interaction_effects_in_regression_analysis:answer_ex2
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> summary(m1)
Call:
lm(formula = read ~ math)
Residuals:
Min 1Q Median 3Q Max
-17.2392 -4.8701 -0.3633 4.6803 23.5592
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 14.07254 3.11582 4.516 1.08e-05 ***
math 0.72481 0.05827 12.438 < 2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 7.701 on 198 degrees of freedom
Multiple R-squared: 0.4386, Adjusted R-squared: 0.4358
F-statistic: 154.7 on 1 and 198 DF, p-value: < 2.2e-16
math의 read 분산에 대한 설명력: 43.9%
> summary(m2)
Call:
lm(formula = read ~ socst)
Residuals:
Min 1Q Median 3Q Max
-23.3961 -6.4365 -0.3152 5.6686 18.6686
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 21.12595 2.84404 7.428 3.22e-12 ***
socst 0.59353 0.05317 11.163 < 2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 8.053 on 198 degrees of freedom
Multiple R-squared: 0.3862, Adjusted R-squared: 0.3831
F-statistic: 124.6 on 1 and 198 DF, p-value: < 2.2e-16
socst의 read 분산에 대한 설명력: 38.6%
> summary(m3)
Call:
lm(formula = read ~ math + socst)
Residuals:
Min 1Q Median 3Q Max
-18.8729 -4.8987 -0.6286 5.2380 23.6993
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 7.14654 3.04066 2.350 0.0197 *
math 0.50384 0.06337 7.951 1.41e-13 ***
socst 0.35414 0.05530 6.404 1.08e-09 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 7.024 on 197 degrees of freedom
Multiple R-squared: 0.5354, Adjusted R-squared: 0.5306
F-statistic: 113.5 on 2 and 197 DF, p-value: < 2.2e-16
math와 socst의 설명력 (combined): 53.5%
math + socst = 43.9 + 38.6 = 82.5%
겹친부분 의 설명력: 82.5 - 53.5 = 29%
따라서 math 고유의 영향력: 43.9 - 29 = 14.9
socst 고유의 영향력: 38.6 - 29 = 9.6
위의 두 변인을 동시에 투입(enter)한 경우,
math 는 14.9 로 설명력을 평가받고 (t-test),
socst는 9.6 로 설명력을 평가받는다 (t-test, too).
> library(ppcor) > spcor.test(read, math, socst) estimate p.value statistic n gp Method 1 0.3861521 1.770448e-08 5.875646 200 1 pearson > spcor.test(read, math, socst)$estimate^2 [1] 0.1491134 > spcor.test(read, socst, math)$estimate^2 [1] 0.09674116 >
즉, 두 변인 고유 영향력이 통계적으로 유의미하다.
그런데 . . . .
아래를 보면
> summary(m4)
Call:
lm(formula = read ~ math * socst)
Residuals:
Min 1Q Median 3Q Max
-18.6071 -4.9228 -0.7195 4.5912 21.8592
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 37.842715 14.545210 2.602 0.00998 **
math -0.110512 0.291634 -0.379 0.70514
socst -0.220044 0.271754 -0.810 0.41908
math:socst 0.011281 0.005229 2.157 0.03221 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 6.96 on 196 degrees of freedom
Multiple R-squared: 0.5461, Adjusted R-squared: 0.5392
F-statistic: 78.61 on 3 and 196 DF, p-value: < 2.2e-16
y hat ~ 37.842715 + -0.110512 x1 + -0.220044 x2 + 0.011281 x1x2 y hat ~ 37.842715 + -0.220044 x2 + (-0.110512 + 0.011281 x2) x1 # x1으로 regression한 결과 y hat ~ 37.842715 + -0.110512 x1 + (-0.220044 + 0.011281 x1) x2 # x2
interaction_effects_in_regression_analysis/answer_ex2.1686066706.txt.gz · Last modified: 2023/06/07 00:51 by hkimscil