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
|
- How closely related is the new client base to sales performance? Draw the scatterplot and compute the correlation and describe the relationship
-
-
Find the least-squares equation to predict sales from number of clients. Can the least squares equation be used to predict sales?
-
What does the slope represent?
-
What would a new broker who brings in 30 clients sell, on average?
-
How much of the variability in sales is not explained by the number of new clients?
-
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
|
-
-
-
What type of variable is novel?
-
What is the estimated multiple linear regression equation derived from this data?
-
What are the regression coefficients for each X variable? Interpret the regression coefficient.
-
Will Jean be pleased with the results?
-
Interpret the intercept value.
-
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
|
-
Calculate the moving averages for this time series.
-
Find the seasonal index for each quarter.
-
From the fourth quarter of 1997 to the first quarter of 1998, revenues declined. What happened on a seasonally adjusted basis?
-
Compute the forecast for the second quarter of 2002.
-
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.
-
|
Weeknight
|
Saturday
|
Distance
|
|
29
|
32
|
25
|
|
27
|
33
|
24
|
|
30
|
31
|
24
|
|
27
|
34
|
25
|
|
28
|
30
|
26
|
-
State the Null hypothesis and the Research hypothesis to be tested
-
Calculate the F statistic.
-
Should the Null hypothesis be rejected at the 5% level of significance?
-
Draw box plots for the different programs.
-
Using the least-significant difference test, identify the significant differences between the programs.