====== Analysis of Covariance ======
with lm function
> library(Cars93)
> lm.model4 <- lm(Cars93$MPG.city ~ Cars93$EngineSize + Cars93$Price + Cars93$DriveTrain)
> summary(lm.model4)
Call:
lm(formula = Cars93$MPG.city ~ Cars93$EngineSize + Cars93$Price +
Cars93$DriveTrain)
Residuals:
Min 1Q Median 3Q Max
-8.3153 -2.1589 -0.3703 1.3227 16.5032
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 31.3617 1.6298 19.242 < 2e-16 ***
Cars93$EngineSize -3.0608 0.4842 -6.321 1.04e-08 ***
Cars93$Price -0.1699 0.0522 -3.255 0.00161 **
Cars93$DriveTrainFront 2.6231 1.2716 2.063 0.04207 *
Cars93$DriveTrainRear 3.4548 1.6120 2.143 0.03486 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 3.747 on 88 degrees of freedom
Multiple R-squared: 0.5748, Adjusted R-squared: 0.5555
F-statistic: 29.74 on 4 and 88 DF, p-value: 1.199e-15
> lm.model3 <- lm(Cars93$MPG.city ~ Cars93$EngineSize + Cars93$Price)
> summary(lm.model3)
Call:
lm(formula = Cars93$MPG.city ~ Cars93$EngineSize + Cars93$Price)
Residuals:
Min 1Q Median 3Q Max
-7.4511 -2.0637 -0.5156 1.6239 16.9372
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 33.34647 1.12251 29.707 < 2e-16 ***
Cars93$EngineSize -2.98885 0.47808 -6.252 1.33e-08 ***
Cars93$Price -0.15415 0.05134 -3.002 0.00347 **
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 3.815 on 90 degrees of freedom
Multiple R-squared: 0.5492, Adjusted R-squared: 0.5392
F-statistic: 54.83 on 2 and 90 DF, p-value: 2.674e-16
> anova(lm.model3, lm.model4)
Analysis of Variance Table
Model 1: Cars93$MPG.city ~ Cars93$EngineSize + Cars93$Price
Model 2: Cars93$MPG.city ~ Cars93$EngineSize + Cars93$Price + Cars93$DriveTrain
Res.Df RSS Df Sum of Sq F Pr(>F)
1 90 1309.7
2 88 1235.5 2 74.185 2.6419 0.07687 .
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
>
====== Ex. 1 ======
mtcars 데이터를 이용하여 milleage에 영향을 주는 요소로 hp(horsepower)와 wt(weight)로 하여 regression을 하시오.
또한 이에 더하여 cyl 숫자를 더하여 regression을 하시오. 그리고 그 차이점에 대해서 논하시오.
{{tag> statistics r "analysis of covaraince" ancova}}