- Thread starter Sylviastat
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Sylvia

You

So, one solution is to first do a regression,

then calculate the residuals,

then estimate their AR(1) coefficient rho (in essence the degree of autocorrelation) by regressing all residuals onto their previous values,

then use this value to remove the autocorrelation (this is called pre-whitening),

then regress again (couple of extra tricks there)

All this has to be done with rather meticulous attention to detail, so unless you feel heroic it would be best to use a standard package for it ... don't know if it's in SPSS or STATA but surely there is a package for R!

You

So, one solution is to first do a regression,

then calculate the residuals,

then estimate their AR(1) coefficient rho (in essence the degree of autocorrelation) by regressing all residuals onto their previous values,

then use this value to remove the autocorrelation (this is called pre-whitening),

then regress again (couple of extra tricks there)

All this has to be done with rather meticulous attention to detail, so unless you feel heroic it would be best to use a standard package for it ... don't know if it's in SPSS or STATA but surely there is a package for R!

You

So, one solution is to first do a regression,

then calculate the residuals,

then estimate their AR(1) coefficient rho (in essence the degree of autocorrelation) by regressing all residuals onto their previous values,

then use this value to remove the autocorrelation (this is called pre-whitening),

then regress again (couple of extra tricks there)

All this has to be done with rather meticulous attention to detail, so unless you feel heroic it would be best to use a standard package for it ... don't know if it's in SPSS or STATA but surely there is a package for R!

This indeed is not easy. Is there a way to do something simpler - like doing a normal regression and then extrapolating the trend? (if so what to do with years - can it be treated as independent varaible or does it need to be transformed?)

and how about a logistic curve? does it make sense to do logistic regression and then extrapolate (how?)

THANKS

So, all you need then is an ordinary least squares regression with time as independent variable (no transformation). Write down the equation for the modeled function (linear, logit, whatever), plug in the year 2020, and tell us our future

So, all you need then is an ordinary least squares regression with time as independent variable (no transformation). Write down the equation for the modeled function (linear, logit, whatever), plug in the year 2020, and tell us our future

Coefficients(a)

Unstandardized Coefficients Standardized Coefficients

Model B Std. Error

Beta t Sig.Unstandardized Coefficients Standardized Coefficients

Model B Std. Error

1 (Constant) -1.631E8 4801028.350 -33.973 .000

Year 83544.071 2407.111 .989 34.707 .000

a. Dependent Variable: Singapore

Beta is 83,544

how should I treat variable "year" in the equation?

y=83544*t-163100000

Plug t=2010 into this, and get about 4.8 million, which is (Wikipedia ... Singapore ... hang on ...) quite close to the 2010 population of Singapore?

BUT: The population before ca. 1952 was negative according to this model - maybe you need to consider e.g. an exponential instead ...

y=83544*t-163100000

Plug t=2010 into this, and get about 4.8 million, which is (Wikipedia ... Singapore ... hang on ...) quite close to the 2010 population of Singapore?

BUT: The population before ca. 1952 was negative according to this model - maybe you need to consider e.g. an exponential instead ...

Another way of looking at it would be that for each year we would get 83,544 extra people, correct?

I will also try logistic reg to compare.

I've sort of been wondering this the entire thread... How are you going to use logistic regression here? What outcome are you modeling?

If you have a suggestion for a not very complex model, please do let me know.

for parameters

This model is difficult to linearize by transformation (at least if all three parameters have to be estimated), so you may have to use a nonlinear regression method .

for parameters

This model is difficult to linearize by transformation (at least if all three parameters have to be estimated), so you may have to use a nonlinear regression method .

This is the output:

Logistic

Model Summary

R R Square Adjusted R Square Std. Error of the Estimate

.995 .990 .990 .014

The independent variable is Year.

ANOVA

Sum of Squares df Mean Square F Sig.

Regression .569 1 .569 2771.558 .000

Residual .006 27 .000

Total .575 28

The independent variable is Year.

Coefficients

Unstandardized Coefficients Standardized Coefficients

B Std. Error Beta t Sig.

Year .984 .000 .370 3166.533 .000

(Constant) 537904.449 338891.324 1.587 .124

The dependent variable is ln(1 / SEAsia).

Is A- contsant, B- year? where is C?........

for parameters

This model is difficult to linearize by transformation (at least if all three parameters have to be estimated), so you may have to use a nonlinear regression method .

we used NCSS statistical package to estimate the parameters of the logistic curve because - unlike SPSS - its logaritm does not require a user defined value for the upper asymptote" (A)....

Yes.

This is the output:

Logistic

Model Summary

R R Square Adjusted R Square Std. Error of the Estimate

.995 .990 .990 .014

The independent variable is Year.

ANOVA

Sum of Squares df Mean Square F Sig.

Regression .569 1 .569 2771.558 .000

Residual .006 27 .000

Total .575 28

The independent variable is Year.

Coefficients

Unstandardized Coefficients Standardized Coefficients

B Std. Error Beta t Sig.

Year .984 .000 .370 3166.533 .000

(Constant) 537904.449 338891.324 1.587 .124

The dependent variable is ln(1 / SEAsia).

Is A- contsant, B- year? where is C?........

This is the output:

Logistic

Model Summary

R R Square Adjusted R Square Std. Error of the Estimate

.995 .990 .990 .014

The independent variable is Year.

ANOVA

Sum of Squares df Mean Square F Sig.

Regression .569 1 .569 2771.558 .000

Residual .006 27 .000

Total .575 28

The independent variable is Year.

Coefficients

Unstandardized Coefficients Standardized Coefficients

B Std. Error Beta t Sig.

Year .984 .000 .370 3166.533 .000

(Constant) 537904.449 338891.324 1.587 .124

The dependent variable is ln(1 / SEAsia).

Is A- contsant, B- year? where is C?........

After further reading it seems that I will have to estimate A (upper asymptote - population ceiling), but which is B and which is C from the above output? please help.

After further reading it seems that I will have to estimate A (upper asymptote - population ceiling), but which is B and which is C from the above output? please help.

If you use a nonlinear procedure instead, you can fit all three parameters simultaneously.

(The program Past does this automatically by first setting a to the max value of the data as an initial guess, then estimating b and c by linearization and regression, then optimizing all the parameters with the Levenberg method).

Correct, if you want to fit the logistic function using linearization, you must estimate *a* independently. Honestly I don't quite understand what transformation SPSS did for you (it says the dependent variable is (1/SEAsia), which I can't quite fit in with the logistic model?).

If you use a nonlinear procedure instead, you can fit all three parameters simultaneously.

(The program Past does this automatically by first setting a to the max value of the data as an initial guess, then estimating b and c by linearization and regression, then optimizing all the parameters with the Levenberg method).

If you use a nonlinear procedure instead, you can fit all three parameters simultaneously.

(The program Past does this automatically by first setting a to the max value of the data as an initial guess, then estimating b and c by linearization and regression, then optimizing all the parameters with the Levenberg method).

Here is the area and the equation:

y=1 / ( 0 + 13677.83972385804 * 0.9853271471417606**x )

graph doesnt want to copy...

But I think it's ok. It is South East Asia. Based on the above formula, I can announce that he population of South East Asia in 2025 will be 730,423,364

Next ARIMA, but that will be a long process..........