**ERIC Number:**ED445073

**Record Type:**RIE

**Publication Date:**2000-Jan

**Pages:**21

**Abstractor:**N/A

**Reference Count:**N/A

**ISBN:**N/A

**ISSN:**N/A

Moving the Bar: Transformations in Linear Regression.

Miranda, Janet

The assumption that is most important to the hypothesis testing procedure of multiple linear regression is the assumption that the residuals are normally distributed, but this assumption is not always tenable given the realities of some data sets. When normal distribution of the residuals is not met, an alternative method can be initiated. As an alternative, data for one or more of the variables under study can be transformed in order to increase conformity to the required distributional assumptions of linear regression. Such transformations are discussed in this paper, including: (1) transforming data by powers and roots; (2) transforming for skewness; (3) transforming for non-linearity; (4) transforming for non-constant spread; and (5) transforming proportions via probit analysis and logit analysis. Power and root transformations provide a means for improving data distributions and at the same time preserve the directionality of "X." A skewed distribution, represented by a set of scores that form a non-symmetrical curve when plotted on a frequency graph, can be transformed by ascending the ladder of powers to correct a negative skew or descending the ladder of powers to correct a positive skew. For dichotomous quantities, logit and probit are the data transformations best applied. A logit transforms both the upper and lower boundaries of the scale. The probit is similar to the logit but in a different metric. Transformations are useful in examining and modeling data when the assumptions of linear regression are not met. Such transformations do indeed change the original research question. By manipulation of the data, the question is also "transformed." An appendix contains a table of sample data. (Author/SLD)

**Publication Type:**Reports - Descriptive; Speeches/Meeting Papers

**Education Level:**N/A

**Audience:**N/A

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A

**Note:**Paper presented at the Annual Meeting of the Southwest Educational Research Association (Dallas, TX, January 27-29, 2000).