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--- using_dummy_variables [2026/06/09 23:33] – hkimscil
+++ using_dummy_variables [2026/06/14 23:15] (current) – [Regression with two Catogorical IVs] hkimscil
@@ Line 1137: / Line 1137: @@
 >
 >
+</code>
+{{pasted:20260609-230452.png?600}}
+<code>
 > # 1. 평균을 빼준 값을 새로운 변인으로 저장
 > df$meals_centered <-
@@ Line 1180: / Line 1184: @@
 >
 >
+</code>
+{{pasted:20260609-230505.png?600}}
+<code>
 > # Install the package if you do not have it
 > # install.packages("interactions")
@@ Line 1189: / Line 1197: @@
 >
 >
+</code>
+{{pasted:20260609-230516.png?600}}
+<code>
 > m.ellyr_rnd <- lm(api00~ell+yr_rnd, data=df)
 > summary(m.ellyr_rnd)
@@ Line 1289: / Line 1301: @@
 >
 </code>
+{{pasted:20260609-230601.png?600}}
 </tabbox>
-{{pasted:20260609-230452.png?600}}
-{{pasted:20260609-230505.png?600}}
-{{pasted:20260609-230516.png?600}}
-{{pasted:20260609-230601.png?600}}
 ===== Regression with a categorical and a continuous IV: e.g. 2 =====
@@ Line 1518: / Line 1528: @@
 > nobr.to100 <- coefs[1]+coefs[2]+coefs[4]
 > cat(br.to46, br.to80, br.to100)
-.0131 644.2758 526.33> cat(nobr.to46, nobr.to80, nobr.to100)
+.0131 644.2758 526.33
+> cat(nobr.to46, nobr.to80, nobr.to100)
 .0531 601.3157 483.3699>
+</code>
+예측식은 아래와 같다.
+<code>
+y hat = 808.013 + -42.960*(yr_rndno_break) + -163.737(mealcat47-80) + -281.683(mealcat81-100)
+yr_rnd:
+break = 방학있음
+no_break = 방학없음
+mealcat:
+-46% free meals
+-80%
+-100%
+</code>
+이에 대한 해석은 각각의 독립변인의 종류 수인 2개와 3개를 곱한 6개의 경우로 나누어서 생각할 수 있다. 즉,
+''y hat = 808.013 + -42.960*(yr_rndno_break) + -163.737(mealcat47-80) + -281.683(mealcat81-100)''
+을 바탕으로 각각의 조건을 고려하여 y hat를 계산하면 아래와 같다.
+<wrap #two_dummy_table />
+TABLE. Two dummy variables
+^                 ^ mealcat0-46  ^ mealcat47-80   ^ mealcat81-100    ^
+| yr_rndbreak     | <wrap> yr_rndbreak = 1
+yr_rndno_break = 0
+mealcat0-46 = 1
+mealcat47-80 = 0
+mealcat81-100 = 0 경우
+''y hat = 808.013''
+</wrap>  | <wrap> yr_rndbreak = 1
+yr_rndno_break = 0
+mealcat0-46 = 0
+mealcat47-80 = 1
+mealcat81-100 = 0 경우
+''**y hat = 808.013 - 163.737 = 644.276**''
+</wrap>  | <wrap> yr_rndbreak = 1
+yr_rndno_break = 0
+mealcat0-46 = 0
+mealcat47-80 = 0
+mealcat81-100 = 1 경우
+''**y hat = 808.013 - 281.683 = 526.33**''
+</wrap>  |
+| yr_rndno_break  | <wrap> yr_rndbreak = 0
+yr_rndno_break = 1
+mealcat0-46 = 1
+mealcat47-80 = 0
+mealcat81-100 = 0 경우
+''**y hat = 808.013 - 42.960 = 765.053**''
+</wrap>  | <wrap> yr_rndbreak = 0
+yr_rndno_break = 1
+mealcat0-46 = 0
+mealcat47-80 = 1
+mealcat81-100 = 0 경우
+''**y hat = 808.013 - 42.960 - 163.737 = 601.316**''
+</wrap>  | <wrap> yr_rndbreak = 0
+yr_rndno_break = 1
+mealcat0-46 = 0
+mealcat47-80 = 0
+mealcat81-100 = 1 경우
+''**y hat = 808.013 - 42.960 - 281.683 = 483.37**''
+</wrap>  |
+<code>
 > # 해석. interaction
 > m.yrrndxmealcat <- lm(api00~yr_rnd*mealcat, data=df)
@@ Line 1563: / Line 1635: @@
 > nobr.to100 <- coefs[1]+coefs[2]+coefs[4]+coefs[6]
 > cat(br.to46, br.to80, br.to100)
-.6855 645.2735 521.4925> cat(nobr.to46, nobr.to80, nobr.to100)
+.6855 645.2735 521.4925
+> cat(nobr.to46, nobr.to80, nobr.to100)
 .4286 593.5333 488
 >
 </code>
-</tabbox>
+위의 테스트는 두 개의 독립변인이 모두 종류이고 종속변인이 숫자일 때의 조건을 만족하니 factorial anova를 해도 된다. 아래는 그 결과이다.
