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When reporting regression results, it is important to provide a summary of the main findings, including the estimated parameters or coefficients, the goodness-of-fit measures, and any relevant statistics. It is also important to discuss the implications of the findings, and the limitations of the analysis. Additionally, it is important to provide sufficient information for readers to be able to replicate the analysis.
In statistics, linear regression models are used to quantify the relationship between one or more predictor variables and a .
We can use the following general format to report the results of a :
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 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).