One A sales manager is interested in monitoring the number of sales calls made by its sales staff in three

Question One

A sales manager is interested in monitoring the number of sales calls made by its sales staff in three different branches. The firm samples six sales people from each of the three branches and determines the number of sales called made by each on a given day. The data is as follows

	Sales Calls
	Branch
Sales Person	Branch A	Branch B	Branch C
1	36	41	53
2	45	47	45
3	51	38	57
4	48	39	61
5	45	52	51
6	41	37	39

Required

Using Analysis of Variance (ANOVA) test at the 5% level if there are significant differences in the mean sales calls made across the three branches.

Question Two

A regional education authority is responsible for ranking the performance of secondary schools over which it has authority. Schools are ranked on a number of factors. These are:

the school’s ability to retain its students (i.e a low drop-out rate)
post-secondary participation (i.e. the proportion of graduates who go on to college or university)
the performance of each school’s graduates when they get to post-secondary institutions
academic achievement on examinations

There are 71 schools in the authority and the ranks for each are presented below.

School Number	Retention rank	Post-secondary participation rank	Post-secondary achievement rank	Academic achievement rank
1	17	29	51	28
2	25	51	48	62
3	29	52	66	69
4	52	65	25	24
5	65	60	50	34
6	53	61	56	64
7	48	66	30	6
8	33	70	23	27
9	16	45	57	21
10	12	34	63	66
11	3	1	2	2
12	18	9	20	32
13	22	2	45	31
14	34	5	5	56
15	61	50	44	9
16	32	36	10	51
17	4	40	14	15
18	23	63	59	65
19	27	25	55	49
20	8	4	1	1
21	59	31	32	36
22	67	39	27	33
23	56	33	61	63
24	21	37	17	43
25	24	3	36	45
26	54	62	68	68
27	1	21	29	12
28	47	67	34	40
29	39	44	3	14
30	46	43	37	54
31	13	22	58	46
32	15	35	21	17
33	19	17	26	4
34	10	12	13	8
35	58	41	43	44
36	2	14	31	60
37	64	47	40	52
38	51	15	42	48
39	62	11	70	70
40	40	19	7	3
41	68	16	18	10
42	31	28	28	47
43	66	48	35	42
44	38	69	12	18
45	26	57	52	16
46	11	8	46	55
47	42	10	62	13
48	14	7	65	59
49	30	42	41	37
50	55	18	69	61
51	37	23	67	50
52	36	27	9	20
53	49	26	54	67
54	50	56	53	41
55	70	32	33	35
56	41	55	16	30
57	9	13	4	19
58	43	46	15	29
59	60	58	38	22
60	45	49	47	39
61	35	54	6	11
62	28	53	39	7
63	44	59	19	38
64	20	20	22	5
65	69	24	11	23
66	57	30	49	26
67	5	68	60	58
68	7	38	8	53
69	6	6	64	57
70	63	64	24	25

Required

Calculate Spearman’s rank correlation for Retention rank and Post-Secondary Participation rank.
Calculate Spearman’s rank correlation for Post-Secondary Achievement rank and Academic Achievement rank on exams.
Calculate Spearman’s rank correlation for Post-Secondary Participation rank and Post-Secondary Achievement rank.
Comment on your results.

Question Three

A market research firm is interested in assessing whether there is a relationship between age and consumption patterns of a particular product. They sample 15 individuals and ask their age and the amount they spent on that product in the previous year. The figures are as follows:

Individual	Age	Amount spent
1	25	68
2	47	46
3	58	31
4	37	56
5	59	35
6	21	81
7	55	45
8	43	38
9	47	42
10	24	68
11	61	28
12	55	18
13	29	65
14	50	31
15	39	55

Required

Calculate Pearson’s correlation coefficient between age and amount spent on this particular product.
Test this correlation for statistical significance (at a 5% significance level).
Estimate a linear regression to examine the relationship between age and amount spent on this product.
If an individual was 40 years old, what would you predict his/her amount spent on this product to be for the previous year?
Comment on any potential problems there might be with this regression.

Question Four

A telemarketing firm relies heavily on casual workers and as such they constantly need to monitor and plan for turnover. They collect quarterly data on employee turnover (resignations) for a three year period.

	Q1	Q2	Q3	Q4
2006	48	68	56	31
2007	51	70	57	30
2008	52	71	59	32
2009	54	75	61	33

Required

Use a linear regression to identify the trend in the firm’s turnover.
Based on these results, would you describe turnover as increasing or decreasing?
Using this data and incorporating seasonal effects, forecast quarterly turnover for 2010.
Describe the relative impact of the trend and seasonal effects on this forecast.

