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--- multiple_regression [2022/05/21 22:51] – [in R] hkimscil
+++ multiple_regression [2023/10/19 08:39] (current) – [Determining IVs' role] hkimscil
@@ Line 44: / Line 44: @@
 ====== e.g.======
 Data set again.
+<code>
+datavar <- read.csv("http://commres.net/wiki/_media/regression01-bankaccount.csv") </code>
 ^  DATA for regression analysis   ^^^
@@ Line 393: / Line 395: @@
 그렇다면 각각의 독립변인 고유의 설명력은 얼마인가? --> see [[:partial and semipartial correlation]]
-====== 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] 0.9994836
->
-> 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       8
-.8544  4.5254 -3.6333 -7.6402 -0.2467 -3.1997 -5.2665 10.6066
-Coefficients:
-            Estimate Std. Error t value Pr(>|t|)
-(Intercept)  104.842      8.169  12.834 5.11e-05 ***
-LSS          -14.162     35.447  -0.400    0.706
-RSS           26.305     35.034   0.751    0.487
----
-Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
-Residual standard error: 7.296 on 5 degrees of freedom
-Multiple R-squared:  0.9599,	Adjusted R-squared:  0.9439
-F-statistic: 59.92 on 2 and 5 DF,  p-value: 0.000321
->
-> ##Fitting RSS or LSS separately gives a significant result.
-> summary(lm(weights ~ LSS))
-Call:
-lm(formula = weights ~ LSS)
-Residuals:
-   Min     1Q Median     3Q    Max
--6.055 -4.930 -2.925  4.886 11.854
-Coefficients:
-            Estimate Std. Error t value Pr(>|t|)
-(Intercept)  103.099      7.543   13.67 9.53e-06 ***
-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: 7.026 on 6 degrees of freedom
-Multiple R-squared:  0.9554,	Adjusted R-squared:  0.948
-F-statistic: 128.6 on 1 and 6 DF,  p-value: 2.814e-05
->
-</code>
@@ Line 493: / Line 420: @@
 |  | Standard Multiple   | Sequential   |  comments   |
-| r<sub>i</sub><sup>2</sup>  \\ squared correlation \\ **zero-order** correlation   | IV<sub>1</sub> : (a+b) / (a+b+c+d)   | IV<sub>1</sub> : (a+b) / (a+b+c+d)   | overlapped effects   |
+| r<sub>i</sub><sup>2</sup>  \\ squared correlation \\ squared **zero-order** \\ correlation in spss  | IV<sub>1</sub> : (a+b) / (a+b+c+d)   | IV<sub>1</sub> : (a+b) / (a+b+c+d)   | overlapped effects   |
 | ::: | IV<sub>2</sub> : (c+b) / (a+b+c+d)   | IV<sub>2</sub>: (c+b) / (a+b+c+d)   | ::: |
-| sr<sub>i</sub><sup>2</sup>  \\ squared **semipartial** correlation \\ **part in spss**   | IV<sub>1</sub> : (a) / (a+b+c+d)   | IV<sub>1</sub> : (a+b) / (a+b+c+d)   | Usual setting \\ Unique contribution to Y   |
+| sr<sub>i</sub><sup>2</sup>  \\ squared \\ **semipartial** correlation \\ **part in spss**   | IV<sub>1</sub> : (a) / (a+b+c+d)   | IV<sub>1</sub> : (a+b) / (a+b+c+d)   | Usual setting \\ Unique contribution to Y   |
 | ::: | IV<sub>2</sub> : %%(c%%) / (a+b+c+d)   | IV<sub>2</sub> : %%(c%%) / (a+b+c+d)   | ::: |
-| pr<sub>i</sub><sup>2</sup>  \\ squared **partial** correlation \\ **partial in spss**   | IV<sub>1</sub> : (a) / (a+d)   | IV<sub>1</sub> : (a+b) / (a+b+d)   | Like adjusted r<sup>2</sup>  \\ Unique contribution to Y   |
+| pr<sub>i</sub><sup>2</sup>  \\ squared \\ **partial** correlation \\ **partial in spss**   | IV<sub>1</sub> : (a) / (a+d)   | IV<sub>1</sub> : (a+b) / (a+b+d)   | Like adjusted r<sup>2</sup>  \\ Unique contribution to Y   |
 | ::: | IV<sub>2</sub> : %%(c%%) / (c+d)   | IV<sub>2</sub> : %%(c%%) / (c+d)   | ::: |
 | IV<sub>1</sub> 이 IV<sub>2</sub> 보다 먼저 투입되었을 때를 가정   ||||
@@ Line 654: / Line 581: @@
 </code>
+[[:Multiple Regression Exercise]]
 ====== Resources ======