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FIT Procedure: Evaluating Model Fitness with Descriptive Statistics, Study notes of Mathematical Statistics

Alliance UniversityMathematical Statistics

The fit procedure is a statistical tool used to assess the goodness of fit of one or more models by displaying various descriptive statistics computed from the residual series. The notation used and the statistics computed, including mean error, mean percent error, mean absolute error, mean absolute percent error, sum of square error, mean square error, root mean square error, and durbin-watson statistics.

Typology: Study notes

2011/2012

Uploaded on 10/31/2012

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1
FIT
Procedure FIT displays a variety of descriptive statistics computed from the
residual series as an aid in evaluating the goodness of fit of one or more models.
Notation
The following notation is used throughout this chapter unless otherwise stated:
DFH Hypothesis degrees of freedom
DFE Error degrees of freedom
ee
n1,,K Residual (error) series
XX
n1,,K Observed series
n Number of cases
Statistics Computed in FIT
Mean Error (ME)
ME e n
i
i
n
=
=
โˆ‘
1
Mean Percent Error (MPE)
MPE neX
ii
i
n
=
=
โˆ‘
100
1
pf3

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1

Procedure FIT displays a variety of descriptive statistics computed from theresidual series as an aid in evaluating the goodness of fit of one or more models.

Notation

The following notation is used throughout this chapter unless otherwise stated: DFH Hypothesis degrees of freedom DFE Error degrees of freedom e 1 , K, en Residual (error) series X 1 , K, X (^) n Observed series n Number of cases

Statistics Computed in FIT

Mean Error (ME)

ME e (^) i n i

= n โˆ‘= 1

Mean Percent Error (MPE)

MPE (^) n ei Xi i

= n โˆ‘=

1

Mean Absolute Error (MAE)

MAE e (^) i n i

= n โˆ‘= 1

Mean Absolute Percent Error (MAPE)

MAPE (^) n e (^) i Xi i

= n โˆ‘=

1

Sum of Square Error (SSE)

SSE ei i

= n โˆ‘= 2 1

Mean Square Error (MSE)

MSE

SSE n DFE DFH SSE DFE DFE DFH DFE n DFH

% &KK 'KK

if none of and is specified if is specified or is specified; then = -.

Root Mean Square Error (RMS)

RMS = MSE