economic and business statistics

1. Computing the simple index numbers for each year using the wages and costs in 2005 as the base.

Year Hourly Wages Index Average Materials Cost Index

2005 $30.10 100.00 $66,500.00 100.00

2006 $30.50 101.33 $68,900.00 103.61

2007 $31.70 105.32 $70,600.00 106.17

2008 $32.50 107.97 $70,900.00 106.62

2009 $34.00 112.96 $71,200.00 107.07

2010 $35.50 117.94 $71,700.00 107.82

2011 $35.10 116.28 $72,500.00 109.02

2012 $35.05 16.61 $73,700.00 110.83

2013 $34.90 115.95 $73,400.00 110.38

2014 $33.80 112.29 $74,100.00 111.43

2015 $34.20 113.62 $74,000.00 111.28

Time-Series Plots

Both graphs show an upward trend with random components. The average material cost time series exhibits a cyclical component with a recurrence period of five years. The hourly wages time series may be indicating a cyclical component with a recurrence period of nine years. However, there is not enough data to determine if this pattern will repeat.

2. First we must convert hourly wages to reflect their impact on the cost of a house.

So, in 2005: 60%(cost of a house) = $66,500 Cost of a house = ($66,500)∕(60%) = $110,833 Labor cost = $110833 – $66,500 = $44,333

In 2010 60%(cost of a house) = $71,700 Cost of a house =($71,700)∕(60%) = $119,500 Labor cost = $119000 – $71,700 = $47,800

Paasche Index = 100 )44333(4.)66500(6.

)47800(4.)71700(6. 100

0

 +

+ =

 

PQ

PQ

t

tt = 107.82

where: Qt = Weighting percentage at time t Pt = Price in time period t P0 = Price in the base period

Laspeyres Index = 100 00

0 

 

PQ

PQ t

= 0.6(71700)+0.4(47800)

0.6(66500)+0.4(44333) × 100=

62140

57,633.20 × 100=107.82

where: P0 = Price in the base period

Both indices are the same as the weights are the same in 2005 and 2010.

3.a

Month Cash

Balance

2-Month Moving

Averages

3-Month Moving

Averages

1 75

2 70

3 77 72.50

4 89 73.50 74.00

5 80 83.00 78.67

6 92 84.50 82.00

7 91 86.00 87.00

8 102 91.50 87.67

9 106 96.50 95.00

10 130 104.00 99.67

11 155 118.00 112.67

12 160 142.50 130.33

13 180 157.50 148.33

14 199 170.00 165.00

15 240 189.50 179.67

16 305 219.50 206.33

Mean Square Error, MSE

1083.85 1522.74

Please note we calculating the MSE values starting in time period 4 for both forecasting techniques so that we can make a fair comparison between them. Since the 3 month moving average generates a lower MSE, we might conclude that 3 month moving average provides a better prediction than 2 month moving average.

0

50

100

150

200

250

300

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Time Period

Cash Balance 2-Month Moving Averages 3-Month Moving Averages

3b.

Alpha (α) 1.00

Month Cash

Balance Forecasted

1 75 75 2 70 75 3 77 70 4 89 77 5 80 89 6 92 80 7 91 92 8 102 91 9 106 102

10 130 106 11 155 130 12 160 155 13 180 160 14 199 180 15 240 199 16 305 240

MSE 564.93

0

50

100

150

200

250

300

350

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Time Period

Cash Balance Forecasted

3c.

SUMMARY OUTPUT for Linear Trend yhat = 24.225+12.966(t)

Regression Statistics

Multiple R 0.909

R Square 0.8268

Adjusted R Square 0.814

Standard Error 29.246

Observations 16

ANOVA

df SS MS F Sig F

Regression 1 57161.389 57161.39 66.830 1E-06

Residual 14 11974.549 855.3249

Total 15 69135.938

Coefficients Stand Error t Stat P-value Lower 95% Uppr95%

Intercept 24.225 15.3367 1.580 0.137 -8.669 57.119

t 12.966 1.5861 8.175 0.000 9.564 16.368

SUMMARY OUTPUT for Quadratic Trend yhat = 92.020 -9.632 (t) + 1.329 (t2)

Regression Statistics

Multiple R 0.986

R Square 0.9728

Adjusted R Square 0.9686 The Quadratic Trend Model seems to be better

Standard Error 12.029 since it has a higher Adj. R2 and a lower Standard

Observations 16 Error, indicating better fitness of the model.

ANOVA

df SS MS F Sig F

Regression 2 67254.81492 33627.40746 232.39118 6.69323E-11

Residual 13 1881.122584 144.7017372

Total 15 69135.9375

Coefficients Stand Error t Stat P-value Lower 95% Uppr 95%

Intercept 92.020 10.280 8.951 0.000 69.810 114.229

t -9.632 2.783 -3.461 0.004 -15.645 -3.619

t2 1.329 0.159 8.352 0.000 0.985 1.673

y = 1.3293x2 - 9.632x + 92.02 R² = 0.9728

y = 12.966x + 24.225

0

50

100

150

200

250

300

350

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

C a

sh B

a la

n ce

Time Period

Cash Balance

Poly. (Cash Balance)

Linear (Cash Balance)