Question

Brokerage	Speed	Satisfaction
Scottrade, Inc.	3.5	3.3
Charles Schwab	3.5	3.3
Fidelity Brokerage Services	3.8	3.2
TD Ameritrade	3.7	3.7
E*Trade Financial	3.0	3.2
Vanguard Brokerage Services	2.8	3.6
USAA Brokerage Services	3.5	3.7
Thinkorswim	2.6	2.6
Wells Fargo Investments	2.2	2.6
Interactive Brokers	4.0	4.0
Zecco.com	2.3	2.3

1. Develop the least squares estimated regression equation.  (to 3 decimals)

2. Suppose Wells Fargo Investments 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 2.2 to the average speed of execution rating for the other 10 brokerage firms that were surveyed, what value would you predict for the overall satisfaction rating?

   (to 3 decimals)

Answer 1

Solution:

Part a

Here, we have to find the regression equation for the prediction of the dependent variable satisfaction based on the independent variable speed. The required regression model by using excel is given as below:

Regression Statistics
Multiple R	0.818394617
R Square	0.669769749
Adjusted R Square	0.633077498
Standard Error	0.322912842
Observations	11
ANOVA
	df	SS	MS	F	Significance F
Regression	1	1.903363849	1.903363849	18.2537115	0.002072873
Residual	9	0.938454333	0.104272704
Total	10	2.841818182
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	1.005620609	0.529032845	1.900866116	0.089763685	-0.191134828	2.202376046
Speed	0.700234192	0.163895761	4.272436249	0.002072873	0.329476222	1.070992162

The required least squares estimated regression equation is given as below:

y = a + b*x

y = 1.006 + 0.700*x

Satisfaction = 1.006 + 0.700*Speed

Part b

Here, we have to find the predicted value of the dependent variable satisfaction for the given value of speed as 2.2.

Satisfaction = 1.006 + 0.700*Speed

Satisfaction = 1.006 + 0.700*2.2

Satisfaction = 2.546

Answer: 2.546