rm(list = ls())
# lm 회귀분석 사용함수
model <- lm(mpg~hp, data = mtcars) # 독립변수 1개, 단순선형(직선) 회귀
summary(model)
##
## Call:
## lm(formula = mpg ~ hp, data = mtcars)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.7121 -2.1122 -0.8854 1.5819 8.2360
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 30.09886 1.63392 18.421 < 2e-16 ***
## hp -0.06823 0.01012 -6.742 1.79e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.863 on 30 degrees of freedom
## Multiple R-squared: 0.6024, Adjusted R-squared: 0.5892
## F-statistic: 45.46 on 1 and 30 DF, p-value: 1.788e-07
##
## Call:
## lm(formula = mpg ~ hp, data = mtcars)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.7121 -2.1122 -0.8854 1.5819 8.2360
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 30.09886 1.63392 18.421 < 2e-16 ***
## hp -0.06823 0.01012 -6.742 1.79e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.863 on 30 degrees of freedom
## Multiple R-squared: 0.6024, Adjusted R-squared: 0.5892
## F-statistic: 45.46 on 1 and 30 DF, p-value: 1.788e-07
# Residuals : 잔차(오차)
# Coefficients : 회귀계수(Estimate)
# (Intercept) : 절편(상수) : 30.9886
# 독립변수 hp 회귀계수는: -0.06823
# Pr(>|t|) 유의확률입니다.
# 0.000000179 < 유의수준 0.05
# 귀무가설 : 회귀계수는 0이다.
# 대립가설 : 회귀계수는 0이 아니다.
# 따라서 귀무가설 기각, 통계적으로 유의한 변수라고 한다.
format(1.79e-07, scientific=FALSE)
## [1] "0.000000179"
## [1] "0.000000179"
data("faithful")
summary(faithful)
## eruptions waiting
## Min. :1.600 Min. :43.0
## 1st Qu.:2.163 1st Qu.:58.0
## Median :4.000 Median :76.0
## Mean :3.488 Mean :70.9
## 3rd Qu.:4.454 3rd Qu.:82.0
## Max. :5.100 Max. :96.0
## eruptions waiting
## Min. :1.600 Min. :43.0
## 1st Qu.:2.163 1st Qu.:58.0
## Median :4.000 Median :76.0
## Mean :3.488 Mean :70.9
## 3rd Qu.:4.454 3rd Qu.:82.0
## Max. :5.100 Max. :96.0
model1 <- lm(eruptions~waiting, data = faithful)
summary(model1)
##
## Call:
## lm(formula = eruptions ~ waiting, data = faithful)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.29917 -0.37689 0.03508 0.34909 1.19329
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.874016 0.160143 -11.70 <2e-16 ***
## waiting 0.075628 0.002219 34.09 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4965 on 270 degrees of freedom
## Multiple R-squared: 0.8115, Adjusted R-squared: 0.8108
## F-statistic: 1162 on 1 and 270 DF, p-value: < 2.2e-16
##
## Call:
## lm(formula = eruptions ~ waiting, data = faithful)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.29917 -0.37689 0.03508 0.34909 1.19329
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.874016 0.160143 -11.70 <2e-16 ***
## waiting 0.075628 0.002219 34.09 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4965 on 270 degrees of freedom
## Multiple R-squared: 0.8115, Adjusted R-squared: 0.8108
## F-statistic: 1162 on 1 and 270 DF, p-value: < 2.2e-16
# Residuals : 잔차(오차)
# Coefficients : 회귀계수(Estimate)
# (Intercept) : 절편(상수) : -1.874016
# 독립변수 waiting 회귀계수는: 0.075628
# Pr(>|t|) 유의확률입니다.
# 0.0000000000000002 < 유의수준 0.05
format(2e-16, scientific=FALSE)
