Question

A new course in Data Mining is being offered and the number of students registered in the course is monitored. Supposed the academic year is divided into four quarters: Q₁, Q₂ Q₃ and Q_4. The number of students registered in the course for the last 4 years is recorded in the table below.

Quarter	2014	2015	2016	2017
Q1	42	45	48	52
Q2	58	60	68	70
Q3	51	53	57	60
Q4	58	60	68	72

Plot the course registration over time and identify the patterns. Derive a linear model to predict Registration. Describe the model. Predict Registration for the four quarters of 2018. Calculate the corresponding Mean Absolute Deviation.

Answer 1

y	Q1	Q2	Q3	t
42	1	0	0	1
58	0	1	0	2
51	0	0	1	3
58	0	0	0	4
45	1	0	0	5
60	0	1	0	6
53	0	0	1	7
60	0	0	0	8
48	1	0	0	9
68	0	1	0	10
57	0	0	1	11
68	0	0	0	12
52	1	0	0	13
70	0	1	0	14
60	0	0	1	15
72	0	0	0	16

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.98878382
R Square	0.977693443
Adjusted R Square	0.969581968
Standard Error	1.550659684
Observations	16
ANOVA
	df	SS	MS	F	Significance F
Regression	4	1159.3	289.825	120.5321	5.26038E-09
Residual	11	26.45	2.404545
Total	15	1185.75
	Coefficients	Standard Error	t Stat	P-value	Lower 95%
Intercept	54.625	1.162994763	46.96926	4.99E-14	52.06526579
Q1	-14.7875	1.12689865	-13.1223	4.62E-08	-17.26778721
Q2	1.475	1.110103394	1.328705	0.21085	-0.968321096
Q3	-8.2625	1.099903147	-7.51203	1.18E-05	-10.6833705
t	0.9875	0.086684512	11.39189	1.98E-07	0.796708676

t	y^
17	56.625
18	73.875
19	65.125
20	74.375