# Linear Regression: Coefficients Analysis in R

Last Update: February 21, 2022

Linear Regression: Coefficients Analysis in R can be done using `stats` package `lm`, `summary.lm` functions and `coefficients` value for analyzing linear relationship between one dependent variable and two or more independent variables. It is also used for evaluating whether adding independent variables individually improved linear regression model. Main parameters within `lm` function are `formula` with `y ~ x1 + … + xp` model description and `data` with `data.frame` object including model variables. Main parameter within `summary.lm` function is `object` with previously fitted `lm` model.

As example, we can estimate coefficients table from multiple linear regression of house price explained by its lot size and number of bedrooms using data included within `AER` package `HousePrices` object .

First, we load package `AER` for data .

``````In :
library(AER)
``````

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

``````In :
data(HousePrices)
``````
``````Out :
price lotsize bedrooms
1 42000    5850        3
2 38500    4000        2
3 49500    3060        3
4 60500    6650        3
5 61000    6360        2
6 66000    4160        3
``````

Third, we fit model with `lm` function using variables within `HousePrices` data object and store outcome within `mlr` object. Within `lm` function, parameter `formula = price ~ lotsize + bedrooms` fits model where house price is explained by its lot size and number of bedrooms.

``````In :
mlr <- lm(formula = price ~ lotsize + bedrooms, data = HousePrices)
``````

Fourth, we can print `mlr` model summary results which include estimated coefficients table using `summary.lm` function.

``````In :
summary.lm(mlr)
``````
``````Out :
Call:
lm(formula = price ~ lotsize + bedrooms, data = HousePrices)

Residuals:
Min     1Q Median     3Q    Max
-65665 -12498  -2075   8970  97205

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 5.613e+03  4.103e+03   1.368    0.172
lotsize     6.053e+00  4.243e-01  14.265  < 2e-16 ***
bedrooms    1.057e+04  1.248e+03   8.470 2.31e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 21230 on 543 degrees of freedom
Multiple R-squared:  0.3703,	Adjusted R-squared:  0.3679
F-statistic: 159.6 on 2 and 543 DF,  p-value: < 2.2e-16
``````

Fifth, we can also store model summary results within `smlr` object using `summary.lm` function and print its `coefficients` value with estimated coefficients table.

``````In :
smlr <- summary.lm(mlr)
smlr\$coefficients
``````
``````Out :
Estimate   Std. Error   t value     Pr(>|t|)
(Intercept)  5612.599731 4102.8189131  1.367986 1.718822e-01
lotsize         6.053022    0.4243331 14.264788 1.938847e-39
bedrooms    10567.351501 1247.6764642  8.469625 2.314456e-16
``````

Courses

My online courses are hosted at Teachable website.

For more details on this concept, you can view my Linear Regression in R Course.

 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.

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

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