Plymouth Rock Securities is interested in finding out if there is a relationship

1. Plymouth Rock Securities is interested in finding out if there is a relationship between the number of new clients brought into the firm by a broker and the sales performance of the broker. A random sample of 11 brokers' records are reviewed to determine the number of new clients enrolled last year and total sales in millions of dollars:  (12pts)

Broker	1	2	3	4	5	6	7	8	9	10	11
Clients	27	11	42	33	15	15	25	36	28	30	17
Sales, $	52	37	64	55	29	34	58	59	44	48	31

1. How closely related is the new client base to sales performance?  Draw the scatterplot and compute the correlation and describe the relationship

2. Find the least-squares equation to predict sales from number of clients. Can the least squares equation be used to predict sales?

3. What does the slope represent?

4. What would a new broker who brings in 30 clients sell, on average?

5. How much of the variability in sales is not explained by the number of new clients?

1. Jean Siskel is an entertainment analyst for West Coast Securities. He is trying to develop a model to estimate gross earning generated by a new movie release.  He has collected the following data on 20 movies: Gross Earnings, Production Costs, Promotion Costs, and if the movie is based on a bestseller novel: (12 pts)

	Gross Earnings	Production Cost	Promotion Cost
Movie	Millions $	Millions $	Millions $	Novel
1	28	4.2	1	0
2	35	6	3	1
3	50	5.5	6	1
4	20	3.3	1	0
5	75	12.5	11	1
6	60	9.6	8	1
7	15	2.5	0.5	0
8	72	10	12	1
9	45	6.4	8	1
10	37	7.5	5	0
11	30	5.0	1	1
12	63	10.1	10	0
13	58	7.8	9	1
14	50	6.9	10	0
15	24	3.5	4	0
16	82	11.0	15	1
17	48	10.7	1	1
18	34	6.6	2	0
19	50	8.4	3	1
20	45	10.8	5	0

1. What type of variable is novel?

2. What is the estimated multiple linear regression equation derived from this data?

3. What are the regression coefficients for each X variable?  Interpret the regression coefficient.

4. Will Jean be pleased with the results?

5. Interpret the intercept value.

1. The following data represent revenues in thousands of dollars for a manufacturer of small electric appliances. (15 pts)

Year	Quarter	Revenues
1996	1	514
1996	2	822
1996	3	648
1996	4	976
1997	1	616
1997	2	884
1997	3	678
1997	4	996
1998	1	658
1998	2	850
1998	3	714
1998	4	1052

1. Calculate the moving averages for this time series.

2. Find the seasonal index for each quarter.

3. From the fourth quarter of 1997 to the first quarter of 1998, revenues declined.  What happened on a seasonally adjusted basis?

4. Compute the forecast for the second quarter of 2002.

1. Bay Area University enrolls MBA students in three cohort programs: Weeknight, Saturday, and Distance. Dean Ed Epstein wants to know if there is a difference in the average of the students in the three programs.  He has his assistant take a random sample of 5 students from each program and record their ages. (15 pts)

Weeknight	Saturday	Distance
29	32	25
27	33	24
30	31	24
27	34	25
28	30	26

1. State the Null hypothesis and the Research hypothesis to be tested

2. Calculate the F statistic.

3. Should the Null hypothesis be rejected at the 5% level of significance?

4. Draw box plots for the different programs.

5. Using the least-significant difference test, identify the significant differences between the programs.

Please describe the different parts of a statistical report and what is included in each section.  (5pts)