Question

Consider the following time series data.

Consider the following time series data. Quarter Year 1 Year 2 Year 3 1 3 6 8 2 2 4 8 3 4 7 9 4 6 9 11 (a) Choose the correct time series plot. (i) $cameba02h.p8-23_g1_v6.JPG$ (ii) $cameba02h.p8-23_g2_v6.JPG$ (iii) $cameba02h.p8-23_g3_v6_res.JPG$ (iv) $cameba02h.p8-23_g4_v6.JPG$ - Select your answer -Plot (i)Plot (ii)Plot (iii)Plot (iv)Item 1 What type of pattern exists in the data? - Select your answer -Positive trend pattern, no seasonalityHorizontal pattern, no seasonalityNegative trend pattern, no seasonalityPositive trend pattern, with seasonalityHorizontal pattern, with seasonalityItem 2 (b) Use a multiple regression model with dummy variables as follows to develop an equation to account for seasonal effects in the data. Qtr1 = 1 if Quarter 1, 0 otherwise; Qtr2 = 1 if Quarter 2, 0 otherwise; Qtr3 = 1 if Quarter 3, 0 otherwise. If required, round your answers to three decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300) If the constant is "1" it must be entered in the box. Do not round intermediate calculation. ŷ =   +   Qtr1 +   Qtr2 +   Qtr3 (c) Compute the quarterly forecasts for next year based on the model you developed in part (b). If required, round your answers to three decimal places. Do not round intermediate calculation. Year Quarter Ft 4 1 4 2 4 3 4 4 (d) Use a multiple regression model to develop an equation to account for trend and seasonal effects in the data. Use the dummy variables you developed in part (b) to capture seasonal effects and create a variable t such that t = 1 for Quarter 1 in Year 1, t = 2 for Quarter 2 in Year 1,… t = 12 for Quarter 4 in Year 3. If required, round your answers to three decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300) ŷ =   +  Qtr1 +  Qtr2 +  Qtr3 +   t (e) Compute the quarterly forecasts for next year based on the model you developed in part (d). Do not round your interim computations and round your final answer to three decimal places. Year Quarter Period Ft 4 1 13 4 2 14 4 3 15 4 4 16 (f) Is the model you developed in part (b) or the model you developed in part (d) more effective? If required, round your intermediate calculations and final answer to three decimal places. Model developed in part (b) Model developed in part (d) MSE - Select your answer -Model developed in part (b)Model developed in part (d)Item 22 Justify your answer. The input in the box below will not be graded, but may be reviewed and considered by your instructor. Hide Feedback Partially Correct

Answer 1

A)

12 10 10 12 14

option C) plot iii) is correct

positive trend , and seasonality

b)

data

y	t	Q1	Q2	Q3
3	1	1	0	0
2	2	0	1	0
4	3	0	0	1
6	4	0	0	0
6	5	1	0	0
4	6	0	1	0
7	7	0	0	1
9	8	0	0	0
8	9	1	0	0
8	10	0	1	0
9	11	0	0	1
11	12	0	0	0

excel result

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.562657013
R Square	0.316582915
Adjusted R Square	0.060301508
Standard Error	2.661453237
Observations	12
ANOVA
	df	SS	MS	F	Significance F
Regression	3	26.25	8.75	1.235294	0.358900532
Residual	8	56.66666667	7.083333333
Total	11	82.91666667
	Coefficients	Standard Error	t Stat	P-value	Lower 95%
Intercept	8.667	1.536590743	5.640191903	0.000487	5.123282059
Q1	-3	2.173067468	-1.38053698	0.204764	-8.011102568
Q2	-4	2.173067468	-1.840715973	0.102932	-9.011102568
Q3	-2	2.173067468	-0.920357987	0.384298	-7.011102568

y^ = 8.667 -3 Q1 -4 Q2 - 2 Q3

c)

Year	Quarter	Ft
4	1	5.667
4	2	4.667
4	3	6.667
4	4	8.667

d)

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.990659899
R Square	0.981407035
Adjusted R Square	0.970782484
Standard Error	0.469295318
Observations	12
ANOVA
	df	SS	MS	F	Significance F
Regression	4	81.375	20.34375	92.37162162	3.88693E-06
Residual	7	1.541666667	0.220238095
Total	11	82.91666667
	Coefficients	Standard Error	t Stat	P-value	Lower 95%
Intercept	3.417	0.428	7.975	0.000	2.403647325
t	0.656	0.041	15.821	0.000	0.558164824
Q1	-1.031	0.403	-2.560	0.038	-1.983905691
Q2	-2.688	0.392	-6.855	0.000	-3.614564915
Q3	-1.344	0.385	-3.486	0.010	-2.255115597

y^= 3.417 -1.031 Q1 -2.688 Q2 -1.344 Q3 + 0.656 t

e)

Year	Quarter	Period	Ft
4	1	13	10.917
4	2	14	9.917
4	3	15	11.917
4	4	16	13.917