Question 513:

Asked on November 17, 2008

Tags: Regression Analysis , Time-Series , autocorrelation

1

Answer:

No answer provided yet.

You are dealing with one person and successive scores of progress for that 1 person over time. You can use regression, however you are likely violating the model's assumption of independence between observations and error terms. If we consider your data like say, the total sales of a product over time and correlate that to some external factor, like industry sales, we'd have something similar, would you agree? That is, you'd have n=1 product and the sales data would be akin to your performance scores. There is only 1 Y per data-point X (say by quarter). I do see this then as a time-series analysis.

It is my understanding with time series regression that you are dealing with autocorrelation, that is, the error terms are correlated with each other. This makes sense since we'd expect one data-point to have an effect on the subsequent data points.  With autocorrelated data the regression model needs to be modified to deal with this violation of independence.

It might not be the case that your data are autocorrelated. You'd want to setup your regression model with the data, store the residuals, then plot the residuals over time to see if there is a correlation. The Durbin-Watson statistic provides a p-value on the null-hypothesis that the error correlation is 0. What stats package are you using to run the data?

To correct the autocorrelation and have a valid regression model and standard error for prediction, you can include a categorical times series variable, or transform the variable. This procedure is outline for example in Applied Linear Statistics Models by Neter et al , page 497-520 as well as in Statistics for Experimenters Box, Hunter and Hunter Chapter 18.

Without seeing your data or fully understanding the objective of the 1 person's scores over time (e,g. are you trying to predict the next value with a confidence interval?) .  In addition to autocorrelation and dependence, the other issue is whether your X variable has a linear relationship with the Y. 

I hope I've provided you with some insight. If you send me a sample of your data, I'd be happy to take a look and see if I can better understand your research goal and perhaps suggest either alternatives or more clarification down the path you're going with time-series.