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).

Brokerage	Satisfaction with Trade Price	Satisfaction with Speed of Execution	Overall Satisfaction with Electronic Trades
Scottrade, Inc.	3.2	3.1	3.2
Charles Schwab	3.3	3.1	3.2
Fidelity Brokerage Services	3.1	3.3	4.0
TD Ameritrade	2.8	3.5	3.7
E*Trade Financial	2.9	3.2	3.0
(Not listed)	2.4	3.2	2.7
Vanguard Brokerage Services	2.7	3.8	2.7
USAA Brokerage Services	2.4	3.7	3.4
Thinkorswim	2.6	2.6	2.7
Wells Fargo Investments	2.3	2.7	2.3
Interactive Brokers	3.7	3.9	4.0
Zecco.com	2.5	2.5	2.5
Firstrade Securities	3.0	3.0	3.0
Banc of America Investment Services	1.0	4.0	2.0

(a)	Develop an estimated regression equation using trade price and speed of execution to predict overall satisfaction with the broker.
	Let x1 represent satisfaction with Trade Price.
	Let x2 represent satisfaction with speed of execution.
	If required, round your answers to four decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)
	=  +  x1 +  x2
	What is the coefficient of determination?
	If required, round your answers to four decimal places.
	Interpret the coefficient of determination.
	The input in the box below will not be graded, but may be reviewed and considered by your instructor.
(b)	Use the t test to determine the significance of each independent variable. What are your conclusions at the 0.05 level of significance?
	The input in the box below will not be graded, but may be reviewed and considered by your instructor.
(c)	Interpret the estimated regression parameters. Are the relationships indicated by these estimates what you would expect?
	The input in the box below will not be graded, but may be reviewed and considered by your instructor.
(d)	Finger Lakes Investments has developed a new electronic trading system and would like to predict overall customer satisfaction assuming they can provide satisfactory levels of service levels (3) for both trade price and speed of execution. Use the estimated regression equation developed in part (a) to predict overall satisfaction level for Lakes Investments if they can achieve these performance levels.
	If required, round your answer to one decimal places. Do not round intermediate calculations.
(e)	What concerns (if any) do you have with regard to the possible responses the respondents could select on the survey?
	The input in the box below will not be graded, but may be reviewed and considered by your instructor.

Answer 1

a)

The coefficient of determination = 0.7256

Interpretation: The approximately 72.56% variance of the dependent variable Y is explained by the regression model.

Explanation:

The regression equation is defined as,

where

X1 = Satisfaction with Trade Price

X2 = Satisfaction with Speed of Execution

Y = Overall Satisfaction with Electronic Trades

Now, the regression analysis is done in excel by following steps

Step 1: Write the data values in excel. The screenshot is shown below,

Step 2: DATA > Data Analysis > Regression > OK. The screenshot is shown below,

Step 3: Select Input Y Range: 'Y' column, Input X Range: 'X1 and X2' column then OK. The screenshot is shown below,

The result is obtained. The screenshot is shown below,

The regression equation is,

The coefficient of determination (R square value) = 0.7256

Interpretation: The R square value tells how well the regression model fits the data values. The R square value is 0.7256 which means approximately 72.56% variance of the dependent variable Y is explained by the regression model.

b)

From, the result summary,

	t Stat	P-value		Significance level
X1	5.0926	0.0003	<	0.05	Significant
X2	2.4290	0.0335	<	0.05	Significant

The P-value for each independent variable is less than 0.05 at a 5% significance level hence we can conclude that independent variables are significant in the model.

c)

	Coefficients	Interpretation
X1	0.7746	For one unit increase in the Satisfaction with Trade Price, the Overall Satisfaction with Electronic Trades increases by 0.7746
X2	0.4897	For one unit increase in the Satisfaction with Speed of Execution, the Overall Satisfaction with Electronic Trades increases by 0.4897

Yes, it is expected that the overall satisfaction with the broker increases with Satisfaction with Trade Price and Satisfaction with Electronic Trades

d)

The regression equation is,

Fro X1 = 3 and X2 = 3

e)

There may be response bias in the satisfaction score due to the untruthful or misleading response