Brokerage Satisfaction with Satisfaction with Overall Satisfaction with Trade Pr
ID: 3155333 • Letter: B
Question
Brokerage Satisfaction with Satisfaction with Overall Satisfaction with Trade Price Speed of Execution Electronic Trades AA 3.4 3.1 3.4 BB 3 3.3 3.3 CC 3.1 3.3 4 DD 2.8 3.5 3.7 EE 2.9 3.2 2.9 FF 2.4 3.2 2.7 GG 2.6 3.8 2.6 HH 2.4 3.8 3.4 II 2.6 2.6 2.7 JJ 2.3 2.7 2.3 KK 3.7 3.9 4 LL 2.5 2.5 2.5 MM 3 3 3 NN 4 1 2 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 (O), 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 Satisfaction with Satisfaction with Overall Satisfaction with Brokerage Speed of Execution 3.1 3.3 3.3 3.5 3.2 3.2 Electronic Trades 3.4 3.3 Trade Price 3.4 3.1 3.7 2.9 2.7 2.6 2.6 2.6 2.3 3.7 2.5 2.6 2.7 3.9 2.5 2.7 2.3 2.5 (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 asign before the blank. (Example: 300) x2 What is the coefficient of determination? If required, round your answers to four decimal places. Interpret the coefficient of determination.Explanation / Answer
Solution:
The required regression analysis is given as below:
Regression Analysis
Regression Statistics
Multiple R
0.8416
R Square
0.7084
Adjusted R Square
0.6553
Standard Error
0.3631
Observations
14
ANOVA
df
SS
MS
F
Significance F
Regression
2
3.5221
1.7611
13.3596
0.0011
Residual
11
1.4500
0.1318
Total
13
4.9721
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
-0.9438
0.8730
-1.0811
0.3028
-2.8653
0.9777
Satisfaction with Trade Price
0.6017
0.2100
2.8656
0.0154
0.1396
1.0639
Satisfaction with Speed of Execution
0.7278
0.1451
5.0144
0.0004
0.4083
1.0473
Part a Solution:
The required regression is given as below:
Y = -0.9438 + 0.6017*X1 + 0.7278*X2
The coefficient of determination is given as below:
Coefficient of determination = R-square = 0.7084
Interpretation of coefficient of determination:
About 70.84% of the variation in the dependent variable overall satisfaction with electronic trades is explained by the independent variables satisfaction with trade price and satisfaction with speed of execution.
Part b) Solution:
The F test for checking the overall relationship between the dependent variable overall satisfaction with electronic trades and independent variables satisfaction with trade price and satisfaction with speed of execution is given as below:
ANOVA
df
SS
MS
F
Significance F
Regression
2
3.5221
1.7611
13.3596
0.0011
Residual
11
1.4500
0.1318
Total
13
4.9721
For this F test we get the p-value as 0.0011 which is less than the given level of significance or alpha value 0.05, so we reject the null hypothesis that there is no significant relationship exists between the dependent variable overall satisfaction with electronic trades and independent variables satisfaction with trade price and satisfaction with speed of execution.
Now, we have to see the t tests for significance of the independent variables satisfaction with trade price and the satisfaction with speed of execution which is given as below:
Coefficients
Standard Error
t Stat
P-value
Intercept
-0.9438
0.8730
-1.0811
0.3028
Satisfaction with Trade Price
0.6017
0.2100
2.8656
0.0154
Satisfaction with Speed of Execution
0.7278
0.1451
5.0144
0.0004
For the independent variable satisfaction with trade price, the p-value is given as 0.0154 which is less than the given level of significance or alpha value 0.05 so we reject the null hypothesis that the coefficient for the variable satisfaction with trade price is not significant.
For the independent variable satisfaction with speed of execution, the p-value is given as 0.0004 which is less than the given level of significance or alpha value 0.05, so we reject the null hypothesis that the coefficient for the variable satisfaction with speed of execution is not significant.
Part c Solution:
Here we have to interpret the parameters for the regression line. The y-intercept for this regression line is given as -0.9438 which indicate that the constant decrease when there is no change in independent variables satisfaction with trade price and satisfaction with speed of execution.
The slope for the independent variable satisfaction with trade price is given as 0.6017 which indicate the unit increase in the overall satisfaction due to trade price.
The slope for the independent variable satisfaction with speed of execution is given as 0.7278 which indicate that unit increase in the overall satisfaction due to speed of execution.
Part d Solution:
Here, we have to predict the overall satisfaction with electronic trades when the satisfaction with trade price is 4 and satisfaction with speed of execution is 4. The regression line is given as below:
Y = -0.9438 + 0.6017*X1 + 0.7278*X2
Y = -0.9438 + 0.6017*4 + 0.7278*4
Y = 4.3743
Required answer = predicted overall satisfaction with electronic trades = 4.3743
Part e Solution:
With regarding this regression model, we can estimate the overall satisfaction with electronic trades for the collected responses for the satisfaction with trade price and speed of execution. For this regression model, we get the strong positive relationship or correlation coefficient so we can use this regression model for finding the overall satisfaction with electronic trades for the collected responses.
Regression Analysis
Regression Statistics
Multiple R
0.8416
R Square
0.7084
Adjusted R Square
0.6553
Standard Error
0.3631
Observations
14
ANOVA
df
SS
MS
F
Significance F
Regression
2
3.5221
1.7611
13.3596
0.0011
Residual
11
1.4500
0.1318
Total
13
4.9721
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
-0.9438
0.8730
-1.0811
0.3028
-2.8653
0.9777
Satisfaction with Trade Price
0.6017
0.2100
2.8656
0.0154
0.1396
1.0639
Satisfaction with Speed of Execution
0.7278
0.1451
5.0144
0.0004
0.4083
1.0473
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