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In statistics, linear regression models are used to quantify the relationship between one or more predictor variables and a response variable.

We can use the following general format to report the results of a simple linear regression model:

Simple linear regression was used to test if [predictor variable] significantly predicted [response variable].

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The fitted regression model was: [fitted regression equation]

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The overall regression was statistically significant (R

^{2}= [R^{2}value], F(df regression, df residual) = [F-value], p = [p-value]).Â

It was found that [predictor variable] significantly predicted [response variable] (Î² = [Î²-value], p = [p-value]).

And we can use the following format to report the results of a multiple linear regression model:

Multiple linear regression was used to test if [predictor variable 1], [predictor variable 2], â€¦ significantly predicted [response variable].

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The fitted regression model was: [fitted regression equation]

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The overall regression was statistically significant (R

^{2}= [R^{2}value], F(df regression, df residual) = [F-value], p = [p-value]).Â

It was found that [predictor variable 1] significantly predicted [response variable] (Î² = [Î²-value], p = [p-value]).

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It was found that [predictor variable 2] did not significantly predict [response variable] (Î² = [Î²-value], p = [p-value]).

The following examples show how to report regression results for both a simple linear regression model and a multiple linear regression model.

**Example: Reporting Results of Simple Linear Regression**

Suppose a professor would like to use the number of hours studied to predict the exam score that students will receive on a certain exam. He collects data for 20 students and fits a simple linear regression model.

The following screenshot shows the output of the regression model:

Here is how to report the results of the model:

Simple linear regression was used to test if hours studied significantly predicted exam score.

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The fitted regression model was: Exam score = 67.1617 + 5.2503*(hours studied).

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The overall regression was statistically significant (R

^{2}= .73, F(1, 18) = 47.99, pÂ

It was found that hours studied significantly predicted exam score (Î² = 5.2503, p

**Example: Reporting Results of Multiple Linear Regression**

Suppose a professor would like to use the number of hours studied and the number of prep exams taken to predict the exam score that students will receive on a certain exam. He collects data for 20 students and fits a multiple linear regression model.

The following screenshot shows the output of the regression model:

Here is how to report the results of the model:

Multiple linear regression was used to test if hours studied and prep exams taken significantly predicted exam score.

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The fitted regression model was: Exam Score = 67.67 + 5.56*(hours studied) â€“ 0.60*(prep exams taken)

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The overall regression was statistically significant (R

^{2}= 0.73, F(2, 17) = 23.46, p =Â

It was found that hours studied significantly predicted exam score (Î² = 5.56, p =

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It was found that prep exams taken did not significantly predict exam score (Î² = -0.60, p = 0.52).

**Additional Resources**

How to Read and Interpret a Regression Table

Understanding the Null Hypothesis for Linear Regression

Understanding the F-Test of Overall Significance in Regression