Question

The American Association of Individual Investors (AAII) 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 (1), 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 (AAII website, February 7, 2012).

Brokerage	Speed of execution	Satisfaction
Scottrade, Inc.	3.4	3.5
Charles Schwab	3.3	3.4
Fidelity Brokerage Services	3.4	3.9
TD Ameritrade	3.6	3.7
E*Trade Financial	3.2	2.9

We want to predict "Satisfaction" using "Speed of execution".

A- Compute F statistic.

B- Based on the F statistic, Use 5% significance level. What is the critical value for F statistic

Answer 1

using excel data analysis tool for regression,steps are:

write data>menu>data>data analysis>regression>enter required labels>ok> and following o/p is obtained

Multiple R	0.75144
R Square	0.56466
Adjusted R Square	0.41955
Standard Error	0.28710
Observations	5
ANOVA
	df	SS	MS	F	Significance F
Regression	1	0.32	0.32	3.8912	0.1431
Residual	3	0.25	0.08
Total	4	0.57
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-2.9727	3.2737	-0.9081	0.4308	-13.391	7.446
X	1.9091	0.9678	1.9726	0.143083161	-1.171	4.989

A)

from above o/p

F-stat = 3.891

B)

at α=0.05,df=1 and 3

F-critical value=10.128 excel function: =F.INV.RT(0.05,1,3) ]

since, F-stat < critical value, Fail to reject Ho