Question

problem 08-23 Algo (Using Regression Analysis for Forecasting

Quarter:1,2,3,4

year 1: 2,0,5,5

year 2: 5,2,8,8

year 3: 7,6,10,10

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

Can you please show me how to step up excel spreadsheet for this problem. How to figure out the problems on this question.

Answer 1

c)

Actual Demand y	t	Q1	Q2	Q3	quarter
2	1	1	0	0	4.66666667
0	2	0	1	0	2.66666667
5	3	0	0	1	7.66666667
5	4	0	0	0	7.66666667
5	5	1	0	0	4.66666667
2	6	0	1	0	2.66666667
8	7	0	0	1	7.66666667
8	8	0	0	0	7.66666667
7	9	1	0	0	4.66666667
6	10	0	1	0	2.66666667
10	11	0	0	1	7.66666667
10	12	0	0	0	7.66666667
	13	1	0	0	4.66666667
	14	0	1	0	2.66666667
	15	0	0	1	7.66666667
	16	0	0	0	7.66666667

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.698535473
R Square	0.487951807
Adjusted R Square	0.295933735
Standard Error	2.661453237
Observations	12
ANOVA
	df	SS	MS	F	Significance F
Regression	3	54	18	2.541176471	0.129679966
Residual	8	56.66666667	7.083333333
Total	11	110.6666667
	Coefficients	Standard Error	t Stat	P-value	Lower 95%
Intercept	7.666666667	1.536590743	4.98940053	0.001066868	4.123282059
Q1	-3	2.173067468	-1.38053698	0.204763892	-8.011102568
Q2	-5	2.173067468	-2.300894967	0.050400371	-10.01110257
Q3	6.28037E-16	2.173067468	2.89009E-16	1	-5.011102568
q1	4.666666667
q2	2.666666667
q3	7.666666667
q4	7.666666667

regression of y on q1,q2 ,q3 yields above result

y^ = 7.66666 -3Q1 -5Q2

d)

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.99301021
R Square	0.986069277
Adjusted R Square	0.978108864
Standard Error	0.469295318
Observations	12
ANOVA
	df	SS	MS	F	Significance F
Regression	4	109.125	27.28125	123.8716216	1.42033E-06
Residual	7	1.541666667	0.220238095
Total	11	110.6666667
	Coefficients	Standard Error	t Stat	P-value	Lower 95%
Intercept	2.416666667	0.428406053	5.641065646	0.000781715	1.403647325
t	0.65625	0.041480238	15.82078687	9.77012E-07	0.558164824
Q1	-1.03125	0.402878254	-2.559706285	0.037567703	-1.983905691
Q2	-3.6875	0.392055911	-9.405546243	3.19973E-05	-4.614564915
Q3	0.65625	0.385416667	1.702702703	0.132407607	-0.255115597

e)

13	10.94791667	-1.03125	9.916666667
14	11.60416667	-3.6875	7.916666667
15	12.26041667	0.65625	12.91666667
16	12.91666667		12.91666667