## [1] "0.0000000000000002"
## [1] "0.0000000000000002"
# 귀무가설 : 회귀계수는 0이다.
# 대립가설 : 회귀계수는 0이 아니다.
# 따라서 귀무가설 기각, 통계적으로 유의한 변수라고 한다.
data(pressure)
summary(pressure)
## temperature pressure
## Min. : 0 Min. : 0.0002
## 1st Qu.: 90 1st Qu.: 0.1800
## Median :180 Median : 8.8000
## Mean :180 Mean :124.3367
## 3rd Qu.:270 3rd Qu.:126.5000
## Max. :360 Max. :806.0000
## temperature pressure
## Min. : 0 Min. : 0.0002
## 1st Qu.: 90 1st Qu.: 0.1800
## Median :180 Median : 8.8000
## Mean :180 Mean :124.3367
## 3rd Qu.:270 3rd Qu.:126.5000
## Max. :360 Max. :806.0000
model2 <- lm(pressure~temperature, data = pressure)
summary(model2)
##
## Call:
## lm(formula = pressure ~ temperature, data = pressure)
##
## Residuals:
## Min 1Q Median 3Q Max
## -158.08 -117.06 -32.84 72.30 409.43
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -147.8989 66.5529 -2.222 0.040124 *
## temperature 1.5124 0.3158 4.788 0.000171 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 150.8 on 17 degrees of freedom
## Multiple R-squared: 0.5742, Adjusted R-squared: 0.5492
## F-statistic: 22.93 on 1 and 17 DF, p-value: 0.000171
##
## Call:
## lm(formula = pressure ~ temperature, data = pressure)
##
## Residuals:
## Min 1Q Median 3Q Max
## -158.08 -117.06 -32.84 72.30 409.43
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -147.8989 66.5529 -2.222 0.040124 *
## temperature 1.5124 0.3158 4.788 0.000171 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 150.8 on 17 degrees of freedom
## Multiple R-squared: 0.5742, Adjusted R-squared: 0.5492
## F-statistic: 22.93 on 1 and 17 DF, p-value: 0.000171
# Residuals : 잔차(오차)
# Coefficients : 회귀계수(Estimate)
# (Intercept) : 절편(상수) : -147.8989
# 독립변수 temperature 회귀계수는: 1.5124
# Pr(>|t|) 유의확률입니다.
# 0.000171 < 유의수준 0.05
# 귀무가설 : 회귀계수는 0이다.
# 대립가설 : 회귀계수는 0이 아니다.
# 따라서 귀무가설 기각, 통계적으로 유의한 변수라고 한다.
data(women)
summary(women)
## height weight
## Min. :58.0 Min. :115.0
## 1st Qu.:61.5 1st Qu.:124.5
## Median :65.0 Median :135.0
## Mean :65.0 Mean :136.7
## 3rd Qu.:68.5 3rd Qu.:148.0
## Max. :72.0 Max. :164.0
## height weight
## Min. :58.0 Min. :115.0
## 1st Qu.:61.5 1st Qu.:124.5
## Median :65.0 Median :135.0
## Mean :65.0 Mean :136.7
## 3rd Qu.:68.5 3rd Qu.:148.0
## Max. :72.0 Max. :164.0
model3 <- lm(weight~height, data = women)
summary(model3)
##
## Call:
## lm(formula = weight ~ height, data = women)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.7333 -1.1333 -0.3833 0.7417 3.1167
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -87.51667 5.93694 -14.74 1.71e-09 ***
## height 3.45000 0.09114 37.85 1.09e-14 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.525 on 13 degrees of freedom
## Multiple R-squared: 0.991, Adjusted R-squared: 0.9903
## F-statistic: 1433 on 1 and 13 DF, p-value: 1.091e-14
##
## Call:
## lm(formula = weight ~ height, data = women)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.7333 -1.1333 -0.3833 0.7417 3.1167
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -87.51667 5.93694 -14.74 1.71e-09 ***
## height 3.45000 0.09114 37.85 1.09e-14 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.525 on 13 degrees of freedom
## Multiple R-squared: 0.991, Adjusted R-squared: 0.9903
## F-statistic: 1433 on 1 and 13 DF, p-value: 1.091e-14
# Residuals : 잔차(오차)
# Coefficients : 회귀계수(Estimate)
# (Intercept) : 절편(상수) : -87.51667
# 독립변수 temperature 회귀계수는: 3.45000
# Pr(>|t|) 유의확률입니다.
format(1.09e-14, scientific=FALSE)
## [1] "0.0000000000000109"
## [1] "0.0000000000000109"