Question

1) The worksheet Engines in the HW8 data workbook on Moodle describe a suppliers shipments of engines per year to their customers from 1999 through 2018.

a) Use simple regression with Shipments as the independent or Y variable and Year as the dependent or X variable to fit the data. Determine MAE, MSE and MAPE for the simple regression model. Construct a chart that has the observed data and the fit line by Year. Use the simple regression model to predict Shipments for years 2019 and 2020.

b) Use a three time period Moving Average to fit the rate data. Determine MAE, MSE and MAPE for the Moving Average model. Construct a chart that has the observed data and the fit line by Year. Use the Moving Average model to predict Shipments for years 2019 and 2020.

c) Use exponential smoothing with a smoothing constant of 0.15 to fit the data. Determine MAE, MSE and MAPE for the exponential smoothing model. Use the model to forecast Shipments for years 2019 and 2020.

d) Short answer. Which of the three above forecasting models (simple regression, moving average and exponential smoothing) would you use to model the data and why would you use that model.

Year	Shipments
1999	157
2000	168
2001	186
2002	171
2003	198
2004	222
2005	246
2006	233
2007	342
2008	413
2009	517
2010	588
2011	600
2012	524
2013	384
2014	403
2015	522
2016	604
2017	815
2018	955

Answer 1

a) The regression equation is
Shipments (Y) = - 68043 + 34.1 Year (X)

MAE, MSE and MAPE for the simple regression model

MAPE	20.96
MAD	80.669
MSD	10229.875

The Graph of the above model is

Predicted Shipments for years 2019 and 2020 is given below table.

Year	Shipment
2019	804.9
2020	839

b) The moving Average Chart is given below

The Accuracy measure of above model is given below

MAPE	23.2
MAE	118.3
MSE	22158.5

Predicted Shipments for years 2019 and 2020 is given below table.

Year	Shipment
2019	791.33
2020	791.33

c) The exponential smoothing chart with Alpha =0.15 is given below

The Accuracy measure of above model is given below.

MAPE	25.9
MAE	134
MSE	35590.1

Predicted Shipments for years 2019 and 2020 is given below table.

Year	Shipment
2019	625.83
2020	625.83

d) If we will compared the accuracy measure of above three model simple regression has the least among all. So it is better to have simple regression comparatively.

	Exponential Smoothing	Moving Average	Simple regression
MAPE	25.9	23.2	20.96
MAE	134	118.3	80.669
MSE	35590.1	22158.5	10229.875