1. The American Association of Individual Investors (AAII) On-Line Discount Brok

ID: 3074953 • Letter: 1

Question

The American Association of Individual Investors (AAII) On-Line Discount Broker Survey polls members on their experiences with electronic trades handled by discount brokers. As part of the survey, members were asked to rate their satisfaction with the trade price and the speed of execution, as well as provide an overall satisfaction rating. 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 computing a weighted average of the scores provided by each respondent. A portion the survey results follow (AAII website, February 7, 2012).

A recent 10-year study conducted by a research team at the Great Falls Medical School was conducted to assess how age, systolic blood pressure, and smoking relate to the risk of strokes. Assume that the following data are from a portion of this study. Risk is interpreted as the probability (times 100) that the patient will have a stroke over the next 10-year period. For the smoking variable, define a dummy variable with 1 indicating a smoker and 0 indicating a nonsmoker.

Brokerage Satisfaction with
Trade Price Satisfaction with
Speed of Execution Overall Satisfaction with
Electronic Trades Scottrade, Inc. 3.3 3.1 3.4 Charles Schwab 3.2 3.3 3.3 Fidelity Brokerage Services 3.1 3.3 4.0 TD Ameritrade 2.9 3.5 3.7 E*Trade Financial 2.8 3.2 2.9 (Not listed) 2.4 3.2 2.7 Vanguard Brokerage Services 2.6 3.8 2.8 USAA Brokerage Services 2.4 3.8 3.6 Thinkorswim 2.6 2.6 2.6 Wells Fargo Investments 2.3 2.7 2.3 Interactive Brokers 3.7 4.0 4.0 Zecco.com 2.5 2.5 2.5 Firstrade Securities 3.0 3.0 3.0 Banc of America Investment Services 4.0 1.0 2.0

Explanation / Answer

Question 1

Solution:

Required regression model for the given scenario is given as below:

Regression Statistics

Multiple R

0.874619606

R Square

0.764959456

Adjusted R Square

0.722224812

Standard Error

0.329926119

Observations

ANOVA

Significance F

Regression

3.896922029

1.948461014

17.90021814

0.000347765

Residual

1.197363685

0.108851244

Total

5.094285714

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Intercept

-0.910453889

0.773290321

-1.177376549

0.263891974

-2.612454408

0.79154663

Satisfaction with trade price

0.569917585

0.188841927

3.017961081

0.011698256

0.154279307

0.985555863

Satisfaction with speed of execution

0.751016674

0.128693643

5.835693636

0.000113227

0.467763876

1.034269473

Part a

Develop an estimated regression equation using trade price and speed of execution to predict overall satisfaction with the broker.

Required regression equation is given as below:

Y = -0.9105 + 0.5699*X1 + 0.7510*X2

Overall satisfaction with electronic trades = -0.9105 + 0.5699*Satisfaction with trade price + 0.7510*Satisfaction with speed of execution

The coefficient of determination or the value of R square is given as 0.7650.

Interpretation of coefficient of determination: About 76.50% of the variation in the dependent variable overall satisfaction with electronic trades is explained by the independent variables satisfaction with trade price and satisfaction with speed of execution.

Part b

The p-value for the t-test for intercept of the regression equation is given as 0.2639 which is greater than alpha value 0.05, so we conclude that this intercept is not statistically significant.

The p-value for the t-test for the coefficient of satisfaction with trade price is given as 0.0117 which is less than alpha value 0.05, so we conclude that this coefficient is statistically significant.

The p-value for the t-test for a coefficient of a speed of execution is given as 0.0001 which is less than the alpha value 0.05, so we conclude that this coefficient is statistically significant.

Part c

The regression coefficient for the independent variable satisfaction with trade price is positive in nature which shows the positive relationship with dependent variable overall satisfaction. Also, the regression coefficient of the independent variable satisfaction with speed of execution is positive nature which shows the positive relationship with dependent variable overall satisfaction. Increase in these two independent variables will result in an increase in a dependent variable.

Part d

We have