a. Develop an estimated regression equation using trade price and speed of execu
ID: 3133833 • Letter: A
Question
a. Develop an estimated regression equation using trade price and speed of execution to predict overall satisfaction with the broker.
b. 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 esti- mated repression equation developed in part (a) to predict overall satisfaction level for Finger Lakes Investments if they can achieve these performance level
c. Develop a 95% confidence interval estimate of the overall satisfaction of electronic trades for all brokers that provide satisfactory levels of service for both trade price and speed of execution.
d. Develop a 95% prediction interval of overall satisfaction for Finger Lakes Investments assuming they achieve service levels of 3 for both trade price and speed of ex
Explanation / Answer
Regression
a. Develop an estimated regression equation using trade price and speed of execution to predict overall satisfaction with the broker.
Solution:
The estimated regression equation using the trade price and speed of execution to predict overall satisfaction with the broker is given as below:
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.826272314
R Square
0.682725937
Adjusted R Square
0.625039744
Standard Error
0.410845374
Observations
14
ANOVA
df
SS
MS
F
Significance F
Regression
2
3.995409718
1.997705
11.83517
0.001810882
Residual
11
1.856733139
0.168794
Total
13
5.852142857
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Lower 95.0%
Upper 95.0%
Intercept
-0.783476184
0.942278832
-0.83147
0.42339
-2.857417908
1.29046554
-2.857417908
1.29046554
Trade price
0.557957136
0.23317013
2.392919
0.035677
0.04475314
1.071161131
0.04475314
1.071161131
Speed of Execution
0.734175363
0.155738212
4.714163
0.000635
0.39139787
1.076952857
0.39139787
1.076952857
The regression equation is given as below:
Satisfaction electronic trades = -0.7835 + 0.55796*trade price + 0.73418*speed of execution
b. 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 esti- mated repression equation developed in part (a) to predict overall satisfaction level for Finger Lakes Investments if they can achieve these performance level
Solution:
The estimated values for the overall satisfaction by using the above regression line are given as below:
Trade price
Speed of Execution
Estimated Satisfaction Electronic trades
3.4
3.4
3.6097688
3.2
3.3
3.4247599
3.1
3.4
3.4423817
2.9
3.6
3.4776253
2.9
3.2
3.1839553
2.5
3.2
2.9607725
2.6
3.8
3.4570732
2.4
3.8
3.3454818
2.6
2.6
2.5760632
2.3
2.7
2.4820936
3.7
4
4.2176609
2.5
2.5
2.44685
3
3
3.092916
4
1
2.182523
c. Develop a 95% confidence interval estimate of the overall satisfaction of electronic trades for all brokers that provide satisfactory levels of service for both trade price and speed of execution.
Solution:
The 95% confidence interval estimate of the overall satisfaction of electronic trades for all brokers is given as below:
Confidence Interval Estimate for the overall satisfaction of electronic trades
Data
Sample Standard Deviation
0.670943243
Sample Mean
3.135714286
Sample Size
14
Confidence Level
95%
Intermediate Calculations
Standard Error of the Mean
0.179317124
Degrees of Freedom
13
t Value
2.1604
Interval Half Width
0.3874
Confidence Interval
Interval Lower Limit
2.75
Interval Upper Limit
3.52
d. Develop a 95% prediction interval of overall satisfaction for Finger Lakes Investments assuming they achieve service levels of 3 for both trade price and speed of execution.
Solution:
The 95% prediction interval of overall satisfaction for Finger Lakes Investments is given as below:
Prediction Interval
Data
Sample Standard Deviation
0.554381569
Sample Mean
3.135708943
Sample Size
14
Confidence Level
95%
Intermediate Calculations
Standard Error of the Mean
0.148164707
Degrees of Freedom
13
t Value
2.1604
Interval Half Width
0.3201
Confidence Interval
Interval Lower Limit
2.82
Interval Upper Limit
3.46
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.826272314
R Square
0.682725937
Adjusted R Square
0.625039744
Standard Error
0.410845374
Observations
14
ANOVA
df
SS
MS
F
Significance F
Regression
2
3.995409718
1.997705
11.83517
0.001810882
Residual
11
1.856733139
0.168794
Total
13
5.852142857
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Lower 95.0%
Upper 95.0%
Intercept
-0.783476184
0.942278832
-0.83147
0.42339
-2.857417908
1.29046554
-2.857417908
1.29046554
Trade price
0.557957136
0.23317013
2.392919
0.035677
0.04475314
1.071161131
0.04475314
1.071161131
Speed of Execution
0.734175363
0.155738212
4.714163
0.000635
0.39139787
1.076952857
0.39139787
1.076952857
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