Question

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 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

Data

KY

data -> data analysis -> regression

SUMMARY OUTPUT Regression Statistics Multiple R 0.967229149 R Square 0.935532227 Adjusted R Square 0.921960064 Standard Error 5.519803718 Observations 24 ANOVA df F Significance F 4.82886E-11 Regression Residual Total 68.93022438 M S 2100.182143 30.46823308 4 19 23 SS 8400.728571 578.8964286 8979.625 t Intercept 6 Coefficients 37.7030 2.1482 -14.1482 -24.2964 -38.2780 Standard Error 2.893042719 0.164935683 3.191125424 3.203887141 3.225044451 Stat 13.03229156 13.02455749 -4.433612724 -7.583422106 -11.86897631 P-value 6.35104E-11 .41613E-11 0.000285081 3.6742E-07 3.11803E-10 Lower 95% Upper 95% 31.64776819 43.7581842 1.802999934 2.49342864 -20.82731656 -7.46911201 -31.00224143 -17.5906157 -45.0280718 -31.5278806 Q2 Q3 Q4

y^ = 37.7030 + 2.1482 t -14.1482 Q2 - 24.2964 Q3 - 38.2780 Q4

e)

p-value of t = 0 < alpha

hence there is an upward trend

f)

p-value of model = 0 < alpha

hence this model has explanatory power

g)

Year Quarter Period Ft 25 26 91.41 79.41