Question

# Consider the following time series data. Quarter Year 1 Year 2 Year 3 1 2 5...

Consider the following time series data.

 Quarter Year 1 Year 2 Year 3 1 2 5 7 2 0 2 6 3 5 8 10 4 5 8 10
(a) Choose the correct time series plot.
 (i) (ii) (iii) (iv)
What type of pattern exists in the data?
Positive trend pattern, no seasonality- 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).
 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
The input in the box below will not be graded, but may be reviewed and considered by your instructor.

I just need help with b c d e f thank you! please show all work

 Year Ft Q1 Q2 Q3 t (period) 1 2 1 0 0 1 1 0 0 1 0 2 1 5 0 0 1 3 1 5 0 0 0 4 2 5 1 0 0 5 2 2 0 1 0 6 2 8 0 0 1 7 2 8 0 0 0 8 3 7 1 0 0 9 3 6 0 1 0 10 3 10 0 0 1 11 3 10 0 0 0 12

b) Without t

Excel > Data > Data Analysis > Regression

 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% Upper 95% Lower 95.0% Upper 95.0% Intercept 7.666666667 1.536590743 4.98940053 0.001066868 4.123282059 11.21005127 4.123282059 11.21005127 Q1 -3 2.173067468 -1.38053698 0.204763892 -8.011102568 2.011102568 -8.011102568 2.011102568 Q2 -5 2.173067468 -2.300894967 0.050400371 -10.01110257 0.011102568 -10.01110257 0.011102568 Q3 6.28037E-16 2.173067468 2.89009E-16 1 -5.011102568 5.011102568 -5.011102568 5.011102568

Y =  7.670-3.000*Q1-5.000*Q2+0.000*Q3

c)

Ft = 7.670-3.000*Q1-5.000*Q2+0.000*Q3

 Quarter Year Ft Q1 Q2 Q3 1 4 4.670 1 0 0 2 4 2.670 0 1 0 3 4 7.670 0 0 1 4 4 7.670 0 0 0

d) with t

 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% Upper 95% Lower 95.0% Upper 95.0% Intercept 2.416666667 0.428406053 5.641065646 0.000781715 1.403647325 3.429686009 1.403647325 3.429686009 Q1 -1.03125 0.402878254 -2.559706285 0.037567703 -1.983905691 -0.078594309 -1.983905691 -0.078594309 Q2 -3.6875 0.392055911 -9.405546243 3.19973E-05 -4.614564915 -2.760435085 -4.614564915 -2.760435085 Q3 0.65625 0.385416667 1.702702703 0.132407607 -0.255115597 1.567615597 -0.255115597 1.567615597 t 0.65625 0.041480238 15.82078687 9.77012E-07 0.558164824 0.754335176 0.558164824 0.754335176

Y = 2.417-1.031*Q1-3.688*Q2+0.656*Q3+0.656*t

e)

Ft = 2.417-1.031*Q1-3.688*Q2+0.656*Q3+0.656*t

 Quarter Year Ft Q1 Q2 Q3 t 1 4 9.918 1 0 0 13 2 4 7.918 0 1 0 14 3 4 12.918 0 0 1 15 4 4 12.918 0 0 0 16

f)

MSE from above output tables(MS Residuals)

 Model developed in part (b) Model developed in part (d) MSE 7.083 0.220

MSE in part b > MSE part d

So, part d model is effective

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