How to Perform
Multiple Linear
Regression in R

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What is a Multiple Linear Regression?

Multiple linear regression is a statistical technique in which we have one dependent and several independent variables. Suppose the problem we are looking at can be treated as a problem of one dependent and several independent variables. In that case, it is suitable to use the multiple regression method for data analysis.

Where is linear regression usually used?

Multiple linear regression is a generalization of simple linear regression, in the sense that this approach makes it possible to evaluate the linear relationships between a response variable (quantitative) and several explanatory variables (quantitative or qualitative). 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 Multiple Regression Analysis

For example, a researcher wants to examine whether stress level and anxiety level predict test scores. In that case, we have one dependent variable – the exam result, and two independent variables – stress level and anxiety level.

Therefore, we test the following hypotheses:

Null hypothesis: The stress level and anxiety level do not significantly predict exam scores.

Alternative hypothesis: The stress level and anxiety level significantly predict exam scores.

R function to Compute Multiple Linear Regression

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

lm (DV~ IV1 +IV2,+…+IVx data = dataframe)

DV: dependent variable

IV: Independent variables

Running Simple Multiple Regression in Rstudio

In this section, we will show you how to run the multiple 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 multiple linear regression in APA format.

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

# PERFORM MULTIPLE LINEAR REGRESSION

reg <- lm(exams ~ anxiety + stress, data = data)
summary(regression)

> reg <- lm(exams ~ anxiety + 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 Multiple Linear Regression in R

Multiple regression was conducted to determine whether stress level and anxiety level predict exam scores. The equation for the regression line is

exam score = 60.72 + 1.26*anxiety level – 0.47*stress level

R-squared = 0.03, indicating that just 3% of the variance in exam scores is explained by stress level and anxiety level. The results of ANOVA were non-significant, F(2, 96) = 1.41, p = 0.249. We, therefore, fail to reject the null hypothesis that the slope of our regression line is zero and conclude that stress level and anxiety level do not significantly predict exam scores. Anxiety level is non-significant positive predictor of exam score (b = 1.26, p = 0.111). Stress level is non-significant negative predictor of exam score (B = -0.47, p = 0.546)

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How to Perform Multiple Linear Regression in R