How to fit a linear model to two columns of data (in R)

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Task

Let’s say we have two columns of data, one for a single independent variable $x$ and the other for a single dependent variable $y$. How can I find the best fit linear model that predicts $y$ based on $x$?

In other words, what are the model coefficients ${\beta }_0$ and ${\beta }_1$ that give me the best linear model $\hat{y}={\beta }_0+{\beta }_{1}x$ based on my data?

Related tasks:

• How to compute R-squared for a simple linear model
• How to fit a multivariate linear model
• How to predict the response variable in a linear model

Solution

This solution uses fake example data. When using this code, replace our fake data with your real data.

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# Here is the fake data you should replace with your real data.
xs <- c( 393, 453, 553, 679, 729, 748, 817 )
ys <- c(  24,  25,  27,  36,  55,  68,  84 )

# If you need the model coefficients stored in variables for later use, do:
model <- lm( ys ~ xs )
beta0 = model$coefficients[1]
beta1 = model$coefficients[2]

# If you just need to see the coefficients, do this alone:
lm( ys ~ xs )

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Call:
lm(formula = ys ~ xs)

Coefficients:
(Intercept)           xs  
   -37.3214       0.1327  

The linear model in this example is approximately $y=0.133x-37.32$.

Content last modified on 24 July 2023.

See a problem? Tell us or edit the source.

Contributed by Nathan Carter (ncarter@bentley.edu)