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--- r:multiple_regression [2021/11/03 23:01] – [Multiple Regression] hkimscil
+++ r:multiple_regression [2023/10/18 23:23] (current) – hkimscil
@@ Line 104: / Line 104: @@
   * unemployment rate (UNEM) = 9%, 12%, 3%
   * spring high school graduating class (HGRAD) = 100000, 98000, 78000
-  * a per capita income (INC) of $30,000, $2800, $36000
+  * a per capita income (INC) of \$30000, \$28000, \$36000
   * 일 때, enrollment는 어떻게 predict할 수 있을까?
@@ Line 111: / Line 111: @@
 여기에 위의 정보를 대입해 보면 된다.
+<code>
 new.data <- data.frame(UNEM=c(9, 12, 3), HGRAD=c(100000, 98000, 78000), INC=c(30000, 28000, 36000))
 predict(three.predictor.model, newdata=new.data)
+</code>
 <code>
@@ Line 161: / Line 163: @@
 sd.inc <- sd(INC)
+b.unem <- three.predictor.model$coefficients[2]
+b.hgrad <- three.predictor.model$coefficients[3]
+b.inc <- three.predictor.model$coefficients[4]
+## or
 b.unem <- 4.501e+02
 b.hgrad <- 4.065e-01
 b.inc <- 4.275e+00
 b.unem * (sd.unem / sd.roll)
@@ Line 172: / Line 180: @@
 </code>
+output of the above
+<code>
+> sd.roll <- sd(ROLL)
+> sd.unem <- sd(UNEM)
+> sd.hgrad <- sd(HGRAD)
+> sd.inc <- sd(INC)
+>
+> b.unem <- three.predictor.model$coefficients[2]
+> b.hgrad <- three.predictor.model$coefficients[3]
+> b.inc <- three.predictor.model$coefficients[4]
+>
+> ## or
+> b.unem <- 4.501e+02
+> b.hgrad <- 4.065e-01
+> b.inc <- 4.275e+00
+>
+>
+> b.unem * (sd.unem / sd.roll)
+[1] 0.1554
+> b.hgrad * (sd.hgrad / sd.roll)
+[1] 0.3656
+> b.inc * (sd.inc / sd.roll)
+[1] 0.6062
+>
+> lm.beta(three.predictor.model)
+Call:
+lm(formula = ROLL ~ UNEM + HGRAD + INC, data = datavar)
+Standardized Coefficients::
+(Intercept)        UNEM       HGRAD         INC
+.0000      0.1554      0.3656      0.6062
+>
+</code>
 see also [[:sequential_regression#eg_3_college_enrollment_in_new_mexico_university|Sequential method]] regression modeling by hand
 see also [[:statistical regression methods]] regression modeling by computing
+<code>
+> fit <- three.predictor.model
+> step <- stepAIC(fit, direction="both")
+Start:  AIC=381.2
+ROLL ~ UNEM + HGRAD + INC
+        Df Sum of Sq      RSS AIC
+<none>               11237313 381
+- UNEM   1   6522098 17759411 392
+- HGRAD  1  12852039 24089352 401
+- INC    1  33568255 44805568 419
+>
+</code>
 ====== Housing ======
 {{housing.txt}}