Question

The owner of anderson belts inc., is studing absenteeism among his employees. His workforce is ssmall, consisting of only 5 employees. For the last 3 years, 2014 through 2016, he recorded the following number of employee absences, in days, for each quarter.

Year	Q1	Q2	Q3	Q4
2014	4	10	7	3
2015	5	12	9	4
2016	6	16	12	4

Answer info for

Quarter	Absenses	Moving Avg	Ratio to CMA	S/J	Seasonal Index	Desentasize
Q12014	4				0.6900	5.7972
Q22014	10				1.6655	6.0042
Q32014	7	6.125	1.1429	1.1616	1.1685	5.9906
Q42014	3	6.5	0.4615	0.4732	0.4760	6.3024
Q12015	5	7	0.7143	0.6859	0.6900	7.2465
Q22015	12	7.375	1.6271	1.6557	1.6655	7.2050
Q32015	9	7.625	1.1803	3.9764	1.1685	7.7022
Q42015	4	8.25	0.4848		0.4760	8.4032
Q12016	6	9.125	0.6575		0.6900	8.6958
Q22016	16	9.5	1.6842		1.6655	9.6067
Q32016	12				1.1685	10.2696
Q42016	4				0.4760	8.4032

The seasonal index is

Quarter	Seasonal Index
1	0.6859
2	1.6557
3	1.1616
4	0.4732

Determine the linear trend equation based on the deseasonalized quarterly data for the three years. (round answer to 4 decimal places)

y = _____ + _____t

Answer 1

Solution:

We take x = 1, 2, ... and so on and y = Desentasize column

Using excel, <DATA < DATA ANALYSIS < REGRESSION

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.924502
R Square	0.854705
Adjusted R Square	0.840175
Standard Error	0.590411
Observations	12
ANOVA
	df	SS	MS	F	Significance F
Regression	1	20.50566	20.50566	58.82534	1.7E-05
Residual	10	3.485855	0.348585
Total	11	23.99151
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	5.17415	0.363373	14.23922	5.76E-08	4.364504	5.983796
X Variable 1	0.378677	0.049373	7.669768	1.7E-05	0.268668	0.488686

The linear trend equation is

Y = 5.1742 + 0.3787t