How to Perform
Simple Linear
Regression in R

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What is a Simple Linear Regression?

Regression analysis is a statistical technique used to show the relationship between two variables that estimate the value of the dependent variable Y based on the selected value of the independent variable X. Regression aims to determine the nature of the relationship, that is, the form of dependence between observed phenomena. We achieve this using a suitable regression model, which is the closest to the quantitative agreement of the variations of the observed phenomena. In simple regression analysis, we have one dependent and one independent variable.

Where is linear regression usually used?

Linear regression is commonly used for predictive analysis and modeling. For example, it can be used to quantify the relative impacts of age, gender, and diet (the predictor variables) on height (the outcome variable).

An Example Of Simple Regression Analysis

For example, a researcher wants to examine whether stress level predicts test scores. Stress level is the independent variable, and exam score is the dependent variable.

Therefore, we test the following hypotheses:

Null hypothesis: The stress level does not significantly predict exam scores.

Alternative hypothesis: The stress level significantly predicts exam scores.

R function to Compute Simple Linear Regression

The code to run a Linear Regression using R is as follows:

lm (DV~ IV, data = dataframe)

DV: dependent variable

IV: Independent variable

Running Simple Linear Regression in Rstudio

In this section, we will show you how to run the simple linear regression using the r studio program and how to interpret the test results after we obtain the result of the test. In the first part, we present the r program code and function for the linear regression analysis. Next, you will see the outputs as a result of running the r codes. In the last section, you can find the interpretation of the simple linear regression in APA format.

# LOAD DATA
library(readxl)
Data <- read_excel(“Data.xlsx“)
# VIEW DATA
View(Data)
# NAME VARIABLES
data <- Data
stress <- data$stress
exams <- data$exams

# PERFORM SIMPLE LINEAR REGRESSION
regression <- lm(exams ~ stress, data = data)
summary(regression)

> regression <- lm(exams ~ stress, data = data)
> summary(regression)

## 
## Call:
## lm(formula = exams ~ stress, data = data)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -31.50 -15.87  -8.88  22.82  34.76 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  67.2573     4.6028  14.612   <2e-16 ***
## stress       -0.3769     0.7793  -0.484     0.63    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 21.55 on 97 degrees of freedom
## Multiple R-squared:  0.002406,   Adjusted R-squared:  -0.007879 
## F-statistic: 0.2339 on 1 and 97 DF,  p-value: 0.6297

Reporting Simple Linear Regression in R

Simple linear regression was conducted to determine whether stress level predicts exam scores. The equation for the regression line is

exam score = 67.26 – 0.38*stress level

R-squared = 0.002, indicating that just %0.20 of the variance in exams score is explained by the stress level. The results of ANOVA were non-significant, F(1, 97) = 0.23, p = 0.63. We, therefore, fail to reject the null hypothesis that the slope of our regression line is zero and conclude that stress level does not significantly predict exam scores. Stress level is non-significant negative predictor of exam score (b = -0.38, p = 0.63).

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How to Perform Simple Linear Regression in R