변수 선택법(Variable Selection)

1. 전진선택법(Forward Selection)

> yard<-c(31, 31, 27, 39, 30, 32, 28, 23, 28, 35)

> area<-c(58, 51, 47, 35, 48, 42, 43, 56, 41, 41)

> park<-c(1, 1, 5, 5, 2, 4, 5, 1, 1, 3)

> dist<-c(492, 426, 400, 125, 443, 412, 201, 362, 192, 423)

> popul<-c(4412, 2061, 4407, 1933, 4029, 4180, 3444, 1683, 3020, 4459)

> price<-c(12631, 12084, 12220, 15649, 11486, 12276, 15527, 12666, 13180, 10169)

> result<-step(lm(price ~ 1), scope=list(lower-1, upper=~yard+aread+park+dist+popul), direction='forward')

> result<-step(lm(price ~ 1), scope=list(lower=~1, upper=~yard+area+park+dist+popul), direction='forward')

Start: AIC=149.52

price ~ 1

Df Sum of Sq RSS AIC

+ dist 1 16958139 8557243 140.60

+ popul 1 5431481 20083900 149.13

+ park 1 4895399 20619982 149.39

<none> 25515382 149.52

+ area 1 2806386 22708996 150.36

+ yard 1 282704 25232677 151.41

Step: AIC=140.6

price ~ dist

Df Sum of Sq RSS AIC

+ area 1 2214900 6342343 139.60

<none> 8557243 140.60

+ park 1 376540 8180703 142.15

+ popul 1 90527 8466716 142.49

+ yard 1 53104 8504139 142.53

Step: AIC=139.6

price ~ dist + area

Df Sum of Sq RSS AIC

+ park 1 2922548 3419795 135.43

<none> 6342343 139.60

+ yard 1 975693 5366650 139.93

+ popul 1 326295 6016048 141.07

Step: AIC=135.43

price ~ dist + area + park

Df Sum of Sq RSS AIC

+ yard 1 1338046 2081748 132.46

<none> 3419795 135.43

+ popul 1 879 3418916 137.42

Step: AIC=132.46

price ~ dist + area + park + yard

Df Sum of Sq RSS AIC

<none> 2081748 132.46

+ popul 1 54218 2027530 134.20

> summary(result)

Call:

lm(formula = price ~ dist + area + park + yard)

Residuals:

1 2 3 4 5 6 7 8 9 10

211.9 193.4 -451.5 -193.6 247.8 801.9 387.0 -486.6 100.3 -810.6

Coefficients:

Estimate Std. Error t value Pr(>|t|)

(Intercept) 3045.689 4084.218 0.746 0.48939

dist -16.446 2.489 -6.609 0.00119 **

area 230.563 61.193 3.768 0.01305 *

park 436.801 155.508 2.809 0.03760 *

yard 117.922 65.779 1.793 0.13300

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 645.3 on 5 degrees of freedom

Multiple R-squared: 0.9184, Adjusted R-squared: 0.8531

F-statistic: 14.07 on 4 and 5 DF, p-value: 0.006267

2. 후진소거법(Backward Elimination)

> yard<-c(31, 31, 27, 39, 30, 32, 28, 23, 28, 35)

> area<-c(58, 51, 47, 35, 48, 42, 43, 56, 41, 41)

> park<-c(1, 1, 5, 5, 2, 4, 5, 1, 1, 3)

> dist<-c(492, 426, 400, 125, 443, 412, 201, 362, 192, 423)

> popul<-c(4412, 2061, 4407, 1933, 4029, 4180, 3444, 1683, 3020, 4459)

> price<-c(12631, 12084, 12220, 15649, 11486, 12276, 15527, 12666, 13180, 10169)

> result<-step(lm(price~1), scope=list(lower=~1, upper=~yard+area+park+dist+popul), direction='both')

Start: AIC=149.52

price ~ 1

Df Sum of Sq RSS AIC

+ dist 1 16958139 8557243 140.60

+ popul 1 5431481 20083900 149.13

+ park 1 4895399 20619982 149.39

<none> 25515382 149.52

+ area 1 2806386 22708996 150.36

+ yard 1 282704 25232677 151.41

Step: AIC=140.6

price ~ dist

Df Sum of Sq RSS AIC

+ area 1 2214900 6342343 139.60

<none> 8557243 140.60

+ park 1 376540 8180703 142.15

+ popul 1 90527 8466716 142.49

+ yard 1 53104 8504139 142.53

- dist 1 16958139 25515382 149.52

Step: AIC=139.6

price ~ dist + area

Df Sum of Sq RSS AIC

+ park 1 2922548 3419795 135.43

<none> 6342343 139.60

+ yard 1 975693 5366650 139.93

- area 1 2214900 8557243 140.60

+ popul 1 326295 6016048 141.07

- dist 1 16366653 22708996 150.36

Step: AIC=135.43

price ~ dist + area + park

Df Sum of Sq RSS AIC

+ yard 1 1338046 2081748 132.46

<none> 3419795 135.43

+ popul 1 879 3418916 137.42

- park 1 2922548 6342343 139.60

- area 1 4760908 8180703 142.15

- dist 1 17088473 20508268 151.34

Step: AIC=132.46

price ~ dist + area + park + yard

Df Sum of Sq RSS AIC

<none> 2081748 132.46

+ popul 1 54218 2027530 134.20

- yard 1 1338046 3419795 135.43

- park 1 3284902 5366650 139.93

- area 1 5910682 7992431 143.91

- dist 1 18183500 20265249 153.22

> summary(result)

