Question

Satisfaction with Satisfaction with Overall Satisfaction with Brokerage Trade Price speed of Execution Electronic Trades Scottrade, Inc. 3.4 3.4 Charles Schwab Fidelity Brokerage Services TD Ameritrade E*Trade Financial (Not listed) Vanguard Brokerage Services USAA Brokerage Services Thinkorswim Wells Fargo Investments Interactive Brokers Zecco.com Firstrade Securities Banc of America Investment Services in Na Na N (a) Develop an estimated regression equation using trade price and speed of execution to predict overall satisfaction with the broker. Let X1 represent satisfaction with Trade Price. Let x2 represent satisfaction with speed of execution. If required, round your answers to four decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300) X1 + What is the coefficient of determination? If required, round your answers to four decimal places. X2

Answer 1

a)

The regression equation is defined as,

$\widehat{Y}=\beta_0+\beta_1X_1+\beta_2X_2$

Now, the regression analysis is done in excel by following steps

Step 1: Write the data values in excel. The screenshot is shown below,

А в х2 у 3.2 3.1 2.9 3.4 3.3 3.4 3.6 3.9 1

Step 2: DATA > Data Analysis > Regression > OK. The screenshot is shown below,

DATA REVIEW Data Analysis ? X Гок HE INSERT PAGE LAYOUT FORMULAS AL ZA X - Data Analysis Analysis Tools Fourier Analysis Histogram Moving Average Random Number Generation Rank and Percentile Regression Sampling t-Test: Paired Two Sample for Means t-Test: Two-Sample Assuming Equal Variances t-Test: Two-Sample Assuming Unequal Variances Cancel Help 36.6

Step 3: Select Input Y Range: 'Y' column, Input X Range: 'x1 and x2' column then OK. The screenshot is shown below,

1x1 X2 xa 3.4 3.2 ly 3.41 3.3 3.41 2.1 39 Regression Input Input Y Range: Гок SCS1:SCS15 SA$1:$B$15 Cancel Input X Range: Help Labels Confidence Level: Constant is Zero 95 % SES2 Output options O Qutput Range: New Worksheet Ply: O New Workbook Residuals Residuals Standardized Residuals Residual Plots Line Fit Plots

The result is obtained. The screenshot is shown below,

F G H I J K 2 SUMMARY OUTPUT 4. Regression Statistics 5 Multiple R 0.826272 6 R Square 0.682726 7 Adjusted R Square 0.62504 8 Standard Error 0.410845 9 Observations 14 10 df 11 ANOVA 12 13 Regression 14 Residual 15 Total 16 SS MS F gnificance F 2 3.99541 1.997705 11.83517 0.001811 11 1.856733 0.168794 13 5.852143 18 Intercept 19 x1 20 x2 Coefficientsandard Err Stat P-value Lower 95%Upper 95% -0.78348 0.942279 -0.83147 0.42339 -2.85742 1.290466 0.557957 0.23317 2.392919 0.035677 0.044753 1.071161 0.734175 0.155738 4.714163 0.000635 0.391398 1.076953

The regression equation is,

$\widehat{y}=-0.7835+0.5580\times x_1+0.7342 \times x_2$

The coefficient of determination is the R squared value in the regression model. From the regression model in part a)

R Square

0.6827