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beta_coefficients [2019/05/21 12:35] hkimscilbeta_coefficients [2020/12/09 18:47] (current) – [e.g.] hkimscil
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 ====== Beta coefficients in linear regression ====== ====== 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> <code>
Line 81: Line 84:
  
 </code> </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 1  276.12    45.36     83.04 26.52
 +2 2   53.40    47.16     54.12 12.48
 +3 3   20.64    55.08     83.16 11.16
 +4 4  181.80    49.56     70.20 22.20
 +5 5  216.96    12.96     70.08 15.48
 +6 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 
 + 0.000000000  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  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
 +> 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 
 +베타를 구하고 나면 서로의 계수값을 절대비교할 수 있다. 
 +''lm.beta(mod)''의 아웃풋을 보고 
 +''youtube'', ''facebook'', and ''newspaper'' 순으로 설명력을 갖는다고 말할 수 있다 (혹은 newspaper를 분석에서 제외하고 다시 분석하여 둘만의 설명력을 보는 것도 방법이다.
 +
  
beta_coefficients.1558409717.txt.gz · Last modified: 2019/05/21 12:35 by hkimscil

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