Fitting Linear Regression Using R

Stat 203 Lecture 7

Syntax

Goal is to understand how to create linear regression models in R, get the coefficients, and use the model to plot lines of best fit.

General syntax

library(GLMsData); data(gestation);
gest.wtd <- lm(Weight ~ Age, data=gestation, weights=Births)
summary(gest.wtd)

General syntax

library(GLMsData); data(gestation);
gest.wtd <- lm(Weight ~ Age, data=gestation, weights=Births)
summary(gest.wtd)

Call:
lm(formula = Weight ~ Age, data = gestation, weights = Births)

Weighted Residuals:
     Min       1Q   Median       3Q      Max 
-1.62979 -0.60893 -0.30063 -0.08845  1.03880 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept) -2.678389   0.371172  -7.216 7.49e-07 ***
Age          0.153759   0.009493  16.197 1.42e-12 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.7753 on 19 degrees of freedom
Multiple R-squared:  0.9325,    Adjusted R-squared:  0.9289 
F-statistic: 262.3 on 1 and 19 DF,  p-value: 1.416e-12

Weighted vs Unweighted

library(GLMsData); data(gestation);
gest.wtd <- lm(Weight ~ Age, data=gestation, weights=Births)
gest.ord <- lm(Weight ~ Age, data=gestation)
coef(gest.wtd)

(Intercept)         Age 
 -2.6783891   0.1537594 

coef(gest.ord)

(Intercept)         Age 
  -3.049879    0.159483 

Plotting

plot( Weight ~ Age, data=gestation, type="n",
    las=1, xlim=c(20, 45), ylim=c(0, 4),
    xlab="Gestational age (weeks)", ylab="Mean birthweight (in kg)" )
points( Weight[Births< 20] ~ Age[Births< 20], pch=1,  data=gestation )
points( Weight[Births>=20] ~ Age[Births>=20], pch=19, data=gestation )
abline( coef(gest.ord), lty=2, lwd=2)
abline( coef(gest.wtd), lty=1, lwd=2)
legend("topleft", lwd=c(2, 2), bty="n",
    lty=c(2, 1, NA, NA), pch=c(NA, NA, 1, 19),   # NA shows nothing
    legend=c("Ordinary regression", "Weighted regression","Based on 20 or fewer obs.","Based on more than 20 obs."))