# Relationship between parameters estimates of continuous variables and dummy variables

I had asked this question on cross validated before, and have deleted it.

Suppose we have a standard wage equation: $$w_{i}=β+β_{1}educ_{i}+x_{i}'\gamma+ϵ_{i}$$

where educ corresponds to education levels, $x_{i}$ is a vector of covariates. If we treat educ as a continuous variables, we obtain a single estimate of $\beta_{1}$ . However, if we create dummy variables for different education levels, and therefore allow for different marginal effects (assuming we have a large enough sample size), we obtain k−1 different estimates of education levels if we include a constant. Can we think of think of the single estimate obtained from treating education as continuous as a weighted average of the k-1 coefficients, weighted by the number of individuals in each education block?