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--- sequential_regression [2020/12/01 14:09] – [e.g. 3. Happiness] hkimscil
+++ sequential_regression [2022/05/22 21:50] (current) – hkimscil
@@ Line 1: / Line 1: @@
+====== Sequential or Hierarchical regression ======
+연구자가 판단하여 독립변인들 중 필요한 것들을 묶어서 스테이지 별로 (단계 별) 넣고 분석하는 것을 말한다. Stepwise regression은 이를 컴퓨터나 계산방법을 통하여 수행하게 된다.
 ====== 데이터 ======
 ^  DATA for regression analysis   ^^^
@@ Line 295: / Line 297: @@
 </code>
-====== e.g. 3. Happiness  ======
+====== e.g. 3. College enrollment in New Mexico University ======
+<code>
+> datavar <- read.csv("http://commres.net/wiki/_media/r/dataset_hlr.csv")
+> str(datavar)
+'data.frame':	29 obs. of  5 variables:
+ $ YEAR : int  1 2 3 4 5 6 7 8 9 10 ...
+ $ ROLL : int  5501 5945 6629 7556 8716 9369 9920 10167 11084 12504 ...
+ $ UNEM : num  8.1 7 7.3 7.5 7 6.4 6.5 6.4 6.3 7.7 ...
+ $ HGRAD: int  9552 9680 9731 11666 14675 15265 15484 15723 16501 16890 ...
+ $ INC  : int  1923 1961 1979 2030 2112 2192 2235 2351 2411 2475 ...
+>
+</code>
+<code>
+onePredictorModel <- lm(ROLL ~ UNEM, data = datavar)
+twoPredictorModel <- lm(ROLL ~ UNEM + HGRAD, data = datavar)
+threePredictorModel <- lm(ROLL ~ UNEM + HGRAD + INC, data = datavar)
+</code>
+<code>summary(onePredictorModel)
+summary(twoPredictorModel)
+summary(threePredictorModel)
+</code>
+<code>> summary(onePredictorModel)
+Call:
+lm(formula = ROLL ~ UNEM, data = datavar)
+Residuals:
+    Min      1Q  Median      3Q     Max
+-7640.0 -1046.5   602.8  1934.3  4187.2
+Coefficients:
+            Estimate Std. Error t value Pr(>|t|)
+(Intercept)   3957.0     4000.1   0.989   0.3313
+UNEM          1133.8      513.1   2.210   0.0358 *
+---
+Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
+Residual standard error: 3049 on 27 degrees of freedom
+Multiple R-squared:  0.1531,	Adjusted R-squared:  0.1218
+F-statistic: 4.883 on 1 and 27 DF,  p-value: 0.03579
+</code>
+<code>> summary(twoPredictorModel)
+Call:
+lm(formula = ROLL ~ UNEM + HGRAD, data = datavar)
+Residuals:
+    Min      1Q  Median      3Q     Max
+-2102.2  -861.6  -349.4   374.5  3603.5
+Coefficients:
+              Estimate Std. Error t value Pr(>|t|)
+(Intercept) -8.256e+03  2.052e+03  -4.023  0.00044 ***
+UNEM         6.983e+02  2.244e+02   3.111  0.00449 **
+HGRAD        9.423e-01  8.613e-02  10.941 3.16e-11 ***
+---
+Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
+Residual standard error: 1313 on 26 degrees of freedom
+Multiple R-squared:  0.8489,	Adjusted R-squared:  0.8373
+F-statistic: 73.03 on 2 and 26 DF,  p-value: 2.144e-11
+> </code>
+<code>
+> summary(threePredictorModel)
+Call:
+lm(formula = ROLL ~ UNEM + HGRAD + INC, data = datavar)
+Residuals:
+     Min       1Q   Median       3Q      Max
+-1148.84  -489.71    -1.88   387.40  1425.75
+Coefficients:
+              Estimate Std. Error t value Pr(>|t|)
+(Intercept) -9.153e+03  1.053e+03  -8.691 5.02e-09 ***
+UNEM         4.501e+02  1.182e+02   3.809 0.000807 ***
+HGRAD        4.065e-01  7.602e-02   5.347 1.52e-05 ***
+INC          4.275e+00  4.947e-01   8.642 5.59e-09 ***
+---
+Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
+Residual standard error: 670.4 on 25 degrees of freedom
+Multiple R-squared:  0.9621,	Adjusted R-squared:  0.9576
+F-statistic: 211.5 on 3 and 25 DF,  p-value: < 2.2e-16
+</code>
+<code>anova(onePredictorModel, twoPredictorModel, threePredictorModel)
+Analysis of Variance Table
+Model 1: ROLL ~ UNEM
+Model 2: ROLL ~ UNEM + HGRAD
+Model 3: ROLL ~ UNEM + HGRAD + INC
+  Res.Df       RSS Df Sum of Sq      F    Pr(>F)
+     27 251084710
+     26  44805568  1 206279143 458.92 < 2.2e-16 ***
+     25  11237313  1  33568255  74.68 5.594e-09 ***
+---
+Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
+>
+</code>
+====== e.g. 4. Happiness  ======
 {{:hierarchical.regression.data.csv}}
@@ Line 472: / Line 581: @@
 >
 </code>
-===== Report =====
+Report in research paper
 {{:pasted:20201201-140842.png}}
+{{:pasted:20201201-141106.png}}
+====== e.g. 5: Stock Market ======
+see [[:r:multiple_regression#partial_semi-partial_correlation_and_r_squared_value|Partial and semipartial example in r]]
+====== e.g. 6: SWISS ======