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====== Analysis of Covariance ======
with lm function

<code>> library(Cars93)</code>

<code>> 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
</code>

<code>> 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
</code>

<code>> 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
> 
</code> 
====== Ex. 1 ======
<WRAP round info 60%>
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.
</WRAP>
{{tag> statistics r "analysis of covaraince" ancova}}