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multiple_regression [2020/12/01 16:23] – [elem e.g. again] hkimscilmultiple_regression [2023/10/19 08:38] – [Determining IVs' role] hkimscil
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 ====== e.g.====== ====== e.g.======
 Data set again.  Data set again. 
 +<code>
 +datavar <- read.csv("http://commres.net/wiki/_media/regression01-bankaccount.csv") </code>
  
 ^  DATA for regression analysis   ^^^ ^  DATA for regression analysis   ^^^
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 ===== in R ===== ===== in R =====
-<code>dvar <- read.csv("http://commres.net/wiki/_media/elemapi2_.csv", fileEncoding="UTF-8-BOM")+<code>dvar <- read.csv("http://commres.net/wiki/_media/elemapi2_.csv", sep = "\t", fileEncoding="UTF-8-BOM")
 mod <- lm(api00 ~ ell + acs_k3 + avg_ed + meals, data=dvar) mod <- lm(api00 ~ ell + acs_k3 + avg_ed + meals, data=dvar)
 summary(mod) summary(mod)
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 </code> </code>
  
- +<code>> mod
-====== 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: Call:
-lm(formula = weights ~ LSS + RSS) +lm(formula = api00 ~ ell + acs_k3 + avg_ed + meals, data = dvar)
- +
-Residuals: +
-      1       2       3       4       5       6       7       8  +
- 4.8544  4.5254 -3.6333 -7.6402 -0.2467 -3.1997 -5.2665 10.6066 +
  
 Coefficients: Coefficients:
-            Estimate Std. Error t value Pr(>|t|)     +(Intercept)          ell       acs_k3       avg_ed        meals   
-(Intercept)  104.842      8.169  12.834 5.11e-05 *** +   709.6388      -0.8434       3.3884      29.0724      -2.9374  
-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 +></code> 
-Multiple R-squared:  0.9599, Adjusted R-squared:  0.9439  +$$ \hat{Y} =  709.6388 + -0.8434 \text{ell} + 3.3884 \text{acs_k3} + 29.0724 \text{avg_ed} + -2.9374 \text{meals} \\$$ 
-F-statistic: 59.92 on 2 and 5 DF,  p-value: 0.000321+
  
->  +그렇다면 각각의 독립변인 고유의 설명력은 얼마인가? --> see [[:partial and semipartial correlation]]
-> ##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>+
  
  
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 |  | Standard Multiple   | Sequential   |  comments   |  |  | 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)   | ::: |  | ::: | 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)   | ::: |  | ::: | 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>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   ||||  | IV<sub>1</sub> 이 IV<sub>2</sub> 보다 먼저 투입되었을 때를 가정   |||| 
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 summary(mod) summary(mod)
 anova(mod) anova(mod)
 +</code>
 +<code>
 +dvar <- read.csv("http://commres.net/wiki/_media/elemapi2_.csv", fileEncoding="UTF-8-BOM")
 +> mod <- lm(api00 ~ ell + acs_k3 + avg_ed + meals, data=dvar)
 +> summary(mod)
  
 +Call:
 +lm(formula = api00 ~ ell + acs_k3 + avg_ed + meals, data = dvar)
 +
 +Residuals:
 +     Min       1Q   Median       3Q      Max 
 +-187.020  -40.358   -0.313   36.155  173.697 
 +
 +Coefficients:
 +            Estimate Std. Error t value Pr(>|t|)    
 +(Intercept) 709.6388    56.2401  12.618  < 2e-16 ***
 +ell          -0.8434     0.1958  -4.307 2.12e-05 ***
 +acs_k3        3.3884     2.3333   1.452    0.147    
 +avg_ed       29.0724     6.9243   4.199 3.36e-05 ***
 +meals        -2.9374     0.1948 -15.081  < 2e-16 ***
 +---
 +Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
 +
 +Residual standard error: 58.63 on 374 degrees of freedom
 +  (21 observations deleted due to missingness)
 +Multiple R-squared:  0.8326, Adjusted R-squared:  0.8308 
 +F-statistic:   465 on 4 and 374 DF,  p-value: < 2.2e-16
 +
 +> anova(mod)
 +Analysis of Variance Table
 +
 +Response: api00
 +           Df  Sum Sq Mean Sq  F value    Pr(>F)    
 +ell         1 4502711 4502711 1309.762 < 2.2e-16 ***
 +acs_k3      1  110211  110211   32.059 2.985e-08 ***
 +avg_ed      1  998892  998892  290.561 < 2.2e-16 ***
 +meals       1  781905  781905  227.443 < 2.2e-16 ***
 +Residuals 374 1285740    3438                       
 +---
 +Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
 +> 
 +</code>
 +<code>
 # install.packages("ppcor") # install.packages("ppcor")
 library(ppcor) library(ppcor)
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 [1] "pearson" [1] "pearson"
 >  > 
 +> 
 +</code>
 +
 +<code>
 +> spcor.test(myvar$api00, myvar$meals, myvar[,c(2,3,4)])
 +    estimate      p.value statistic   n gp  Method
 +1 -0.3190889 2.403284e-10 -6.511264 379  3 pearson
 >  > 
 </code> </code>
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 </code> </code>
  
 +[[:Multiple Regression Exercise]]
  
 ====== Resources ====== ====== Resources ======
multiple_regression.txt · Last modified: 2023/10/19 08:39 by hkimscil
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