~ 10 ~
Figure 6. Quadratic model
The above regression results showed that the most optimal model for us is the quadratic model.
Y^=0.000237*x1-180.364*x2 + 1577222*x3-1138162*a2-550165.1+e
The model we built is almost close to the actual values. We refer to the Durbin-Watson test to check whether there is autocorrelation
between the variables. We calculate residuals and check autocorrelation using Stata software.
.
predict ehat, res
. ac ehat, gen(rk)
. Durbin-Watson d-statistic( 5, 10) = 2.477046
In the figure below, we can see that the 95% confidence band appears in the shaded area. It can be seen that there is no autocorrelation.
Figure 8. Durbin-Watson test results
The next step is to check the normal distribution of the residuals. We do this using the .hist ehat, norm command. From the graph below, we
can see that the residuals are almost normally distributed.
Figure 9. Normal distribution of residuals
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Lag
Bartlett's formula for MA(q) 95% confidence bands
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Residuals
~ 11 ~
At
the next stage of forecasting, we find the next values of all
variables. We calculate the lag values of each variable. For this,
we find
the regression of each variable and its lag.
We give the command reg x1 L.x1 and find the value of variable x1
in the last year 2021 using the formula di _b[_cons]+_b[L1.]*34081448.
We find the forecast value by the lag value of the remaining variables.
Before finding the forecast value for the next year, we perform the
last regression command. reg Y x1 x2 x3 a2 we find through each lag
value.
dib[_cons]+_b[x1]*34644493+_b[x2]*6.49+_b[x3]*0.729+_b[a2]
*0.531=2332.9658
According to our forecasts, GDP per capita for 2022 will be
$2,332,965.
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