# GLM on Unimodal response variable

I am simulating a simple unimodal response Variable Y which is determined by X. $y = c \times exp (- \frac{(x-u)^2}{2t^2} )$.

x <- 1:100
y <- 50 * exp(-((x-50)^2)/(2*10^2))


In this equation, u determines the position of the mode along x If I now run a negative binomial GLM on these data

library(MASS)
g <- glm.nb(y~x)


x is not statistically significant Pr(>|z|) = 0.505. When I move the position of the mode from the middle of x just two units to the left.

y <- 50 * exp(-((x-48)^2)/(2*10^2))


the p-value of x drops to Pr(>|z|) = 0.00106. Why does the position of the mode have such a strong influence?