Location and Scale Estimation with Correlation Coefficients. , unpublished paper (URL: http://www.math.umt.edu/gideon/locscale.pdf

This paper, third in a series on the correlation estimation system (CES), shows how to use any correlation coefficient to produce an estimate of location and scale. Since the normal distribution is so widely used, the method is illustrated using this distribution. Analyzers of normal data are advised to graph a quantile plot to check on the normality assumption before performing their data analysis; (Looney and Gulledge, 1985) shows how to use Pearson's pr as a test of normality. This paper shows that any correlation coefficient can be used to fit a simple linear regression line to a graph and then the slope and intercept are estimates of standard deviation and location. Because a robust correlation will produce robust estimates, this CES can be recommended as a tool for everyday data analysis. Tables of mean square error for simulations indicate that the median with this method using a robust correlation coefficient appears to be nearly as efficient as the mean with good data and much better if there are a few errant data points. Hypothesis testing and confidence intervals are illustrated for the scale parameter. Key words: simple linear regression, robust estimates, hypothesis testing, confidence intervals-2 This work depends in part on earlier unpublished work of Gideon and others and is available on the web site: www.math.umt.edu/gideon. Some of the references will refer to papers posted at this web site