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--- r:dummy_variables_with_significant_interaction [2023/06/01 16:48] – [output] hkimscil
+++ r:dummy_variables_with_significant_interaction [2023/06/05 13:01] (current) – [Regression with a continous + a categorical variables: ANCOVA] hkimscil
@@ Line 1: / Line 1: @@
 ====== Regression with two categorical variables (IVs): Two way anova  ======
+https://advstats.psychstat.org/book/mregression/catpredictor.php#example-4-regression-with-one-categorical-and-one-continuous-predictors-ancova
 <code>
 college <- read.csv("http://commres.net/wiki/_media/r/college.csv")
@@ Line 142: / Line 142: @@
 ====== Regression with a continous + a categorical variables: ANCOVA ======
+<code>
+summary(mod<-lm(salary~cost + location))
+anova(mod)
+</code>
+<code>
+> summary(mod<-lm(salary~cost + location))
+Call:
+lm(formula = salary ~ cost + location)
+Residuals:
+    Min      1Q  Median      3Q     Max
+-20.244  -4.933  -0.572   3.162  29.939
+Coefficients:
+             Estimate Std. Error t value Pr(>|t|)
+(Intercept)  8.78e+01   3.10e+00   28.34  < 2e-16 ***
+cost         6.05e-05   1.73e-05    3.50  0.00076 ***
+locationMW  -2.80e+00   2.57e+00   -1.09  0.27885
+locationNE   9.23e+00   2.42e+00    3.81  0.00027 ***
+locationW   -1.05e+01   2.57e+00   -4.10  0.00010 ***
+---
+Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
+Residual standard error: 8.02 on 80 degrees of freedom
+Multiple R-squared:  0.571,	Adjusted R-squared:  0.549
+F-statistic: 26.6 on 4 and 80 DF,  p-value: 4.96e-14
+> anova(mod)
+Analysis of Variance Table
+Response: salary
+          Df Sum Sq Mean Sq F value  Pr(>F)
+cost       1   2757    2757    42.9 5.1e-09 ***
+location   3   4072    1357    21.1 3.6e-10 ***
+Residuals 80   5141      64
+---
+Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
+>
+</code>
+<code>
+(Intercept)  8.78e+01   3.10e+00   28.34  < 2e-16 ***
+cost         6.05e-05   1.73e-05    3.50  0.00076 ***
+locationMW  -2.80e+00   2.57e+00   -1.09  0.27885
+locationNE   9.23e+00   2.42e+00    3.81  0.00027 ***
+locationW   -1.05e+01   2.57e+00   -4.10  0.00010 ***
+</code>
+''y hat ~ 87.8 + .00006*cost - 2.8 MW + 9.23 NE - 10.5 E ''
+  * S, MW, NE, W 중에서 S가 default
+    * y hat ~ 87.8 + .00006*cost
+  * MW:
+    * y hat ~ 87.8 - 2.8 + .00006*cost
+    * y hat ~ 85 + .00006*cost
+  * NE:
+    * y hat ~ 87.8 - 9.23 + .00006*cost
+    * y hat ~ 78.57 + .00006*cost
+  * E:
+    * y hat ~ 87.8 - 10.5 + .00006*cost
+    * y hat ~ 77.3 + .00006*cost
+<code>
+> summary(mod2<-lm(salary~cost * location))
+Call:
+lm(formula = salary ~ cost * location)
+Residuals:
+     Min       1Q   Median       3Q      Max
+-17.1126  -5.6241  -0.8152   2.6401  28.4861
+Coefficients:
+                  Estimate Std. Error t value Pr(>|t|)
+(Intercept)      8.863e+01  4.995e+00  17.744   <2e-16 ***
+cost             5.480e-05  3.211e-05   1.707   0.0919 .
+locationMW      -5.526e+00  7.213e+00  -0.766   0.4460
+locationNE      -2.866e+00  7.383e+00  -0.388   0.6989
+locationW       -1.876e+00  6.509e+00  -0.288   0.7740
+cost:locationMW  1.885e-05  4.681e-05   0.403   0.6882
+cost:locationNE  7.480e-05  4.533e-05   1.650   0.1030
+cost:locationW  -7.815e-05  4.665e-05  -1.675   0.0980 .
+---
+Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
+Residual standard error: 7.644 on 77 degrees of freedom
+Multiple R-squared:  0.6241,	Adjusted R-squared:  0.5899
+F-statistic: 18.26 on 7 and 77 DF,  p-value: 4.313e-14
+> anova(mod2)
+Analysis of Variance Table
+Response: salary
+              Df Sum Sq Mean Sq F value    Pr(>F)
+cost           1 2757.0 2756.97  47.183 1.470e-09 ***
+location       3 4071.8 1357.26  23.228 8.276e-11 ***
+cost:location  3  641.6  213.86   3.660   0.01596 *
+Residuals     77 4499.2   58.43
+---
+Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
+>
+</code>