Question Five

The Human Resources Manager of a financial services firm is interested in examining the number of days lost and overtime paid to its upper-level clerical employees. She collects a variety of information and provides this to you for analysis. The data is below:

ID	Rate	Overtime	grade	Bank quals.	Age	Tenure	Sex	Married	hours absent
1	5	23.64	4	0	23	7	1	0	36.55
2	5	140.40	5	0	34	15	1	0	22.02
3	5	837.00	5	0	26	9	1	1	102.86
4	4	464.16	5	0	52	35	1	0	145.49
5	4	145.80	6	1	38	20	0	1	94.65
6	5	1406.16	6	1	29	11	0	1	7.73
7	5	1118.76	6	0	27	9	1	1	22.50
8	3	349.80	6	1	31	12	0	0	167.52
9	3	381.60	5	0	21	4	1	0	94.89
10	4	147.60	6	0	34	15	1	1	66.79
11	5	1673.40	5	0	45	19	0	1	7.06
12	4	166.08	5	1	35	15	0	0	7.56
13	5	70.20	5	0	57	25	0	1	65.84
14	5	298.44	6	0	32	14	1	0	254.18
15	4	294.00	5	1	31	13	1	1	52.02
16	5	231.00	5	1	32	14	1	1	160.98
17	5	945.00	5	1	34	15	0	0	43.10
18	3	81.60	4	0	23	6	0	0	95.124
19	4	52.56	6	1	47	29	0	1	73.10
20	5	41.28	6	1	44	27	0	1	15.03
21	5	368.40	5	1	32	15	1	1	37.53
22	5	690.36	5	0	37	20	0	0	0
23	3	1113.84	6	1	54	33	0	1	7.59
24	3	178.20	4	0	39	5	1	1	205.25
25	4	397.80	5	0	35	16	1	1	182.76
26	4	59.04	4	0	21	3	0	0	22.03
27	4	102.00	6	1	49	23	0	1	15.83
28	3	165.84	5	0	36	19	0	1	58.81
29	4	1897.56	6	0	44	20	0	1	65.18
30	4	2967.36	6	0	24	4	0	0	43.17
31	4	99.48	5	1	34	17	1	1	161.25
32	3	1289.64	6	0	35	4	1	1	131.91
33	5	1323.48	4	0	26	8	1	0	6.88
34	4	1518.48	4	0	23	6	1	0	115.73
35	4	361.80	4	0	20	4	1	0	50.84
36	3	20.40	4	0	22	4	1	0	58.82
37	4	530.40	5	0	43	26	1	1	81.32
38	3	56.40	5	0	27	3	1	1	132.68
39	3	1185.84	4	0	24	5	1	0	145.25
40	4	78.96	5	0	30	13	1	1	81.14
41	5	165.00	6	1	41	24	0	1	15.28
42	4	42.96	4	0	24	5	1	0	123.55
43	5	128.64	4	1	25	7	1	0	36.39
44	4	186.00	5	0	45	8	1	1	146.97
45	3	78.60	4	0	23	5	0	0	58.81
46	4	608.04	5	1	51	33	0	0	80.18
47	5	607.08	5	0	31	15	1	1	59.88
48	5	172.56	5	0	35	18	1	1	52.26
49	4	270.00	4	0	31	14	1	1	44.24
50	4	283.56	5	0	32	14	1	1	37.58
51	5	1500.84	6	1	46	26	0	1	0
52	3	248.40	5	0	28	4	1	1	81.51
53	4	610.56	5	0	26	9	1	0	58.13
54	5	230.04	5	1	34	14	0	1	14.56
55	3	57.60	5	0	33	16	1	1	132.64
56	3	834.36	5	0	38	20	0	1	29.52
57	5	605.16	6	1	36	17	0	1	0
58	4	412.56	6	1	41	21	0	1	22.69
59	1	371.28	5	0	36	19	1	1	37.75
60	4	2177.52	5	0	27	9	1	0	0

‘ID’ is the employee’s identification number. They are unique to each employee.

‘Rate’ is the employee’s performance rating. 3 = satisfactory; 4 = superior; 5 = excellent

‘Overtime’ is the amount (in pounds) that the individual was paid in overtime in the previous year.

‘Grade’ is the individual’s grade in the firm’s hierarchy. The higher the grade the more senior the individual.

‘Bank Quals’ takes on the value 1 if the individual has obtained banking qualification; 0 otherwise.

‘Age’ is the employee’s age in years.

‘Tenure’ is the employee’s tenure in years.

‘Sex’ is 1 if the individual is female; 0 if male.

‘Married’ is 1 if the individual is married; 0 otherwise.

‘Hours absent’ is the number of hours the employee was absent from work in the previous year.

Required

Compute a Pearson’s correlation coefficient using hours lost absence and overtime payments. Is this correlation coefficient statistically significant at the 5% level?
Using the data provided estimate a multiple regression predicting hours lost due to absence.
Describe these results.
If an individual were to be promoted by one grade, by how much would you expect absenteeism to change?
Using the data provided estimate a multiple regression predicting overtime payments
Describe these results
If an individual were to be promoted by one grade, by how much would you expect overtime to increase?
What advice can you give to the HR manager?