Created
September 15, 2018 19:26
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An example where dropping the "more important" predictor from a regression makes the "less important" predictor become statistically insignificant
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# In this example, both x1 and x2 predict y and the two predictors are correlated | |
# with each other, but x2 has a much larger regression coefficient that x1. In a | |
# regression with both x1 and x2, both predictors are statistically significant. | |
# However if we drop x2, then x1 becomes insignificant. This is because dropping | |
# x2 dramatically increases the residual standard error. This effect overwhelms the | |
# increase in the estimated coefficient of x1 that arises from its correlation with | |
# the omitted variable x2. | |
library(MASS) | |
set.seed(1234) | |
n <- 100 | |
S <- matrix(c(1, 0.1, | |
0.1, 1), 2, 2, byrow = TRUE) | |
X <- mvrnorm(n, mu = c(0, 0), S) | |
x1 <- X[,1] | |
x2 <- X[,2] | |
epsilon <- rnorm(n) | |
b0 <- 0 | |
b1 <- 0.2 | |
b2 <- 2 | |
y <- b0 + b1 * x1 + b2 * x2 + epsilon | |
reg1 <- lm(y ~ x1 + x2) | |
reg2 <- lm(y ~ x1) | |
reg3 <- lm(y ~ x2) | |
summary(reg1) | |
summary(reg2) |
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