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Simple Linear Regression in R

Last Update: February 21, 2022

Simple linear regression in R can be fitted using stats package lm function. Main parameters within lm function are formula with y ~ x model description and data with data.frame object including model variables. Therefore, lm(y ~ x, data = code line fits model \hat{y}_{i} = \hat{\beta}_{0} + \hat{\beta}_{1} x_{i} using variables included within object.

As example, we can fit simple linear regression of house price explained by its lot size using data included within AER package HousePrices object [1].

First, we load packages AER for data and ggplot2 for charting [2].

In [1]:

Second, we create HousePrices data object from AER package using data function and print first six rows and two columns of data using head function to view data.frame structure.

In [2]:
Out [2]:
  price lotsize
1 42000    5850
2 38500    4000
3 49500    3060
4 60500    6650
5 61000    6360
6 66000    4160

Third, we draw scatter chart with regression line which doesn’t display its confidence interval.

In [3]:
ggplot(data = HousePrices, aes(x = lotsize, y = price)) +
  geom_point() +
  geom_smooth(method = "lm", se = FALSE)
Out [3]:
Figure 1. Simple linear regression scatter chart of house price explained by its lot size.

Fourth, we fit model with lm function using variables within HousePrices data object, store outcome within slr object and print its coefficients estimates. Within lm function, parameter formula = price ~ lotsize fits model \hat{price} = \hat{\beta}_{0} + \hat{\beta}_{1} lotsize where house price is explained by its lot size.

In [4]:
slr <- lm(formula = price ~ lotsize, data = HousePrices)
Out [4]:
lm(formula = price ~ lotsize, data = HousePrices)

(Intercept)      lotsize  
  34136.192        6.599


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[1] Data Description: Sales prices of houses sold in the city of Windsor, Canada, during July, August and September, 1987.

Original Source: Anglin, P., and Gencay, R. (1996). Semiparametric Estimation of a Hedonic Price Function. Journal of Applied Econometrics, 11, 633–648.

[2] AER R Package. Christian Kleiber and Achim Zeileis. (2008). Applied Econometrics with R. Springer-Verlag, New York.

ggplot2 R Package. Hadley Wickham (2016). ggplot2: Elegant Graphics for Data Analysis. Springer-Verlag, New York.

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