Barron’s conducts an annual review of online brokers, including both brokers tha

Question

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 0-5 in each category. The results are weighted to obtain an overall score, and a final star rating, ranging from 0 to 5 stars, is assigned to each broker. Trade execution, ease of use, and range of offerings are three areas evaluated. The following data show some of the point values for trade execution, ease of use, range of offerings, and the star rating for a random sample of 10 of the online brokers that Barron’s evaluated:

Using this data, a multiple regression analysis was used to assess the effect of trade execution, ease of use, and range of offerings on star rating. The results of the analysis follow:

Residual Plot:

a. State the multiple regression equation.

b. Using a significance level of 1%, is there a significant relationship of star rating and the overall set of independent variables – support your answer?

c. Determine the coefficient of multiple determination and interpret its meaning.

d. Is there evidence that multicollinearity is present – support your answer?

A second multiple regression model was fit with only trade execution and range of offerings as the independent variables. The results are as follows:

e. Conduct an F-test, using a level of significance of 5%, to determine if ease of use has a significant effect on star rating.

f. Why did the coefficient for the effect of range of offerings change from .4585 to .4853 when ease of use was dropped from the model?

g. What is the coefficient of partial determination for ease of use?

Broker TradeExUse Range Rating 4.5 4.8 1 Wall St. Access 2 E*Trade (Power) 3 E*Trade (Standard) 4 Preferred Trade 5 my Track 6 TD Waterhouse 7 Brown & Co 8 Brokerage America 9 Merill Lynch Direct 10 Strong Funds 3.7 3.5 3.5 3.5 3.5 3.5 2.5 4.8 4.0 3.7 3.5 4.0 3.2 4.6 3.3 2.5 3.5 2.7 2.7 3.0 2.5 2.0 2.2 2.5

Explanation / Answer

(a)Rating=0.345+0.255 TradeEx+0.132 Use + 0.459 Range

(b) none of variable has p-value less than 0.01, none of variable is significant

(c)coefficient of determination =R-sq=88.6%, this means the model explains 88.6% of variability in dependent or response variable

(d) VIF all the variable is around 1, so there is no problem of multicollinearity

(e)F=MS(regression)/MS(residual error)=23.15 and its p-value=0.001 is less than alpha=0.05, so model is significant

(g)coefficient of partial determination=(SSEreduced- SSEfull)/SSEreduced=

=(0.4072-0.3546)/(0.4072)=0.1292=12.92%

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