Question 3 - Barron’s conducts an annual review of online brokers, including both brokers PDF

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Question 3 Trade Broker Wall Access E Power E Standard Preferred Trade My Track TD Warehouse Brown & Co. Brokerage America Merrick Direct Strong Fund

Ease of Use

Execution 3.7 3.4 2.5 4.8 4.0 3.0 2.7 1.7 2.2 1.4

Range of

Rating

offering 4.5 3.0 4.0 3.7 3.5 3.0 2.5 3.5 2.7 3.6

4.8 4.2 4.0 3.4 3.2 4.6 3.3 3.1 3.0 2.5

4.0 3.5 3.5 3.5 3.5 3.5 3.0 3.0 2.5 2.0

Solution Part A To determine the estimated regression equation, the dependent and independent variables would be determined. In this question, the dependent variable is the star rating while the independent variable is the execution, ease of use and range of offerings. Since there are many variables, this is a multiple linear regression. Assume that trade execution is X1, ease of use is X2 and range of offering is X3. SPSS would, therefore, be used in order to determine the output which would be used to estimate the regression equation. Consider the coefficients table below.

Model

Coefficientsa Unstandardized Coefficients

1

(Constant) Trade_execution Ease_of_use Range_of_offering a. Dependent Variable: Rating

B -.362 .247 .267 .548

Std. Error .542 .087 .144 .126

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Standardize

t

Sig.

d Coefficients Beta .387 .240 .607

-.667 2.829 1.861 4.349

.529 .030 .112 .005

From the table above, the regression equation would be estimated using the unstandardized coefficients as shown below. Y =α + β 1 X 1+ β 2 X 2+ B 3 X 3+ ε Y =− 0.362+ 0.247 X 1+ 0.267 X 2+ 0.548 X 3+ 0.542 Y =0.18+ 0.247 X 1+ 0.267 X 2+ 0.548 X 3

From the estimated regression equation above, a change in X1 (trade execution), X2 (ease of use) and X3 (rang of offering) by one unit would lead to an increase in (Y) the rating by 0.247, 0.267 and 0.548 respectively. Part B Ho: Predictor variables are significant. Ha: Predictor variables are not significant. To compute the F test, the test of ANOVA would be generated either using Excel or SPSS. For this group, the test of ANOVA was generated using SPSS as shown below.

Model

Sum of

ANOVAa df

Mean

F

Squares Square Regression 3.755 3 1.252 20.274 Residual .370 6 .062 Total 4.125 9 a. Dependent Variable: Rating b. Predictors: (Constant), Range_of_offering, Ease_of_use, Trade_execution

1

Sig. .002b

Ideally, if the F test calculated is greater than the one in the table, one would reject the null hypothesis and conclude that the predictor variables are not significant. From the table, the F test is 4.76. At a significance of 0.05, the F test calculated is 20.274 as seen in table above which is lower than that of the Ftest table, one would fail to reject the null hypothesis and conclude that the predictor variables are significant in determining the rating. Part C First, it would be prudent to determine the null and alternate hypothesis for the variables. The null hypothesis and alternate hypothesis can be formulated as shown below. Ho1: Trade execution is significant. Ha1: Trade execution is not significant. Ho2: Ease of use is significant. Ha2: Ease of use is not significant. Page 2 of 5

Ho3: Range of offering is significant. Ha3: Range of offering is not significant. One-Sample Test Test Value = 2.26 t

Trade_execution Ease_of_use Range_of_offering

df

2.031 5.918 5.688

Sig. (2-

Mean

95% Confidence

tailed)

Difference

Interval of the

9 9 9

.073 .000 .000

Difference Lower Upper -.0772 1.4372 .7042 1.5758 .8131 1.8869

.68000 1.14000 1.35000

Ideally, if the t-test calculated is greater than the t-test statistic from the table, one would reject the null hypothesis and conclude that the variable is not significant. On the other hand, if the t-test calculated is lower than the t-test statistic from the table, one would fail to reject the null hypothesis and conclude that the variable is significant. In this question, trade execution has a t-test calculated of 2.031 which is lower than the t-test statistic from the table of 2.26 and thus one would fail to reject the null hypothesis and conclude that it is significant. However, the ease of use and the range of offering have t-test calculated of 5.918 and 5.688 respectively as seen in table above which is greater than the t-test statistic from the table of 2.26 and thus one would reject the null hypothesis and conclude that the ease of use and the range of offering are not significant in determining the rating of the broker. Part D From the t-test analysis, therefore, the ease of use and the range or offering are not significant which means that they will be removed in order to estimate the new regression equation. Consider the table below.

Model

Coefficientsa Unstandardized Coefficients

1

(Constant) Trade_execution a. Dependent Variable: Rating

B 1.923 .451

Std. Error .498 .160

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Standardize

t

Sig.

d Coefficients Beta .705

3.863 2.815

.005 .023

The estimated regression equation after the independent variables that are not significant are removed would be as shown below. Y =α + β 1 X 1+ε Y =1.923+ 0.451 X 1+0.49 8 Y =2.421+0.451 X 1

From the regression analysis in SPSS, the R2 can be compared in order to determine the differences. R2 in part D Mod

R

el

R

Adjuste

Squar

dR

e

Square

Model Summaryb Std. Change Statistics R F df df Sig. F Error 2 Chang of the Squar Chang 1 Estima

.

.498

.435

e

e

nWatso n

Chang

te 1

e

Durbi

.50892

e .498

7.927

1

8

.023

1.547

705a a. Predictors: (Constant), Trade_execution b. Dependent Variable: Rating R2 in part A Mod

R

el

1

.

R

Adjuste

Squar

dR

e

Square

.910

.865

Model Summaryb Change Statistics Std. F df df Sig. F R Error 2 Chang Squar Chang 1 of the e e e Estima Chang te e .24846 .910 20.274 3 6 .002

Durbi nWatso n

1.971

954a a. Predictors: (Constant), Range_of_offering, Ease_of_use, Trade_execution b. Dependent Variable: Rating From the analysis, Part A had an R squared of 0.910 while Part D had an R squared of 0.498. This means that in Part A, 91% of the variables fit the regression model while in Part D, 49.8% of the variables fit the regression model. The primary reason for the differences is

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that Part D used only one independent variable as the others were found to be insignificant while Part A used three independent variables including the insignificant ones.

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