The University of Montana

Department of Mathematical Sciences

Technical report #1/2004

Location and Scale Estimation with Correlation
Coefficients

**Rudy Gideon**

University of Montana

Missoula, MT 59812

and

**Adele Marie Rothan, CSJ**

College of St. Catherine

St. Paul, MN 55105

**Abstract**

This paper, one in a series on estimation with correlation coefficients, 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) show how to use Pearson's r as a test of normality. This paper shows and recommends that, at this same time, several correlation coefficients can be used to fit a simple linear regression line to the graph and to use the slope and intercept as estimates of standard deviation and location. A robust correlation will produce robust estimates. 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 possibly errant data points. Hypothesis testing and confidence intervals are illustrated for the scale parameter.

**Keywords:** simple linear regression, robust estimates, hypothesis
testing, confidence intervals

**AMS Subject Classification:** 62G05, 62G35

**Download Technical Report:** Adobe
pdf (77 KB)