Nicole Becker - Assignment 4 TIME SERIES ANALYSIS

Complete the following questions:

Total Assignment 4 mark out of 35=22

Chapter 16 PDF: Exercises 4, 10, 12, and 26.

4. Listed below is the net sales in $million for Home Depot Inc. and its subsidiaries from 1993 to 2004.

Year / Net Sales / Year / Net Sales
1993 / $9,239 / 1999 / $38,434
1994 / 12477 / 2000 / 45738
1995 / 15470 / 2001 / 53553
1996 / 19535 / 2002 / 58247
1997 / 24156 / 2003 / 64816
1998 / 30219 / 2004 / 73094

Determine the least squares equation. According to this information, what are the estimated sales for 2008 and 2009?

SUMMARY OUTPUT
Regression Statistics
Multiple R / 0.992
R Square / 0.984
Adjusted R Square / 0.982
Standard Error / 2901.118
Observations / 12
ANOVA
df / SS / MS / F / Significance F
Regression / 1 / 5147676005 / 5.15E+09 / 611.618 / 0.000
Residual / 10 / 84164869.9 / 8416487
Total / 11 / 5231840875
Coefficients / Standard Error / t Stat / P-value
Intercept / -11953541.161 / 484844.206 / -24.654 / 0.000
Year / 5999.811 / 242.604 / 24.731 / 0.000

The least square equations are:

y-bar = α + β*x-bar

∑xy = α∑x + β∑x2

Hence the least square equations are:

37081.5 = α + β*1998.5

890146506 = 23982*α + 47928170*β

Therefore here the least square regression line is: Net Sales = -11953541.161 + 5999.811*Year

The estimated sales for 2008 = -11953541.161 + 5999.811*2008 = $94079.327

and for 2009 = -11953541.161 + 5999.811*2009 = $100079.138

Incorrect independent variable. This is a time series. Independent variable is time “t”. Your methodology is correct.

Mark out of 8 = 5

Price(y) / t / ty / t2
1993 / 9239 / 1 / 9239 / 1
1994 / 12477 / 2 / 24954 / 4
1995 / 15470 / 3 / 46410 / 9
1996 / 19535 / 4 / 78140 / 16
1997 / 24156 / 5 / 120780 / 25
1998 / 30219 / 6 / 181314 / 36
1999 / 38434 / 7 / 269038 / 49
2000 / 45738 / 8 / 365904 / 64
2001 / 53553 / 9 / 481977 / 81
2002 / 58247 / 10 / 582470 / 100
2003 / 64816 / 11 / 712976 / 121
2004 / 73094 / 12 / 877128 / 144
Total / 444978 / 78 / 3750330 / 650

Y¢ = -1917.2727 + 5999.8112t

10. The Appliance Centre sells a variety of electronic equipment and home appliances. For the last four years the following quarterly sales (in $ millions) were reported.

Quarter

Year / I / II / III / IV
2005 / 5.3 / 4.1 / 6.8 / 6.7
2006 / 4.8 / 3.8 / 5.6 / 6.8
2007 / 4.3 / 3.8 / 5.7 / 6
2008 / 5.6 / 4.6 / 6.4 / 5.9

Determine a typical seasonal index for each of the four quarters.

Year / I / II / III / IV / Total
2005 / 5.3 / 4.1 / 6.8 / 6.7 / 22.9
2006 / 4.8 / 3.8 / 5.6 / 6.8 / 21
2007 / 4.3 / 3.8 / 5.7 / 6 / 19.8
2008 / 5.6 / 4.6 / 6.4 / 5.9 / 22.5
Total / 20 / 16.3 / 24.5 / 25.4 / 86.2
Seasonal Index / 0.232019 / 0.189095 / 0.284223 / 0.294664

Therefore, the seasonal index for quarter I is 0.232019, quarter II is 0.189095, quarter III is 0.284223 and quarter IV is 0.294664. X quarterly indexes must total 4. mark out of 8 = 0

Average SI Seasonal

Quarter Component Index

1 0.9122 0.9077

2 0.7647 0.7609

3 1.1318 1.1261

4 1.2159 1.2098

Year / Quarter / Sales (y) / t / Four Quarter total / Four Quarter Moving Average / Centred Moving Average / Specific Seasonal
2005 / I / 5.3 / 1
II / 4.1 / 2
22.9 / 5.725
III / 6.8 / 3 / 5.6625 / 1.20088
22.4 / 5.6
IV / 6.7 / 4 / 5.5625 / 1.20449
22.1 / 5.525
2006 / I / 4.8 / 5 / 5.375 / 0.89302
20.9 / 5.225
II / 3.8 / 6 / 5.2375 / 0.72553
21 / 5.25
III / 5.6 / 7 / 5.1875 / 1.07951
20.5 / 5.125
IV / 6.8 / 8 / 5.125 / 1.32682
20.5 / 5.125
2007 / I / 4.3 / 9 / 5.1375 / 0.83698
20.6 / 5.15
II / 3.8 / 10 / 5.05 / 0.75247
19.8 / 4.95
III / 5.7 / 11 / 5.1125 / 1.11491
21.1 / 5.275
IV / 6 / 12 / 5.375 / 1.11627
21.9 / 5.475
2008 / I / 5.6 / 13 / 5.5625 / 1.00674
22.6 / 5.65
II / 4.6 / 14 / 5.6375 / 0.81596
22.5 / 5.625
III / 6.4 / 15
IV / 5.9 / 16
1.20088=6.8/5.6625
Quarter
I / II / III / IV
2005 / 1.20088 / 1.20449
2006 / 0.89302 / 0.72553 / 1.07951 / 1.32682
2007 / 0.83698 / 0.75247 / 1.11491 / 1.11627
2008 / 1.00674 / 0.81596
Total / 2.73674 / 2.29397 / 3.39531 / 3.64760
mean / 0.912 / 0.765 / 1.132 / 1.216 / 4.024548 / adjustment factor / 0.993901
adjusted / 0.907 / 0.76 / 1.125 / 1.208
Ex. / 0.906685 = 0.912249 * 4/4.0245

