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...

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problem 08-23 Algo (Using Regression Analysis forForecasting

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 modelwith dummy variables as follows to develop an equation to accountfor seasonal effects in the data. Qtr1 = 1 if Quarter 1, 0otherwise; Qtr2 = 1 if Quarter 2, 0 otherwise; Qtr3 = 1 if Quarter3, 0 otherwise.
If required, round your answers tothree decimal places. For subtractive or negative numbers use aminus 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 notround intermediate calculation.
ŷ=   +   Qtr1+   Qtr2+   Qtr3
(c)Compute the quarterly forecasts fornext year based on the model you developed in part (b).
If required, round your answers tothree decimal places. Do not round intermediate calculation.
YearQuarterFt
41
42
43
44
(d)Use a multiple regression model todevelop an equation to account for trend and seasonal effects inthe data. Use the dummy variables you developed in part (b) tocapture seasonal effects and create a variable t such thatt = 1 for Quarter 1 in Year 1, t = 2 for Quarter2 in Year 1,… t = 12 for Quarter 4 in Year 3.
If required, round your answers tothree decimal places. For subtractive or negative numbers use aminus sign even if there is a + sign before the blank. (Example:-300)
ŷ=   +  Qtr1+  Qtr2 +  Qtr3+   t
(e)Compute the quarterly forecasts fornext year based on the model you developed in part (d).
Do not round your interimcomputations and round your final answer to three decimalplaces.
YearQuarterPeriodFt
4113
4214
4315
4416
(f)Is the model you developed in part(b) or the model you developed in part (d) more effective?
If required, round yourintermediate calculations and final answer to three decimalplaces.
Model developed in part(b)Model developed in part(d)
MSE

Can you please show me how to step up excel spreadsheetfor this problem. How to figure out the problems on thisquestion.

Answer & Explanation Solved by verified expert
3.5 Ratings (465 Votes)

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

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