It is the proportion of the variance in the response variable that can be explained by the predictor variable. This is often written as r 2, and is also known as the coefficient of determination. In this example, the multiple R is 0.72855, which indicates a fairly strong linear relationship between the predictors study hours and prep exams and the response variable final exam score. Multiple R is the square root of R-squared (see below). A multiple R of 1 indicates a perfect linear relationship while a multiple R of 0 indicates no linear relationship whatsoever. It measures the strength of the linear relationship between the predictor variables and the response variable.
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Here is how to interpret each of the numbers in this section: Multiple R how well the regression model is able to “fit” the dataset. The first section shows several different numbers that measure the fit of the regression model, i.e.
To analyze the relationship between hours studied and prep exams taken with the final exam score that a student receives, we run a multiple linear regression using hours studied and prep exams taken as the predictor variables and final exam score as the response variable. Suppose we have the following dataset that shows the total number of hours studied, total prep exams taken, and final exam score received for 12 different students: This tutorial walks through an example of a regression analysis and provides an in-depth explanation of how to read and interpret the output of a regression table. It’s important to know how to read this table so that you can understand the results of the regression analysis.
When you use software (like R, SAS, SPSS, etc.) to perform a regression analysis, you will receive a regression table as output that summarize the results of the regression. In statistics, regression is a technique that can be used to analyze the relationship between predictor variables and a response variable.
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