12.Team Sports Inc. sells sporting goods to high schools and colleges via a nationally distributed catalogue. Management at Team Sports estimates it will sell 2000 Wilson Model A2000 catcher’s mitts next year. The deseasonalized sales are projected to be the same for each of the four quarters next year. The seasonal factor for the second quarter is 145. Determine the seasonally adjusted sales for the second quarter of next year.

Since the deseasonalized sales are projected to be the same for each of the four quarters next year then the deseasonalized estimate of sales for the second quarter of next year = 2000/4 = 500

Now, the seasonal factor for the second quarter is 145.

Therefore, the seasonally adjusted sales for the second quarter of next year = 500 + 145 = 645 X mark out of 4=2

Sales for each quarter are 500, found by 2000/4. The estimated sales for the second quarter are 725, found by 500(1.45).

26.The quarterly production of pine lumber in millions of board feet, by Northwest Lumber since 2004 is:

Quarter

Winter / Spring / Summer / Fall
7.8 / 10.2 / 14.7 / 9.3
6.9 / 11.6 / 17.5 / 9.3
8.9 / 9.7 / 15.3 / 10.1
10.7 / 12.4 / 16.8 / 10.7
9.2 / 13.6 / 17.1 / 10.3

a) Determine the typical seasonal pattern for the production data using the ratio-to-moving-average method.

b) Interpret the pattern.

The seasonal index for winter = 75.5, for spring = 99.1, for summer = 140.4 and for fall = 85

Therefore, in winter sales is severely decreased for seasonal swing. In spring there is not much effect of seasonality. In summer sales is increased by seasonal effect but in Fall sales is again decreased due to seasonal effect.

c) Deseasonalize the data and determine the linear trend equation.

The following table gives the deseasonalised data:

Year / Specific Seasonal / Deseasonalised data
Winter / 7.8
2004 / Spring / 10.2
Summer / 14.7 / 1.4152 / 10.3875
Fall / 9.3 / 0.89 / 10.45
Winter / 6.9 / 0.6287 / 10.975
2005 / Spring / 11.6 / 1.0243 / 11.325
Summer / 17.5 / 1.5119 / 11.575
Fall / 9.3 / 0.8026 / 11.5875
Winter / 8.9 / 0.8036 / 11.075
2006 / Spring / 9.7 / 0.8899 / 10.9
Summer / 15.3 / 1.363 / 11.225
Fall / 10.1 / 0.8568 / 11.7875
Winter / 10.7 / 0.869 / 12.3125
2007 / Spring / 12.4 / 0.9861 / 12.575
Summer / 16.8 / 1.348 / 12.4625
Fall / 10.7 / 0.8612 / 12.425
Winter / 9.2 / 0.7294 / 12.6125
2008 / Spring / 13.6 / 1.0794 / 12.6
Summer / 17.1
Fall / 10.3

Variable t takes values 1 for summer 2004, 2 for fall 2004

SUMMARY OUTPUT
Regression Statistics
Multiple R / 0.905
R Square / 0.819
Adjusted R Square / 0.806
Standard Error / 0.343
Observations / 16
ANOVA
df / SS / MS / F / Significance F
Regression / 1 / 7.438 / 7.438 / 63.383 / 0.000
Residual / 14 / 1.643 / 0.117
Total / 15 / 9.081
Coefficients / Standard Error / t Stat / P-value
Intercept / 10.385 / 0.180 / 57.810 / 0.000
X Variable 1 / 0.148 / 0.019 / 7.961 / 0.000

Therefore the trend line is: T = 10.385 +0.148*t

d) Project the seasonally adjusted production for the four quarters of 2009.

For the four quarters of 2009, t = 19,20,21,22 respectively for four seasons.

Therefore, we have the seasonally adjusted production for the four quarters of 2009 as:

Year / Season / t / Trend / Seasonal Index / Forecast
Winter / 19 / 13.197 / 75.5 / 10.0
2009 / Spring / 20 / 13.345 / 99.1 / 13.2
Summer / 21 / 13.493 / 140.4 / 18.9
Fall / 22 / 13.641 / 85.0 / 11.6

Mark out of 15=15