+<code>
+> mod4 <- lm(api00 ~ yr_rnd + mealcat + yr_rnd:mealcat, data=datavar)
+> summary(mod4)
+Call:
+lm(formula = api00 ~ yr_rnd + mealcat + yr_rnd:mealcat, data = datavar)
+Residuals:
+     Min       1Q   Median       3Q      Max
+-207.533  -50.764   -1.843   48.874  179.000
+Coefficients:
+                             Estimate Std. Error t value Pr(>|t|)
+(Intercept)                   809.685      6.185 130.911  < 2e-16 ***
+yr_rndno_break                -74.257     26.756  -2.775  0.00578 **
+mealcat47-80                 -164.412      8.877 -18.522  < 2e-16 ***
+mealcat81-100                -288.193     10.443 -27.597  < 2e-16 ***
+yr_rndno_break:mealcat47-80    22.517     32.752   0.687  0.49217
+yr_rndno_break:mealcat81-100   40.764     29.231   1.395  0.16394
+---
+Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
+Residual standard error: 68.87 on 394 degrees of freedom
+Multiple R-squared:  0.7685,	Adjusted R-squared:  0.7656
+F-statistic: 261.6 on 5 and 394 DF,  p-value: < 2.2e-16
+</code>
+<code>
+Coefficients:
+                             Estimate Std. Error t value Pr(>|t|)
+(Intercept)                   809.685      6.185 130.911  < 2e-16 ***
+yr_rndno_break                -74.257     26.756  -2.775  0.00578 **
+mealcat47-80                 -164.412      8.877 -18.522  < 2e-16 ***
+mealcat81-100                -288.193     10.443 -27.597  < 2e-16 ***
+yr_rndno_break:mealcat47-80    22.517     32.752   0.687  0.49217
+yr_rndno_break:mealcat81-100   40.764     29.231   1.395  0.16394
+---
+이전 식
+y hat = 808.013 + -42.960 * (nobr) + -163.737 * (to80) + -281.683 * (to100)
+위의 식
+y hat = 809.685 +  -74.257*(nobr) +
+                  -164.412*(to80) +
+                  -288.193*(to100) +
+.517*(nobr:to80) +   --> aaaaa case
+.764*(nobr:to100)    --> bbbbb case
+yr_rnd:
+break = 방학있음
+no_break = 방학없음
+mealcat:
+-46% free meals
+-80%
+-100%
+</code>
+^                 ^ mealcat0-46  ^ mealcat47-80   ^ mealcat81-100    ^
+| yr_rndbreak     | <wrap> 베이스라인
+yr_rndno_break = 0
+mealcat47-80 = 0
+mealcat81-100 = 0 경우
+''y hat = 809.685''
+</wrap>  | <wrap> yr_rndno_break = 0
+mealcat0-46 = 0
+mealcat81-100 = 0 경우
+''y hat = 809.685 -
+.737
+        = 645.9''
+</wrap>  | <wrap>
+yr_rndno_break = 0
+mealcat0-46 = 0
+mealcat47-80 = 0 경우
+''y hat = 809.685 -
+.683
+        = 528''
+</wrap>  |
+| yr_rndno_break  | <wrap>
+yr_rndbreak = 0
+mealcat47-80 = 0
+mealcat81-100 = 0 경우
+''y hat = 809.685 -
+.257
+        = 735.4''
+</wrap>  | <wrap> aaaaa
+yr_rndbreak = 0
+mealcat0-46 = 0
+mealcat81-100 = 0 경우
+''y hat = 809.685 -
+.257 -
+.412 +
+          <fc #ff0000>22.517</fc>
+        = 593.5''
+</wrap>  | <wrap> bbbbb
+yr_rndbreak = 0
+mealcat0-46 = 0
+mealcat47-80 = 0 경우
+''y hat = 809.685 -
+.257 -
+.193 +
+          <fc #ff0000>40.764</fc>
+        = 488''
+</wrap>  |
+마지막 두 케이스를 보면 no_break학교 중에서 밀카테고리 2와 3에서 떨어지는 정도가 어느 정도 완화되는 경향을 보이지만 통계학적으로 significant하지는 않다.
+</tabbox>