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--- multiple_regression [2019/05/21 21:37] – [e.g.] hkimscil
+++ multiple_regression [2019/05/21 22:40] – [Why overall model is significant while IVs are not?] hkimscil
@@ Line 328: / Line 328: @@
 </code>
-====== 무엇부터? 라는 문제 ======
+====== Why overall model is significant while IVs are not? ======
+see https://www.researchgate.net/post/Why_is_the_Multiple_regression_model_not_significant_while_simple_regression_for_the_same_variables_is_significant
+<code>> RSS = 3:10 #Right shoe size
+> LSS = rnorm(RSS, RSS, 0.1) #Left shoe size - similar to RSS
+> cor(LSS, RSS) #correlation ~ 0.99
+[1] 0.9983294
+>
+> weights = 120 + rnorm(RSS, 10*RSS, 10)
+>
+> ##Fit a joint model
+> m = lm(weights ~ LSS + RSS)
+>
+> ##F-value is very small, but neither LSS or RSS are significant
+> summary(m)
+Call:
+lm(formula = weights ~ LSS + RSS)
+Residuals:
+       2       3       4       5       6       7
+.6231 -4.8706  1.3063  0.9639 -1.3120 -6.1247  2.6604
+
+.7536
+Coefficients:
+            Estimate Std. Error t value Pr(>|t|)
+(Intercept)  103.116      4.832  21.339 4.19e-06 ***
+LSS          -27.546     11.952  -2.305   0.0694 .
+RSS           39.299     12.040   3.264   0.0223 *
+---
+Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
+Residual standard error: 4.508 on 5 degrees of freedom
+Multiple R-squared:  0.9827,	Adjusted R-squared:  0.9757
+F-statistic: 141.6 on 2 and 5 DF,  p-value: 3.964e-05
+>
+> ##Fitting RSS or LSS separately gives a significant result.
+> summary(lm(weights ~ LSS))
+Call:
+lm(formula = weights ~ LSS)
+Residuals:
+    Min      1Q  Median      3Q     Max
+-11.044  -2.203  -0.422   2.774  12.369
+Coefficients:
+            Estimate Std. Error t value Pr(>|t|)
+(Intercept)  105.939      7.679   13.79 9.03e-06 ***
+LSS           11.401      1.115   10.22 5.11e-05 ***
+---
+Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
+Residual standard error: 7.282 on 6 degrees of freedom
+Multiple R-squared:  0.9457,	Adjusted R-squared:  0.9366
+F-statistic: 104.5 on 1 and 6 DF,  p-value: 5.113e-05
+>
+</code>
+====== The problem of "which one is entered first?" ======
 __그림 여기쯤 수록__