# AREG - SPSS Trends

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## IntroductionEdit

The **A**uto**reg**ression procedure estimates true regression coefficients from time series
with first-order autocorrelated errors. It offers three algorithms. Two algorithms
(Prais-Winsten and Cochrane-Orcutt) transform the regression equation to remove
the autocorrelation. The third (maximum likelihood) uses the same algorithm that
the ARIMA procedure uses for estimating autocorrelation. Maximum-likelihood
(ML) estimation is more demanding computationally but gives better results—and it
can tolerate missing data in the series.mnnnnnnnnnnn

## ExampleEdit

Is the consumption of alcoholic spirits in any given year related to real per-capita income and the price level of the spirits in question for that year? A standard regression analysis may not be valid in this case because the variables represent time series. Most time series have some trend, either up or down, and any two trending series will correlate simply because of the trends, regardless of whether they are causally related or not. Autoregression allows you to remove the autocorrelation inherent in many time series and ascertain any statistically significant relationships between dependent variables and candidate regressors.

## StatisticsEdit

For the Prais-Winsten and Cochrane-Orcutt estimation methods: rho value with standard error, Dubin-Watson statistic, and mean squared error at each iteration; R, R², adjusted R², standard error of the estimate, analysis-of-variance table, and regression statistics for the ordinary least-square and final Prais-Winsten or Cochrane-Orcutt estimates. For the maximum-likelihood method: rho, regression coefficients, adjusted sum of squares, and Marquardt constant at each iteration. For the final maximum-likelihood parameter estimates: regression statistics, correlation matrix, covariance matrix, residual sum of squares, adjusted residual sum of squares, residual variance, model standard error, log-likelihood, Akaike’s information criterion, and Schwartz’s Bayesian criterion.

## MethodsEdit

Prais-Winsten, Cochrane-Orcutt, and Exact maximum-likelihood (equivalent to an ARIMA(1,0,0) model).

## DataEdit

The dependent variable and any independent variables should be numeric