Question

Situation:

Fidelity Investment has collected data polling online investors on their experiences. As a part of the survey, the investors were asked to rate the quality of the speed of execution with their brokers and an overall satisfaction rating for online trades. Possible responses were Unsatisfied (score = 1), Somewhat satisfied (score = 2), Satisfied (score = 3), and Very satisfied (score = 4). An average score for each broker was computed and average execution speed in seconds for each investor was recorded as shown in the following table.

Broker	Speed	Satisfaction
1	3.4	3.5
2	3.3	3.4
3	3.4	3.9
4	3.6	3.7
5	3.2	2.9
6	3.8	2.8
7	3.8	3.6
8	2.6	2.6
9	2.7	2.3
10	4.0	4.0
11	2.5	2.5

Action

Perform a correlation and regression analysis to predict satisfaction score using execution speed. Discuss the following:

1. Scatter Diagram
2. R, R2 and 1-R2
3. Show the regression equation. Comment on the interpretation of the slope of regression equation.
4. What is the standard error of estimate value? What is the interpretation of this value?
5. Conduct the appropriate test of hypothesis for the regression model. Use a .05 level of significance. Does trade execution speed appear to be good predictor of the satisfaction rating? Why or why not?

Answer 1

a. Scatter plot

Put the data in excel, select the data and go to insert -> scatterplot as shown in the diagram.

b. Regression equation

Step to run regression in excel.

step 1 : Put the data in excel as shown.

Step 2 : Go to data -> Data Analysis -> Regression

Step 3 : Input the values as shown

Step 4 : Output will be generated as given below.

From the regression output highlighted in blue we get the regression equation give below

y = 0.2046 + 0.9077 Speed(x)

R2 = 0.5983
R = sqrt(0.5983) = 0.7735

Show the regression equation. Comment on the interpretation of the slope of regression equation.
y = 0.2046 + 0.9077 Speed(x)

One unit increase in the speed increase the satisfaction by 0.9077 units.

What is the standard error of estimate value? What is the interpretation of this value?
0.399700743

On an average the actual values are 0.3997 units away from the regression line.

Conduct the appropriate test of hypothesis for the regression model. Use a .05 level of significance. Does trade execution speed appear to be good predictor of the satisfaction rating? Why or why not?

For the beta coefficient, we test the following hypothesis.

Next we check the pvalue for the variable in the regression output and check if the pvalue is less than 0.05, if it is less than 0.05 then we reject the null hypothesis and conclude that the variable is significant.

In this case we find the pvalue is 0.005221191
which is less than 0.05, hence we reject the null hypothesis and conclude that the variable speed is a significant predictor of y.