LR - R Code Examples

x <- house$size
y <- house$price

house.reg <- lm(y ~ x)

# ANOVA TABLE
(anova(house.reg))
Analysis of Variance Table
Response: y
          Df  Sum Sq  Mean Sq  F value    Pr(>F)
x         1    71534    71534   184.62  <2.2e-16 ***
Residuals 56   21698      387

# TESTING FOR ZERO SLOPE
summary(house.reg)
Call:
lm(formula = y ~ x)

Residuals:
    Min      1Q  Median     3Q    Max 
-38.489 -14.512  -1.422 14.919 54.389

Coefficients:
            Estimate Std.  Error  t value  Pr(>|t|)
(Intercept)         5.432  8.191    0.663      0.51
x                  56.083  4.128   13.587    <2e-16 ***
---
Signif. codes: 0'***'0.001'**'0.01'*'0.05'.'0.1' '1

Residual standard error: 19.68 on 56 degrees of freedom
Multiple R-squared: 0.7673, Adjusted R-squared: 0.7631
F-statistic: 184.6 on 1 and 56 DF, p-value: < 2.2e-16

# CONFIDENCE INTERVAL FOR SLOPE
confint(house.reg)
                 2.5 %     97.5 %
(Intercept)  -10.97619   21.83933
x             47.81473   64.35183

# PREDICTION AT A NEW X
x.new <- data.frame(x=3)
(predict(house.reg, newdata=x.new)) 
       1
173.6814

# Use fitted(house.reg) to get the fitted values
# Use resid(house.reg) to get the residuals

Plots for Checking the Gauss-Markov Assumptions

# RESIDUAL PLOT
plot(fitted(house.reg), resid(house.reg))
abline(h=0)

# QQ PLOT
qqnorm(resid(house.reg))
qqline(resid(house.reg))

# TIME SERIES PLOT OF RESIDUALS
plot(resid(house.reg), type="l")
abline(h=0)

library(datasets)
data('cars')
scatter.smooth(x=cars$speed, y=cars$dist, main="Distance ~ Speed")

linearMod <- lm(dist ~ speed, data=cars)
abline(linearMod)

plot(x,y)
linearMod <- lm(y ~ x)
abline(linearMod)

plot(1/x,y)
t = 1/x
linearMod <- lm(y ~ t)
abline(linearMod)