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].
The fitted regression model was: [fitted regression equation]
The overall regression was statistically significant (R2 = [R2 value], F(df regression, df residual) = [F-value], p = [p-value]).
It was found that [predictor variable] significantly predicted [response variable] (β = [β-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], … significantly predicted [response variable].
The fitted regression model was: [fitted regression equation]
The overall regression was statistically significant (R2 = [R2 value], F(df regression, df residual) = [F-value], p = [p-value]).
It was found that [predictor variable 1] significantly predicted [response variable] (β = [β-value], p = [p-value]).
It was found that [predictor variable 2] did not significantly predict [response variable] (β = [β-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.
The fitted regression model was: Exam score = 67.1617 + 5.2503*(hours studied).
The overall regression was statistically significant (R2 = .73, F(1, 18) = 47.99, p < .000).
It was found that hours studied significantly predicted exam score (β = 5.2503, p < .000).
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.
The fitted regression model was: Exam Score = 67.67 + 5.56*(hours studied) – 0.60*(prep exams taken)
The overall regression was statistically significant (R2 = 0.73, F(2, 17) = 23.46, p = < .000).
It was found that hours studied significantly predicted exam score (β = 5.56, p = < .000).
It was found that prep exams taken did not significantly predict exam score (β = -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
how to report simple linear regression for various independent and one dependent variable?
@Zach
Really appreciated your effort in effective stat coach across varied versions and types of statistics.
After having all these guides throuh exploratory knowledge keeping silence is just selfishness!
Thanksgiving 🙏🙏
thanks for the information about the reporting of regression analyses. i have a question and I really need an answer and help. one of my researchs is rejected because of its method. the reviewer says whether an independent variable is a risk for the development of the dependent variable cannot be answered by the design of a cross-sectional study. the reviewer says that It is not a prospective study, it is a cross-sectional study and there is no patient follow-up so no risk can be estimated, only associations. As all variables are collected at the same time it is not possible to know which is the cause and which is the consequence.
how can i report the result of a regression analyse made by using cross-sectional data? can i say that the independent variable predicts the dependent variable? can i use the words predict, predictor, prediction, etc?
if I had a student report a p value of <.000 on an assignment, I would fail the assignment. How on earth can you have a p value that is negative or zero?? It's impossible!
thank you very much this helped a lot
Missing very important elements. You need to show an APA 7 example of a regression equation being reported including the generic equation and use of appropriate symbols (e.g. for weights). This would take the form (with the equation number right-aligned):
equation (of course centered) (1)
This is per APA 7. This is an essential part of reporting results. Note one uses the unstandardized coefficients to report the equation but the standardized (beta) coefficients to speak to relative strength (effect) of predictors.
You have really helped me. Thank you very much. You have simplified work for a non statistician.
Thank you very much, that was helpful