Regression analysis with prediction intervals
Barron's conducts an annual review of online brokers, including both brokers that can be accessed via a Web browser, as well as direct-access brokers that connect customers directly with the broker's network server. Each broker's offerings and performance are evaluated in six areas, using a point value of 0-5 in each category. The results are weighted to obtain an overall score, and a final star rating, ranging from zero to five stars, is assigned to each broker. Trade execution, ease of use, and range of offerings are three of the areas evaluated. A point value of 5 in the trade execution area means the order entry and execution process flowed easily from one step to the next. A value of 5 in the ease of use area means that site was easy to use and can be tailored to show what the user wants to see. A value of 5 in the range offerings area means that all of the investment transactions can be executed online. The following data show the point values for trade execution, ease of use, range of offerings, and the star rating for a sample of 10 of the online brokers that Barron's evaluated (Barron's, March 10, 2003).
|
Broker
|
Trade Execution
|
Use
|
Range
|
Rating
|
|
Wall St. Access
|
3.7
|
4.5
|
4.8
|
4.0
|
|
E*TRADE (Power)
|
3.4
|
3.0
|
4.2
|
3.5
|
|
E*TRADE (Standard)
|
2.5
|
4.0
|
4.0
|
3.5
|
|
Preferred Trade
|
4.8
|
3.7
|
3.4
|
3.5
|
|
My Track
|
4.0
|
3.5
|
3.2
|
3.5
|
|
TD Waterhouse
|
3.0
|
3.0
|
4.6
|
3.5
|
|
Brown & Co.
|
2.7
|
2.5
|
3.3
|
3.0
|
|
Brokerage America
|
1.7
|
3.5
|
3.1
|
3.0
|
|
Merrill Lynch Direct
|
2.2
|
2.7
|
3.0
|
2.5
|
|
Strong Funds
|
1.4
|
3.6
|
2.5
|
2.0
|
a. Determine the estimated regression equation that can be used to predict the star rating given the point values for execution, ease of use, and range of offerings (to 3 decimals).
Rating = ______ + ______ TradeEx + ____ Use + ______ Range
b. Use the t test to determine the significance of each independent variable. What is your conclusion at the .05 level of significance?
TradeEx
Use
Range
c. work out the coefficient of determination for the equation in part (a) (to 3 decimals).
Eliminate any independent variable that is not significant from the estimated regression equation. Now, compute the coefficient of Determination (to 3 decimals).
Portray the difference in the fit provided by the two estimated regression equations.