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 (I), 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. 2.7 3.0 Charles Schwab 3.9 3.8 Fidelity Brokerage Services 3.1 3.5 TD Ameritrade 3.9 3.9 E Trade Financial 3.5 3.9 Vanguard Brokerage Services 4.0 4.0 USAA Brokerage Services 3.8 3.9 Thinkorswim 3.3 3.3 Wells Fargo Investments 3.6 3.2 Interactive Brokers 3.9 3.6 Zecco.com 3.3 3.1 a. Select a scatter diagram for these data with the speed of execution as the independent variable Speed Satisfaction Brokerage 3.0 Scottrade, Inc 3.8 Charles Schwab 3.5 3.1 Fidelity Brokerage Services 3.9 3.9 TD Ameritrade 3.9 3.5 E Trade Financial Vanguard Brokerage Services 3.9 USAA Brokerage Services 3.3 Thinkorswim 3.2 Wells Fargo Investments 3.6 Interactive Brokers 3.1 Zecco.com a. Select a scatter diagram for these data with the speed of execution as the independent variable 4.5 4.5 2.5 2.5 4.5 3.5 2.5 4.5 3.5 2.5 Speed of Execution Speed of Execution 4.5 3.5 3.5 to 2.5 2.5 4.5 3.5 2.5 4.5 3.5 Speed of Execution Speed of Execution -Select your answer b. What does the scatter diagram developed in part (a) indicate about the relationship between the two variables? The scatter diagram indicates a L Select your answer-/ linear relationship between z = speed of execution rating and y = overall satisfaction rating for electronic trades. c. Develop the least squares estimated regression equation. Enter negative value as negative number. Speed (to 4 decimals) Satisfaction d. Provide an interpretation for the slope of the estimated regression equation (to 4 decimals) So, a one unit -Select your answer- in the speed of execution rating will increase the overall satisfaction rating by The slope of the estimated regression line is approximately e. Suppose Scottrade, Inc. 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 2.7 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? points. approximately (to 3 decimals)

Answer 1

(a)
Correct option:

B

(b)

The scatter diagram indicates strong direct linear relationship between x = spped of execution rating and y = overall satisfaction rating for electronic rates.

(c)

From the given data, the following Table is calculated:

X	Y	XY	X2
2.7	3.0	8.1	7.29
3.9	3.8	14.82	15.21
3.1	3.5	10.85	9.61
3.9	3.9	15.21	15.21
3.5	3.9	13.65	12.25
4.0	4.0	16.0	16.0
3.8	3.9	14.82	14.44
3.3	3.3	10.89	10.89
3.6	3.2	11.52	12.96
3.9	3.6	14.04	15.21
3.3	3.1	10.23	10.89
Total = 39.0	39.2	140.13	139.96

$a=\frac{\sum Y\sum X^{2}-\sum X\sum XY}{n\sum X^{2}-(\sum X)^{2}}$

(39.2×139.96)-(39.0×140.13) (11 × 139.96)-392 21.3620 18.5600 1.1510

$b=\frac{n\sum XY-\sum X\sum Y}{n\sum X^{2}-(\sum X)^{2}}$

(11 × 140.13)-(39.0 × 39.2) (11 × 139.96)-392 12.6300 = 0.6805 18.36

So

Least Squares Regression Equation is given by:

Satisfaction = 1.1510+0.6805Speed

(d)

The slope of the estimated regression line is approximately 0.6805. So, one unit increase in the speed of execution rating will increase the overall satisfaction rating by approximately 0.6805 points.

(e)

Average speed of execution rating for other 10 brokerage firms = 36.3/10 = 3.63

For x = 3.63, we get:

1.1510 + (0.6805 × 3.63) Satisfaction 3.6212

So,

Answer is:

3.621