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beta_coefficients

Beta coefficients in linear regression

$$ \beta = b * \frac{sd(x)}{sd(y)} $$

# import test score data "tests_cor.csv"
tests <- read.csv("http://commres.net/wiki/_media/r/tests_cor.csv")
colnames(tests) <- c("ser", "sat", "clep", "gpa")
tests <- subset(tests, select=c("sat", "clep", "gpa"))
attach(tests)
lm.gpa.clepsat <- lm(gpa ~ clep + sat, data = tests) 
summary(lm.gpa.clepsat)
Call:
lm(formula = gpa ~ clep + sat, data = tests)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.197888 -0.128974 -0.000528  0.131170  0.226404 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)  
(Intercept)  1.1607560  0.4081117   2.844   0.0249 *
clep         0.0729294  0.0253799   2.874   0.0239 *
sat         -0.0007015  0.0012564  -0.558   0.5940  
---
Signif. codes:  
0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.1713 on 7 degrees of freedom
Multiple R-squared:  0.7778,	Adjusted R-squared:  0.7143 
F-statistic: 12.25 on 2 and 7 DF,  p-value: 0.005175

> 
> sd.clep <- sd(clep)
> sd.sat <- sd(sat)
> sd.gpa <- sd(gpa)
> lm.gpa.clepsat <- lm(gpa ~ clep + sat, data = tests) 
> summary(lm.gpa.clepsat)

Call:
lm(formula = gpa ~ clep + sat, data = tests)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.197888 -0.128974 -0.000528  0.131170  0.226404 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)  
(Intercept)  1.1607560  0.4081117   2.844   0.0249 *
clep         0.0729294  0.0253799   2.874   0.0239 *
sat         -0.0007015  0.0012564  -0.558   0.5940  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.1713 on 7 degrees of freedom
Multiple R-squared:  0.7778,	Adjusted R-squared:  0.7143 
F-statistic: 12.25 on 2 and 7 DF,  p-value: 0.005175

> b.clep <- 0.0729294
> b.sat <- -0.0007015
> beta.clep <- b.clep * (sd.clep/sd.gpa)
> beta.sat <- b.sat * (sd.sat/sd.gpa)
> lm.beta(lm.gpa.clepsat)

Call:
lm(formula = gpa ~ clep + sat, data = tests)

Standardized Coefficients::
(Intercept)        clep         sat 
  0.0000000   1.0556486  -0.2051189 

> beta.clep
[1] 1.055648
> beta.sat
[1] -0.2051187
> 
beta_coefficients.txt · Last modified: 2019/05/21 22:00 by hkimscil