Question

Baron’s conducts an annual review of on line brokers, including both brokers who can be accessed via a Web browser, as well as direct-access brokers who 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 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 is the ease of use area means that the 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 the investment transactions can be executed online. The data on canvas 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 Baron’s evaluated (Baron’s, March 10, 2003)

Questions:

1. 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.

2. What is the predicted star rating of a broker who has a use score of 4, range score of 4.3 and a TradeEx score of 3.8?

3. What is the predicted star rating of a broker who has a use score of 1.9, range score of 4.2 and a TradeEx score of 3?

4. Is the regression line a good fit? Why?

Broker	TradeEx	Use	Range	Rating
Wall St. Access	3.7	4.5	4.8	4
E*Trade (Power)	3.4	3	4.2	3.5
E*Trade (Standard)	2.5	4	4	3.5
Preferred Trade	4.8	3.7	3.4	3.5
my Track	4	3.5	3.2	3.5
TD Waterhouse	3	3	4.6	3.5
Brown & Co.	2.7	2.5	3.3	3
Brokerage America	1.7	3.5	3.1	3
Merill Lynch Direct	2.2	2.7	3	2.5
Strong Funds	1.4	3.6	2.5	2

Answer 1

1. 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.

The estimated regression equation is:

y = 0.3451 + 0.2548*x1 + 0.1325*x2 + 0.4585*x3

1. What is the predicted star rating of a broker who has a use score of 4, range score of 4.3 and a TradeEx score of 3.8?

​​​​​​​​​​​​​​y = 0.3451 + 0.2548*3.8 + 0.1325*4 + 0.4585*4.3 = 3.81489

1. What is the predicted star rating of a broker who has a use score of 1.9, range score of 4.2 and a TradeEx score of 3?

​​​​​​​​​​​​​​​​​​​​​y = 0.3451 + 0.2548*3 + 0.1325*1.9 + 0.4585*4.2 = 3.28695

1. Is the regression line a good fit? Why?

​​​​​​​R² = 0.886

88.6% of the variation in the model is explained.

This is a good fitted model.