Question

A some association On-Line Discount Broker Survey polls members on their experiences with discount brokers. As part of the survey, members were asked to rate the quality of the speed of execution with their broker as well as provide an overall satisfaction rating for electronic trades. Possible responses (scores) were no opinion (0), unsatisfied (), somewhat satisfied (2), satisfied (3), and very satisfied (4). For each broker summary scores were computed by calculating a weighted average of the scores provided by each respondent. A portion of the survey results follow Brokerage Scottrade, Inc. Charles Schwab Fidelity Brokerage Services TD Ameritrade E*Trade Financial Vanguard Brokerage Services USAA Brokerage Services Thinkorswim Wells Fargo Investments Interactive Brokers Speed Satisfaction 4.0 3.1 2.6 3.2 3.3 2.8 2.4 2.8 3.9 3.2 3.4 3.9 3.1 2.3 3.3 3.5 2.7 2.0 3.1 3.4 3.4 3.4 Zecco.com e.Suppose USAA Brokerage Services developed new software to increase their speed of execution rating. If the new software is able to increase their speed of execution rating from the current value of 2.4 to the average speed of execution rating for the other 10 brokerage firms that were surveyed, what value would you predict for the overall satisfaction rating? 3.100 (to 3 decimals)

Answer 1

A simple regression is applied in this case to find the solution...

V-913357-444 33233223333 M ˇ 1623848924 43233222333 M

X- Mx Y- M (X- My) (x- Mx)(Y- My) 0.8455 0.0545 0.5545 0.0455 0.1455 0.3545 0.7545 0.3545 0.7455 0.0455 0.2455 0.8 0.7148 0.003 0.6764 0.8 0.2 0.4 0.4 1.1 0.0021 0.0212 0.1257 0.5693 0.1257 .5557| 0.0021 0.0602 0.4436 0.0091 0·0582 0.1418 0.83 0.3 0.3 0.3 0.2236 0.0136 0.0736 SS: 2.4873 SP: 2.47

Calculation Summary Sum of X 34.7 Sum of Y 34.1 Mean X-3.1545 Mean Y 3.1 Sum of squares (SSx) 2.4873 Sum of products (SP) - 2.47 Regression Equation-ybX+ a b- SPISSx- 2.47/2.49-0.99306 a My - bMx-3.1-(0.99*3.15)--0.03264 y0.99306X- 0.03264

3.9 3.4 2.9 2.4 1.91 2.5 3.5 4 x-Independent Regression Line(-0.99x-0.03)

So, the Regression Equation is: Satisfaction = 0.993*Speed - 0.032

If Speed = 3.23, (average of remaining 10 firms)

Satisfaction = 0.993*3.23 - 0.032 = 3.175

Actual answer might vary a little as it mostly depends on the decimal places upto which the regression equation is taken..

If you consider the regression equation as Satisfaction = 0.99*Speed - 0.03,

Then,

Satisfaction = 0.99*3.23 - 0.03 = 3.1677

End of the Solution