Question

A 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 follow Brokerage Speed Satisfaction Scottrade, Inc. 3.1 2.6 Charles Schwab 2.9 3.3 Fidelity Brokerage Services 3.2 3.1 TD Ameritrade 2.6 2.7 E*Trade Financial 3.6 3.3 Vanguard Brokerage Services 3.4 3.6 USAA Brokerage Services 3.0 2.6 Thinkorswim 3.3 3.5 Wells Fargo Investments 3.5 3.4 Interactive Brokers 4.0 3.9 Zecco.com 2.8 2.6 a. Select a scatter diagram for these data with the speed of execution as the independent variable. A. B. C. D. - Select your answer -ABCDItem 1 b. What does the scatter diagram developed in part (a) indicate about the relationship between the two variables? The scatter diagram indicates __________ linear relationship between x speed of execution rating and y overall satisfaction rating for electronic trades. c. Develop the least squares estimated regression equation. Enter negative value as negative number. Satisfaction= __ + __ Speed (to 4 decimals) d. Provide an interpretation for the slope of the estimated regression equation (to 4 decimals). The slope of the estimated regression line is approximately _____ . So, a one unit _____ in the speed of execution rating will increase the overall satisfaction rating by approximately _____ points. e. Suppose TD Ameritrade 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 to the average speed of execution rating for the other brokerage firms that were surveyed, what value would you predict for the overall satisfaction rating? (to 3 decimals)

Answer 1

data

x	y
3.1	2.6
2.9	3.3
3.2	3.1
2.6	2.7
3.6	3.3
3.4	3.6
3	2.6
3.3	3.5
3.5	3.4
4	3.9
2.8	2.6

regression result

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.801972628
R Square	0.643160096
Adjusted R Square	0.603511218
Standard Error	0.289051898
Observations	11
ANOVA
	df	SS	MS	F	Significance F
Regression	1	1.35531373	1.35531373	16.22139452	0.002983822
Residual	9	0.751958998	0.083551
Total	10	2.107272727
	Coefficients	Standard Error	t Stat	P-value	Lower 95%
Intercept	0.180182232	0.741382209	0.243035549	0.813426419	-1.496940841
x	0.921412301	0.22877571	4.027579238	0.002983822	0.403885689

a)

b)

The scatter diagram indicates positive linear relationship between x speed of execution rating and y overall satisfaction rating for electronic trades

c)

y^ = 0.1802 + 0.9214 x

d)

the slope is 0.1802

hence

one unit increase in the speed of execution rating will increase the overall satisfaction rating by approximately 0.9214 units