In statistics, the multiple linear regression analysis is an approach to model the relationship between a response variable and several explanatory variables. Typically, a researcher will collect data on several potential explanatory variables, determine which variables are most strongly associated with the response variable, and then incorporate these variables into a mathematical model (a regression equation). The purpose of multiple linear regression analysis, then, is to identify which combination of variables best predicts the response variable.

Here, we suggest some guidelines for reporting a multiple linear regression analysis.

A statement that the assumptions were verified is all that need be included. The assumptions of a multiple linear regression are as follows: 1) The relationship between each explanatory variable and response variable is linear; 2) The distributions of response variables have equal variances at each value of each explanatory variable; 3) Each response variable value is independent of one another for each value of each explanatory variable; and 4) The response variable has a normal distribution at each value of each explanatory variable. Sometimes, data that violate the assumptions can be adjusted (for example, with data transformation) to meet the required assumptions. If such adjustments are made, it should be noted.

Describe the process of selecting the best combination of explanatory variables when the variable selection methods such as stepwise, forward, or backward selection, were used. State whether explanatory variables were assessed for multi-collinearity and tested for interaction.

An example for reporting a multiple linear regression with three explanatory variables is presented in Table 1.2)

The coefficient of multiple determination (R²) indicates how much of the variation in the response variable is explained by the explanatory variables included in the model. An upper-case R should be used.

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