Problem 7-11 The Association of Individual Investors (AII) On-Line Discount Brok
ID: 3240997 • Letter: P
Question
Problem 7-11
The Association of Individual Investors (AII) 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.
Brokerage Satisfaction with
Trade Price Satisfaction with
Speed of Execution Overall Satisfaction with
Electronic Trades AA 3.3 3.1 3.4 BB 3.2 3.3 3.3 CC 3.1 3.3 4 DD 2.9 3.5 3.7 EE 2.8 3.2 2.9 FF 2.4 3.2 2.7 GG 2.6 3.8 2.8 HH 2.4 3.8 3.6 II 2.6 2.6 2.6 JJ 2.3 2.7 2.3 KK 3.7 4 4 LL 2.5 2.5 2.5 MM 3 3 3 NN 4 1 2
Explanation / Answer
Answer:
(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
Overall Satisfaction = -0.9105+0.5699* satisfaction with Trade Price+0.7510* satisfaction with Speed of Execution
What is the coefficient of determination?
If required, round your answers to four decimal places.
R square = 0.7650
Interpret the coefficient of determination.
The input in the box below will not be graded, but may be reviewed and considered by your instructor.
76.5% of variation in Overall Satisfaction is explained by the model.
(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.
Test for Trade Price , Calculated t=3.018, P=0.0117 which is < 0.05 level. satisfaction with Trade Price is significant.
Test for Speed of Execution, Calculated t=5.836, P=0.0001 which is < 0.05 level. satisfaction with Speed of Execution is significant.
(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.
For one unit increase in satisfaction with Trade Price, there is an increase of 0.5699 in Overall Satisfaction.
For one unit increase in satisfaction with Speed of Execution, there is an increase of 0.7510 in Overall Satisfaction.
(d)
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 (4) 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.
Estimated Overall Satisfaction = -0.9105+0.5699*4+0.7510*4
= 4.3731
=4.4
(e)
What concerns (if any) do you have with regard to the possible responses the respondents could select on the survey?
The respondents should be selected by random and independent of each other.
Regression Analysis
R²
0.765
Adjusted R²
0.722
n
14
R
0.875
k
2
Std. Error
0.330
Dep. Var.
Overall Satisfaction
ANOVA table
Source
SS
df
MS
F
p-value
Regression
3.8969
2
1.9485
17.90
.0003
Residual
1.1974
11
0.1089
Total
5.0943
13
Regression output
confidence interval
variables
coefficients
std. error
t (df=11)
p-value
95% lower
95% upper
Intercept
-0.9105
0.7733
-1.177
.2639
-2.6125
0.7915
Trade Price
0.5699
0.1888
3.018
.0117
0.1543
0.9856
Speed of Execution
0.7510
0.1287
5.836
.0001
0.4678
1.0343
(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
Overall Satisfaction = -0.9105+0.5699* satisfaction with Trade Price+0.7510* satisfaction with Speed of Execution
What is the coefficient of determination?
If required, round your answers to four decimal places.
R square = 0.7650
Interpret the coefficient of determination.
The input in the box below will not be graded, but may be reviewed and considered by your instructor.
76.5% of variation in Overall Satisfaction is explained by the model.
(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.
Test for Trade Price , Calculated t=3.018, P=0.0117 which is < 0.05 level. satisfaction with Trade Price is significant.
Test for Speed of Execution, Calculated t=5.836, P=0.0001 which is < 0.05 level. satisfaction with Speed of Execution is significant.
(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.
For one unit increase in satisfaction with Trade Price, there is an increase of 0.5699 in Overall Satisfaction.
For one unit increase in satisfaction with Speed of Execution, there is an increase of 0.7510 in Overall Satisfaction.
(d)
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 (4) 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.
Estimated Overall Satisfaction = -0.9105+0.5699*4+0.7510*4
= 4.3731
=4.4
(e)
What concerns (if any) do you have with regard to the possible responses the respondents could select on the survey?
The respondents should be selected by random and independent of each other.