# SAGE Journal Articles

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**Summary/Abstract: **It is well known that multiple correlation analysis (MCA) calculations and multiple regression analysis (MRA) calculations overlap a bit. What has not been routinely recognized is that the two analysis procedures involve different research questions and study designs, different inferential approaches, different analysis strategies, and different reported information. These differences are described.

#### Questions to Consider:

1. What are the similarities and difference between multiple correlation analysis (MCA) and multiple regression analysis (MRA)?

2. The research question associated with an multiple regression analysis is:

- the relationship between a single response variable (Y) on one hand and a collection of response variables (Xs) on the other hand.
- the relationship between a single response variable (Y) on one hand and using scores on a collection of predictor variables (Xs) on the other hand.
- one of prediction of a criterion variable (Y) score using scores on a collection of predictor variables (Xs).
- one of prediction of a criterion variable (Y) score and a collection of response variables (Xs).

3. The terms ___________ and ___________should not be used in a multiple correlation analysis context.

- skewness; kurtosis
- bias; unbiased
- causal; relationship
- independent variable; dependent variable

**Summary/Abstract: **We have examined the regression effect and its magnitude under the Gaussian distributional assumption. The impact and implication of regression to the mean on the analysis of medical investigations was discussed. For simplicity, we called the approach adjusting for the regression effect a two-stage procedure and noted its relationship to the analysis of covariance model for comparing treatment groups. We also proposed to examine the correlation structure among repeated measurements in the absence of any external interventions through a model more realistic than the one assuming equal correlations. The proposed structure led us to investigate ways to reduce or eliminate regression effect via study designs when patient selection is inevitable. Two examples were given to help illustrate the discussion in this paper.

#### Questions to Consider

1. How is the regression effect related to the distance between a sample mean and a population mean?

2. In order to discount the regression effect, researchers must discount the observed mean change by the amount due to the regression effect. This two-stage process is accomplished by which the following procedures?

- During the first stage, each observed change d is adjusted for the regression effect to yield d*. The adjusted change d* is then averaged in the second stage to obtain the estimated regression effect.
- During the first stage, each observed change d is adjusted for the regression effect to yield d*. The adjusted change d* is then subtracted from d*.
- During the first stage, each score is averaged to yield d*. The adjusted change d* is then averaged in the second stage to obtain the estimated regression effect.
- During the first stage, the regression effect is added to the obtained scores. The adjusted change d* is then averaged in the second stage to obtain the estimated regression effect.

3. The author states that the regression effect can be reduced by basing the selection of individuals:

- on a single measurement.
- on the average of several measurements, instead of a single measurement.
- on a select few measurements.
- whose performance is close to the population mean.