A financial planner tracks the number of new customers added each quarter for a
ID: 3244954 • Letter: A
Question
A financial planner tracks the number of new customers added each quarter for a 6 year period. The data is presented below:
(a) Create a multiple regression equation incorporating both a trend (t=0 in 2010: IV) and dummy variables for the quarters. Let the first quarter represent the reference (or base) group. Complete (e) thru (h) using your results. This is a computer deliverable. (20 pts)
(b) Test for the existence of first order autocorrelation, use alpha = 0.05. The calculated dw = 1.19. (12 pts)
Year Quarter New Year Quarter New 2011 I 31 2014 I 69 II 24 II 54 III 23 III 46 IV 16 IV 32 2012 I 42 2015 I 82 II 35 II 66 III 30 III 51 IV 23 IV 38 2013 I 53 2016 I 91 II 45 II 72 III 39 III 59 IV 27 IV 41Explanation / Answer
Answer:
Data is coded like this:
new customers
Q2
Q3
Q4
t
31
0
0
0
1
24
1
0
0
2
23
0
1
0
3
16
0
0
1
4
42
0
0
0
5
35
1
0
0
6
30
0
1
0
7
23
0
0
1
8
53
0
0
0
9
45
1
0
0
10
39
0
1
0
11
27
0
0
1
12
69
0
0
0
13
54
1
0
0
14
46
0
1
0
15
32
0
0
1
16
82
0
0
0
17
66
1
0
0
18
51
0
1
0
19
38
0
0
1
20
91
0
0
0
21
72
1
0
0
22
59
0
1
0
23
41
0
0
1
24
Regression Analysis
R²
0.936
Adjusted R²
0.922
n
24
R
0.967
k
4
Std. Error
5.520
Dep. Var.
new customers
ANOVA table
Source
SS
df
MS
F
p-value
Regression
8,400.7286
4
2,100.1821
68.93
4.83E-11
Residual
578.8964
19
30.4682
Total
8,979.6250
23
Regression output
confidence interval
variables
coefficients
std. error
t (df=19)
p-value
95% lower
95% upper
Intercept
37.7030
2.8930
13.032
6.35E-11
31.6478
43.7582
Q2
-14.1482
3.1911
-4.434
.0003
-20.8273
-7.4691
Q3
-24.2964
3.2039
-7.583
3.67E-07
-31.0022
-17.5906
Q4
-38.2780
3.2250
-11.869
3.12E-10
-45.0281
-31.5279
t
2.1482
0.1649
13.025
6.42E-11
1.8030
2.4934
Observation
new customers
Predicted
Residual
1
31.0
39.9
-8.9
2
24.0
27.9
-3.9
3
23.0
19.9
3.1
4
16.0
8.0
8.0
5
42.0
48.4
-6.4
6
35.0
36.4
-1.4
7
30.0
28.4
1.6
8
23.0
16.6
6.4
9
53.0
57.0
-4.0
10
45.0
45.0
-0.0
11
39.0
37.0
2.0
12
27.0
25.2
1.8
13
69.0
65.6
3.4
14
54.0
53.6
0.4
15
46.0
45.6
0.4
16
32.0
33.8
-1.8
17
82.0
74.2
7.8
18
66.0
62.2
3.8
19
51.0
54.2
-3.2
20
38.0
42.4
-4.4
21
91.0
82.8
8.2
22
72.0
70.8
1.2
23
59.0
62.8
-3.8
24
41.0
51.0
-10.0
Durbin-Watson =
1.62
The regression model is
New customers = 37.7030 -14.1482*Q2 -24.2964*Q3 -38.2780 *Q4+2.1482*t
(b) Test for the existence of first order autocorrelation, use alpha = 0.05. The calculated dw = 1.19. (12 pts)
Table values : dL=1.04 and dU=1.77
calculated dw in between dL and dU.
The test is inconclusive.
new customers
Q2
Q3
Q4
t
31
0
0
0
1
24
1
0
0
2
23
0
1
0
3
16
0
0
1
4
42
0
0
0
5
35
1
0
0
6
30
0
1
0
7
23
0
0
1
8
53
0
0
0
9
45
1
0
0
10
39
0
1
0
11
27
0
0
1
12
69
0
0
0
13
54
1
0
0
14
46
0
1
0
15
32
0
0
1
16
82
0
0
0
17
66
1
0
0
18
51
0
1
0
19
38
0
0
1
20
91
0
0
0
21
72
1
0
0
22
59
0
1
0
23
41
0
0
1
24
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