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:
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  pvalue  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 pvalue 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:
2017Q1  68.148 
2017Q2  69.97 
Formula:
2017Q1  =22.598+1.822*25 
2017Q2  =22.598+1.822*26 
Get Answers For Free
Most questions answered within 1 hours.