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. 3.5 3.2 3.6 Charles Schwab 3.2 3.3 3.4 Fidelity Brokerage Services 3.1 3.4 3.9 TD Ameritrade 2.8 3.6 3.8 E*Trade Financial 2.9 3.2 2.9 (Not listed) 2.6 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 2.9 4.0 Banc of America Investment Services 4.0 1.0 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) ŷ =  +  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) Here is the summary output of multiple regression

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.807653
R Square	0.652304
Adjusted R Square	0.589087
Standard Error	0.437482
Observations	14
ANOVA
	df	SS	MS	F	Significance F
Regression	2	3.949701	1.97485	10.31842	0.002996
Residual	11	2.105299	0.191391
Total	13	6.055
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-0.82091	1.016283	-0.80775	0.436352	-3.05773	1.415918
Satisfaction with Trade Price	0.574341	0.248552	2.310748	0.041244	0.027282	1.121401
Satisfaction with Speed of Execution	0.739116	0.167645	4.408822	0.001048	0.370132	1.1081

y^ = -0.8209 + 0.5743 x₁ +0.7391 x₂

Coefficient of Determintation = R² = 0.6523

Here interpretation of Coefficient of Determination is " 65.23% of variation in Overall Satisfaction with Electronic Trades for any brokerage is explained by the variation in "Satisifaction with Trade Price" and "satisfaction in Speed of Execution".

(b) Here for variable"Satisifaction with Trade Price"

Test statistic

t = 2.3107

dF = 11 and t_critical = 2.20

so here t > t_critical so regression coefficient is significant here.

for variable "Satisfaction with Speed of Execution"

t = 4.41

t > t_critical so regression coeficient is significant here also.

(c) Here, yes as regression coefficient is around 0.5 to 0.7 range that is what we have predicted as both regresion coefficient is positive and have values between 0.5 and 1.

(d) Here estimated regression line is

y^ = -0.8209 + 0.5743 x₁ +0.7391 x₂

so here x₁ = 3 = x₂

y^ = -0.8209 + 0.5743 * 3  +0.7391 * 3 = 3.1195or 3.12

(e) Here if some possible responses that are vague is like : no opinion" Here no opinion is scored zero but it shall not be included in the sample size becuase it will drastically vary the results.