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--- multiple_regression [2019/05/21 22:40] – [Why overall model is significant while IVs are not?] hkimscil
+++ multiple_regression [2019/11/01 08:36] – [Resources] hkimscil
@@ Line 330: / Line 330: @@
 ====== 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
+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)
+</code>
 <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
+[1] 0.9994836
 >
 > weights = 120 + rnorm(RSS, 10*RSS, 10)
@@ Line 348: / Line 363: @@
 Residuals:
-       2       3       4       5       6       7
+       2       3       4       5       6       7       8
-.6231 -4.8706  1.3063  0.9639 -1.3120 -6.1247  2.6604
+.8544  4.5254 -3.6333 -7.6402 -0.2467 -3.1997 -5.2665 10.6066
-.7536
 Coefficients:
             Estimate Std. Error t value Pr(>|t|)
-(Intercept)  103.116      4.832  21.339 4.19e-06 ***
+(Intercept)  104.842      8.169  12.834 5.11e-05 ***
-LSS          -27.546     11.952  -2.305   0.0694 .
+LSS          -14.162     35.447  -0.400    0.706
-RSS           39.299     12.040   3.264   0.0223 *
+RSS           26.305     35.034   0.751    0.487
 ---
 Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
-Residual standard error: 4.508 on 5 degrees of freedom
+Residual standard error: 7.296 on 5 degrees of freedom
-Multiple R-squared:  0.9827,	Adjusted R-squared:  0.9757
+Multiple R-squared:  0.9599,	Adjusted R-squared:  0.9439
-F-statistic: 141.6 on 2 and 5 DF,  p-value: 3.964e-05
+F-statistic: 59.92 on 2 and 5 DF,  p-value: 0.000321
 >
@@ Line 373: / Line 386: @@
 Residuals:
-    Min      1Q  Median      3Q     Max
+   Min     1Q Median     3Q    Max
--11.044  -2.203  -0.422   2.774  12.369
+-6.055 -4.930 -2.925  4.886 11.854
 Coefficients:
             Estimate Std. Error t value Pr(>|t|)
-(Intercept)  105.939      7.679   13.79 9.03e-06 ***
+(Intercept)  103.099      7.543   13.67 9.53e-06 ***
-LSS           11.401      1.115   10.22 5.11e-05 ***
+LSS           12.440      1.097   11.34 2.81e-05 ***
 ---
 Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
-Residual standard error: 7.282 on 6 degrees of freedom
+Residual standard error: 7.026 on 6 degrees of freedom
-Multiple R-squared:  0.9457,	Adjusted R-squared:  0.9366
+Multiple R-squared:  0.9554,	Adjusted R-squared:  0.948
-F-statistic: 104.5 on 1 and 6 DF,  p-value: 5.113e-05
+F-statistic: 128.6 on 1 and 6 DF,  p-value: 2.814e-05
 >
@@ Line 489: / Line 502: @@
   * https://www.r-bloggers.com/analysis-of-covariance-%E2%80%93-extending-simple-linear-regression/
   * http://www.wekaleamstudios.co.uk/posts/analysis-of-covariance-extending-simple-linear-regression/
+https://www.youtube.com/user/marinstatlectures/search?query=Multiple+Linear+Regression+
 {{tag> "research methods" "statistics" "regression" "multiple regression"}}