Question

A financial planner tracks the number of new customers added each quarter for a 6 year...

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

2014 I 31 2017 I 69

II 24 II 54

III 23 III 46

IV 16 IV 32

2015 I 42 2018 I 82

II 35 II 66

III 30 III 51

IV 23 IV 38

2016 I 53 2019 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 2013: 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 2020.

Create a multiple regression equation incorporating both a trend (t=0 in 2013: 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 2020.

(h) Test for the existence of first order autocorrelation, use alpha = 0.05. The calculated dw = 1.19.

Homework Answers

Answer #1

ANSWER:

We Used the given data and estimated a Simple linear regression equation

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.652093
R Square 0.425225

Adjusted R

Square

0.399099

Standard

Error

15.31675
Observation 24
ANOVA
df SS MS F

Significance

F

Regression 1 3818.365 3818.365 16.27588 0.000555
Residual 22 5161.26 234.6027
Total 23 8979.625
Coefficients

Standard

Error

t Stat p-value Lower 95%

Upper

95%

Lower

95.0%

Upper

95.0%

Intercept 22.59783 6.453718 3.50152 0.002017 9.213633 35.98202 9.213633 35.98202
period 1.822174 0.451666 4.034338 0.000555 0.885476 2.758872 0.885476 2.758872

data used:

period New
1 31
2 24
3 23
4 16
5 42
6 35
7 30
8 23
9 53
10 45
11 39
12 27
13 69
14 54
15 46
16 32
17 82
18 66
19 51
20 38
21 91
22 72
23 59
24 41

(a) Every quarter ahead there is an expected increase of 1.82(approx 2) new customers.

(b) Yes,there is a significant increasing trend since slope for the time variables is positive and significant since p-value is 0.00056<0.001.

So reject H0 and conclude the variable(trend/time) is significant.

(c) Yes the model is significant since:

F

Significant

F

16.27588 0.000555

<0.05

So reject H0 and conclude regression is significant.

(d) Forecast:

2017-Q1 68.148
2017-Q2 69.97

Formula:

2017-Q1 =22.598+1.822*25
2017-Q2 =22.598+1.822*26
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