beta_coefficients
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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.1558445455.txt.gz · Last modified: 2019/05/21 22:30 by hkimscil