution rating and the y-axis represents the overall satisfaction rating. Each point on the graph represents a brokerage firm. The scatter diagram is as shown in the provided image.

b) Develop a scatter diagram for these data with the speed of execution as the independent variable. Create a scatter plot This is a duplicate of part a). The scatter plot is already provided in the image. The x-axis represents the speed of execution rating and the y-axis represents the overall satisfaction rating. Each point on the graph represents a brokerage firm. The scatter diagram is as shown in the provided image.

c) Develop the least squares estimated regression equation. Calculate the mean of x and y $\bar{x} = \frac{3.4 + 3.3 + 3.4 + 3.6 + 3.2 + 3.8 + 3.8 + 2.6 + 2.7 + 4 + 2.5}{10} = 3.23$ $\bar{y} = \frac{3.5 + 3.4 + 3.9 + 3.7 + 2.9 + 2.8 + 3.6 + 2.6 + 2.3 + 4 + 2.5}{10} = 3.12$

Calculate the slope (b1) $b_1 = \frac{\sum(x_i - \bar{x})(y_i - \bar{y})}{\sum(x_i - \bar{x})^2} = \frac{2.081}{2.201} \approx 0.9455$ Calculate the y-intercept (b0) $b_0 = \bar{y} - b_1\bar{x} = 3.12 - (0.9455)(3.23) \approx 0.072$

Write the equation $\hat{y} = b_0 + b_1x = 0.072 + 0.9455x$ $\boxed{\hat{y} = 0.072 + 0.9455x}$

d) Provide an interpretation for the slope of the estimated regression equation. Interpret the slope The slope of the estimated regression line is approximately 0.9455. This means that for every one-unit increase in the speed of execution rating, the overall satisfaction rating is predicted to increase by approximately 0.9455 points. For each one-unit increase in the speed of execution rating, the overall satisfaction rating is predicted to increase by approximately 0.95 points.

e) Suppose Zecco.com 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 2.5 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? Calculate the average speed of execution rating $\bar{x} = 3.23$ (calculated in part c) Calculate the predicted satisfaction rating $\hat{y} = 0.072 + 0.9455(3.23) \approx 3.12$ $\boxed{3.12}$

The scatter diagram is as shown in the provided image. The scatter diagram is as shown in the provided image. $\hat{y} = 0.072 + 0.9455x$ For each one-unit increase in the speed of execution rating, the overall satisfaction rating is predicted to increase by approximately 0.95 points. 3.12