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

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.

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