Call:

lm(formula = price ~ dist + area + park + yard)

Residuals:

1 2 3 4 5 6 7 8 9 10

211.9 193.4 -451.5 -193.6 247.8 801.9 387.0 -486.6 100.3 -810.6

Coefficients:

Estimate Std. Error t value Pr(>|t|)

(Intercept) 3045.689 4084.218 0.746 0.48939

dist -16.446 2.489 -6.609 0.00119 **

area 230.563 61.193 3.768 0.01305 *

park 436.801 155.508 2.809 0.03760 *

yard 117.922 65.779 1.793 0.13300

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 645.3 on 5 degrees of freedom

Multiple R-squared: 0.9184, Adjusted R-squared: 0.8531

F-statistic: 14.07 on 4 and 5 DF, p-value: 0.006267

3. 단계적 방법(stepwise method)

> yard<-c(31, 31, 27, 39, 30, 32, 28, 23, 28, 35)

> area<-c(58, 51, 47, 35, 48, 42, 43, 56, 41, 41)

> park<-c(1, 1, 5, 5, 2, 4, 5, 1, 1, 3)

> dist<-c(492, 426, 400, 125, 443, 412, 201, 362, 192, 423)

> popul<-c(4412, 2061, 4407, 1933, 4029, 4180, 3444, 1683, 3020, 4459)

> price<-c(12631, 12084, 12220, 15649, 11486, 12276, 15527, 12666, 13180, 10169)

> result<-step(lm(price~1), scope=list(lower=~1, upper=~yard+area+park+dist+popul), direction='both')

Start: AIC=149.52

price ~ 1

Df Sum of Sq RSS AIC

+ dist 1 16958139 8557243 140.60

+ popul 1 5431481 20083900 149.13

+ park 1 4895399 20619982 149.39

<none> 25515382 149.52

+ area 1 2806386 22708996 150.36

+ yard 1 282704 25232677 151.41

Step: AIC=140.6

price ~ dist

Df Sum of Sq RSS AIC

+ area 1 2214900 6342343 139.60

<none> 8557243 140.60

+ park 1 376540 8180703 142.15

+ popul 1 90527 8466716 142.49

+ yard 1 53104 8504139 142.53

- dist 1 16958139 25515382 149.52

Step: AIC=139.6

price ~ dist + area

Df Sum of Sq RSS AIC

+ park 1 2922548 3419795 135.43

<none> 6342343 139.60

+ yard 1 975693 5366650 139.93

- area 1 2214900 8557243 140.60

+ popul 1 326295 6016048 141.07

- dist 1 16366653 22708996 150.36

Step: AIC=135.43

price ~ dist + area + park

Df Sum of Sq RSS AIC

+ yard 1 1338046 2081748 132.46

<none> 3419795 135.43

+ popul 1 879 3418916 137.42

- park 1 2922548 6342343 139.60

- area 1 4760908 8180703 142.15

- dist 1 17088473 20508268 151.34

Step: AIC=132.46

price ~ dist + area + park + yard

Df Sum of Sq RSS AIC

<none> 2081748 132.46

+ popul 1 54218 2027530 134.20

- yard 1 1338046 3419795 135.43

- park 1 3284902 5366650 139.93

- area 1 5910682 7992431 143.91

- dist 1 18183500 20265249 153.22

> summary(result)

Call:

lm(formula = price ~ dist + area + park + yard)

Residuals:

1 2 3 4 5 6 7 8 9 10

211.9 193.4 -451.5 -193.6 247.8 801.9 387.0 -486.6 100.3 -810.6

Coefficients:

Estimate Std. Error t value Pr(>|t|)

(Intercept) 3045.689 4084.218 0.746 0.48939

dist -16.446 2.489 -6.609 0.00119 **

area 230.563 61.193 3.768 0.01305 *

park 436.801 155.508 2.809 0.03760 *

yard 117.922 65.779 1.793 0.13300

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 645.3 on 5 degrees of freedom

Multiple R-squared: 0.9184, Adjusted R-squared: 0.8531

F-statistic: 14.07 on 4 and 5 DF, p-value: 0.006267

Variable Selection_step()