A financial planner tracks the number of new customers added each quarter for a
ID: 3259127 • 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:
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 41
Create a simple linear trend regression model. Let t=0 in 2010: IV. This is a computer deliverable.
(a) Interpret the slope coefficient.
(b) Test to see if the number of new customers is increasing over time. Use alpha = 0.01.
(c) Test to see if the model has explanatory power. Use alpha = 0.05.
(d) Forecast the number of new customers in the first and second quarters of 2017.
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.
(e) Test to see if there is an upward trend in new customers. Use alpha = 0.01.
(f) Test to see if the model has explanatory power. Use alpha = 0.05.
(g) Forecast the number of new customers in the first and second quarters of 2017.
Explanation / Answer
Answer:
Create a simple linear trend regression model. Let t=0 in 2010: IV. This is a computer deliverable.
Regression Analysis
r²
0.425
n
24
r
0.652
k
1
Std. Error
15.317
Dep. Var.
new
ANOVA table
Source
SS
df
MS
F
p-value
Regression
3,818.3654
1
3,818.3654
16.28
.0006
Residual
5,161.2596
22
234.6027
Total
8,979.6250
23
Regression output
confidence interval
variables
coefficients
std. error
t (df=22)
p-value
95% lower
95% upper
Intercept
17.1313
7.6672
2.234
.0359
1.2304
33.0322
t
1.8222
0.4517
4.034
.0006
0.8855
2.7589
Predicted values for: new
95% Confidence Intervals
95% Prediction Intervals
t
Predicted
lower
upper
lower
upper
Leverage
28
68.152
54.768
81.536
33.683
102.622
0.178
29
69.974
55.763
84.185
35.175
104.773
0.200
When time increases by one quarter, the number of customers increases by 1.8222
(b) Test to see if the number of new customers is increasing over time. Use alpha = 0.01.
Calculated t=4.034, P=0.0006 which is < 0.01 level. We conclude that the number of new customers is increasing over time.
(c) Test to see if the model has explanatory power. Use alpha = 0.05.
Calculated F=16.28, P=0.0006 which is < 0.05 level. The model is significant.
(d) Forecast the number of new customers in the first and second quarters of 2017.
Predicted new customers in the first and second quarters is 68 and 70 ( rounded).
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.
Regression Analysis
R²
0.936
Adjusted R²
0.922
n
24
R
0.967
k
4
Std. Error
5.520
Dep. Var.
new
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
31.2583
3.2265
9.688
8.75E-09
24.5053
38.0114
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
Predicted values for: new
95% Confidence Intervals
95% Prediction Intervals
Q2
Q3
Q4
t
Predicted
lower
upper
lower
upper
Leverage
0
0
0
28
91.408
84.655
98.161
78.026
104.790
0.342
1
0
0
29
79.408
72.655
86.161
66.026
92.790
0.342
(e) Test to see if there is an upward trend in new customers. Use alpha = 0.01.
Calculated t=13.025, P=0.0000 which is < 0.01 level. We conclude that the number of new customers is increasing over time
(f) Test to see if the model has explanatory power. Use alpha = 0.05.
Calculated F=68.93, P=0.0000 which is < 0.05 level. The model is significant.
(g) Forecast the number of new customers in the first and second quarters of 2017.
Predicted new customers in the first and second quarters is 91 and 79 ( rounded).
Regression Analysis
r²
0.425
n
24
r
0.652
k
1
Std. Error
15.317
Dep. Var.
new
ANOVA table
Source
SS
df
MS
F
p-value
Regression
3,818.3654
1
3,818.3654
16.28
.0006
Residual
5,161.2596
22
234.6027
Total
8,979.6250
23
Regression output
confidence interval
variables
coefficients
std. error
t (df=22)
p-value
95% lower
95% upper
Intercept
17.1313
7.6672
2.234
.0359
1.2304
33.0322
t
1.8222
0.4517
4.034
.0006
0.8855
2.7589
Predicted values for: new
95% Confidence Intervals
95% Prediction Intervals
t
Predicted
lower
upper
lower
upper
Leverage
28
68.152
54.768
81.536
33.683
102.622
0.178
29
69.974
55.763
84.185
35.175
104.773
0.200
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