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

Question

A financial planner tracks the number of new customers added each quarter for a 6 year period. The data is presented below:

2. 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)

(a) Test to see if there is an upward trend in new customers. Use alpha = 0.01. (15 pts)

(b) Test to see if the model has explanatory power. Use alpha = 0.05. (15 pts)

(c) Forecast the number of new customers in the first and second quarters of 2017. (4 pts each)

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

Explanation / Answer

a) p-value for variable t is 5.8544600197936E-12

which is less than 0.01

hence  there is an upward trend in new customers.

b) Significance F = 1.78352057931097E-12

which is less than 0.05

hence the model has explanatory power

c) y^ = 37.76190476 + 2.14285 *t -14.14285714*Q2 -24.2857 * Q3 -38.19047619*Q4

for first quarter of 2017 , t= 25 , Q2 = 0 .Q3 = 0 ,Q4 = 0

hence

y^ = 91.33315

for second quarter of 2017 , t= 26 , Q2 = 1 . Q3 = 0 ,Q4 = 0

hence

y^ =79.333147

SUMMARY OUTPUT Regression Statistics Multiple R 0.973211168 R Square 0.947139978 Adjusted R Square 0.936567974 Standard Error 5.38118415 Observations 25 ANOVA df SS MS F Significance F Regression 4 10377.02 2594.254 89.58944 1.78E-12 Residual 20 579.1429 28.95714 Total 24 10956.16 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 37.76190476 2.747097 13.74611 1.19E-11 32.03156 43.49225 32.03156 43.49225 t 2.142857143 0.149941 14.29135 5.85E-12 1.830086 2.455628 1.830086 2.455628 quarter 2 -14.14285714 3.110444 -4.54689 0.000196 -20.6311 -7.65458 -20.6311 -7.65458 quarter 3 -24.28571429 3.121267 -7.78072 1.79E-07 -30.7966 -17.7749 -30.7966 -17.7749 quarter 4 -38.19047619 2.997567 -12.7405 4.69E-11 -44.4433 -31.9377 -44.4433 -31.9377

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