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--- beta_coefficients [2019/05/21 12:35] – hkimscil
+++ beta_coefficients [2020/12/09 18:45] – [e.g.] hkimscil
@@ Line 1: / Line 1: @@
 ====== Beta coefficients in linear regression ======
-refer to https://www.listendata.com/2015/04/standardized-vs-unstandardized.html
-$$ \beta = b * \frac{sd(x)}{sd(y)} $$
+{{:pasted:20190521-113150.png?200}}
+\begin{align*}
+\large{\beta = b * \frac{sd(x)}{sd(y)}} \
+\end{align*}
 <code>
@@ Line 81: / Line 84: @@
 >
 </code>
+====== e.g. ======
+<code>
+# get marketing data
+marketing <- read.csv("http://commres.net/wiki/_media/marketing_from_datarium.csv")
+head(marketing)
+# note that I need - X to get rid of X column in the marketing data
+mod <- lm(sales ~ . - X, data=marketing)
+summary(mod)
+</code>
+<code>
+> marketing <- read.csv("http://commres.net/wiki/_media/marketing_from_datarium.csv")
+> head(marketing)
+  X youtube facebook newspaper sales
+1  276.12    45.36     83.04 26.52
+2   53.40    47.16     54.12 12.48
+3   20.64    55.08     83.16 11.16
+4  181.80    49.56     70.20 22.20
+5  216.96    12.96     70.08 15.48
+6   10.44    58.68     90.00  8.64
+# note that I need - X to get rid of X column in the marketing data
+> mod <- lm(sales ~ . - X, data=marketing)
+> summary(mod)
+Call:
+lm(formula = sales ~ . - X, data = marketing)
+Residuals:
+     Min       1Q   Median       3Q      Max
+-10.5932  -1.0690   0.2902   1.4272   3.3951
+Coefficients:
+             Estimate Std. Error t value Pr(>|t|)
+(Intercept)  3.526667   0.374290   9.422   <2e-16 ***
+youtube      0.045765   0.001395  32.809   <2e-16 ***
+facebook     0.188530   0.008611  21.893   <2e-16 ***
+newspaper   -0.001037   0.005871  -0.177     0.86
+---
+Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
+Residual standard error: 2.023 on 196 degrees of freedom
+Multiple R-squared:  0.8972,	Adjusted R-squared:  0.8956
+F-statistic: 570.3 on 3 and 196 DF,  p-value: < 2.2e-16
+</code>
+<code>
+install.packages(lm.beta)
+library(lm.beta)
+lm.beta(mod)
+</code>
+<code>
+lm.beta(mod)
+Call:
+lm(formula = sales ~ . - X, data = marketing)
+Standardized Coefficients::
+ (Intercept)      youtube     facebook    newspaper
+.000000000  0.753065912  0.536481550 -0.004330686
+>
+</code>
+These beta coefficients also can be got from the coefficents from standardized data.
+<code>
+mod.formula <- sales ~ youtube + facebook + newspaper
+all.vars(mod.formula)
+marketing.temp <- sapply(marketing[ , all.vars(mod.formula)], scale)
+head(marketing.temp)
+mod.scaled <- lm(sales ~ ., data=marketing.scaled)
+head(marketing.scaled)
+coefficients(mod.scaled)
+</code>
+<code>> mod.formula <- sales ~ youtube + facebook + newspaper
+> all.vars(mod.formula)
+[1] "sales"     "youtube"   "facebook"  "newspaper"
+> marketing.temp <- sapply(marketing[ , all.vars(mod.formula)], scale)
+> head(marketing.temp)
+          sales     youtube   facebook newspaper
+[1,]  1.5481681  0.96742460  0.9790656 1.7744925
+[2,] -0.6943038 -1.19437904  1.0800974 0.6679027
+[3,] -0.9051345 -1.51235985  1.5246374 1.7790842
+[4,]  0.8581768  0.05191939  1.2148065 1.2831850
+[5,] -0.2151431  0.39319551 -0.8395070 1.2785934
+[6,] -1.3076295 -1.61136487  1.7267010 2.0408088
+> mod.scaled <- lm(sales ~ ., data=marketing.scaled)
+> head(marketing.scaled)
+       sales     youtube   facebook newspaper
+  1.5481681  0.96742460  0.9790656 1.7744925
+-0.6943038 -1.19437904  1.0800974 0.6679027
+-0.9051345 -1.51235985  1.5246374 1.7790842
+  0.8581768  0.05191939  1.2148065 1.2831850
+-0.2151431  0.39319551 -0.8395070 1.2785934
+-1.3076295 -1.61136487  1.7267010 2.0408088
+> coefficients(mod.scaled)
+  (Intercept)       youtube      facebook     newspaper
+-5.034110e-16  7.530659e-01  5.364815e-01 -4.330686e-03
+>
+> </code>
+check out that
+''lm.beta(mod) == coefficients(mod.scaled)''
+and
+we can compare the beta coefficients among each other. From the ''lm.beta(mod)'', ''youtube'', ''facebook'', and ''newspaper'' 순으로 설명력을 갖는다고 말할 수 있다.