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 (l), 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	Speed	Satisfaction
Scottrade, Inc.	3.6	3.9
Charles Schwab	2.5	2.3
Fidelity Brokerage Services	2.8	2.6
TD Ameritrade	2.9	2.4
E*Trade Financial	3.4	3.7
Vanguard Brokerage Services	3.8	3.9
USAA Brokerage Services	3.2	3.7
Thinkorswim	3.0	2.8
Wells Fargo Investments	3.3	2.8
Interactive Brokers	3.7	3.8
Zecco.com	2.9	2.4

a. Develop the least squares estimated regression equation. Enter negative value as negative number.

Satisfaction = ___?_____ + ____?____ SPEED (to 4 decimals)

d. Provide an interpretation for the slope of the estimated regression equation (to 4 decimals).

The slope of the estimated regression line is approximately ____?___ . So, a one unit _______(increase/decrease) in the speed of execution rating will increase the overall satisfaction rating by approximately ____?___ points.

e. Suppose Charles Schwab 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 2.5 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? ___________ (to 3 decimals)

Answer 1

	Speed (X)	Satisfaction (Y)	X * Y
	3.6	3.9	14.04	12.96	15.21
	2.5	2.3	5.75	6.25	5.29
	2.8	2.6	7.28	7.84	6.76
	2.9	2.4	6.96	8.41	5.76
	3.4	3.7	12.58	11.56	13.69
	3.8	3.9	14.82	14.44	15.21
	3.2	3.7	11.84	10.24	13.69
	3	2.8	8.4	9	7.84
	3.3	2.8	9.24	10.89	7.84
	3.7	3.8	14.06	13.69	14.44
	2.9	2.4	6.96	8.41	5.76
Total	35.1	34.3	111.93	113.69	111.49

Equation of regression line is


b = 1.4693

a =( 34.3 - ( 1.4693 * 35.1 ) ) / 11
a = -1.5703
Equation of regression line becomes

Part d)

Slope = 1.4693, the slope id positive

The slope of the estimated regression line is approximately 1.4693 . So, a one unit increase in the speed of execution rating will increase the overall satisfaction rating by approximately -0.101 points.

Part e)

= -1.5703 + 1.4693 * 2.5
= 2.103