On R2, Adjusted R2, Mean Squared Error, Penalty Factors, and Model Selection
Akaike AIC is a methodology of how to choose correct variables. Another methodology
is Schwarz Basium criterion (known as SBC in JMP). These are model selection
methodologies. Th
Residual Analysis
Residual by Predicted Plot
With the residual plot above, you can see that there is not really a problem with
heterscadicity.
The R^2 is very high at .98, but this is not really because its such a wonderful fit. Rather,
its due to the nat
Null Hypothesis
This discussion indicates that adjusted R2 can serve as a model selection criterion. We
choose the model for which adjusted R2 is maximum. The factor
yields a penalty factor, as we show below. Many model selection criteria have been
propos
Nonconstant Variance
The plot displays evidence of nonconstant variance (at some time levels, there is more
volatility than others). To try to fix this, lets consider the logged data. There are,
however, ten months during which rainfall was 0, and we cann
Measuring Total Variation
We measure the total variation in the yt values, the original data, by
This is the sample variance of the yt values without division by n 1. R2, the
percentage of the variation of the yt values explained by the variables included
H Variables
H0 states that variable xkt does not enter model (1). The hypothesis is tested via the
t-statistic, which can be calculated as follows in two steps:
1. Fit two models to the data, the full model given by (1), and the reduced model,
(2)
yt = +
Lack of Collinearity
Because of the lack of any collinearity, the estimates and sums of squares for the
parameters in the reduced model fit are the same as in the previous analysis. The
standard errors of the estimates and the t ratios and accompanying p-
Amplitude and Phase Estimates
Amplitude
Fundamental
First harmonic
3.274
1.570
Phase
Degrees Radians
326.03
124.48
5.690
2.173
Peak t (period)
1.133 (12)
3.925, 9.925 (6)
You can see that the fundamental is much stronger than the first harmonic, and the
f
Sin and Cos Dummy Variables
The good thing about using sin and cos as dummy variables is that there is no
collinearity between them. No correlation between any of the explanatory variables,
even the pairs. The result of that is that you can see how much e