Question

1- Nelson Industries manufactures a part for a type of aircraft engine that is becoming obsolete. The sales history for the last 10 years is as follows:

year    sales

Dec-98 945

Dec-99 875

Dec-00 760

Dec-01 690

Dec-02 545

Dec-03 420

Dec-04 305

Dec-05 285

Dec-06 250

Dec-07 210

1. Estimate the regression model for a linear time trend of sales.
2. What is the root-mean-squared error of the linear regression estimates for these 10 years?
3. Using this model, estimate sales for year 11.

Answer 1

1- Nelson Industries manufactures a part for a type of aircraft engine that is becoming obsolete. The sales history for the last 10 years is as follows:

year    sales

Dec-98 945

Dec-99 875

Dec-00 760

Dec-01 690

Dec-02 545

Dec-03 420

Dec-04 305

Dec-05 285

Dec-06 250

Dec-07 210

Estimate the regression model for a linear time trend of sales.

Yt = 1016.7 - 88.76×t

What is the root-mean-squared error of the linear regression estimates for these 10 years?

MSD

2357.52

root-mean-squared error = sqrt(2357.52)

=48.5543

Using this model, estimate sales for year 11.

When t=11,

Estimated sales =1016.7 - 88.76*11

=40.34

Trend Analysis for sales

Method

Model type	Linear Trend Model
Data	sales
Length	10
NMissing	0

Fitted Trend Equation

Yt = 1016.7 - 88.76×t

Accuracy Measures

MAPE	12.03
MAD	40.79
MSD	2357.52

Forecasts

Period	Forecast
11	40.3333

Model Summary

Time	sales	Trend	Detrend
1	945	927.909	17.0909
2	875	839.152	35.8485
3	760	750.394	9.6061
4	690	661.636	28.3636
5	545	572.879	-27.8788
6	420	484.121	-64.1212
7	305	395.364	-90.3636
8	285	306.606	-21.6061
9	250	217.848	32.1515
10	210	129.091	80.9091