A Measure of Linearity

In determining if a set of bivariate data can be accurately modeled by a linear function, one could use linear regression and the value of [R.sup.2]. Unfortunately, some published resources have been found to incorrectly interpret a high value of [R.sup.2] as evidence of a linear relationship between the variables. Indeed, at times the values of the variables may be independent of each other and a linear regression may not be appropriate. Herein, using only mathematics from grades 10-14, we propose a novel measure, [Q.sup.2], to indicate the measure of linearity of a scatterplot of points. While [Q.sup.2] shares many of the properties of [R.sup.2], [Q.sup.2] is invariant under rotation, and so is a more appropriate tool to compare two independent data sets for linearity. Herein, rather than presenting either [Q.sup.2] or [R.sup.2] as superior to the other, we propose the complementary nature of the two measures and that, by investigating [Q.sup.2], students can gain deeper understanding of [R.sup.2]. This paper provides a link to a dynamic applet and instructions to accompany the reading and assist the reader to further investigate this topic and glean additional insights.