Frisch-Waugh Theorem: Why the estimates are slightly different between multiple regression and partitioned regression? I run two kinds of regressions to compare generic version of multiple regression and partitioned regression.
My model is
$$\textrm{ wage}=\beta_0+\beta_1 \textrm{educ}+\beta_2 \textrm{exper}+\beta_3 \textrm{tenure}+u,$$
and for partitioned regression, first I regress $\rm educ$ on $\rm exper,~ tenure$ to get residual
$$\textrm{educ}=\gamma_0+\gamma_1 \textrm{exper}+\gamma_2\textrm{ tenure}+v_1.$$
And then I regress $\textrm{wage}$ on $\textrm{exper}, ~\textrm{tenure}$ to get another residual. That is,
$$\textrm{wage}=\delta_0+\delta_1\textrm{exper}+\delta_2 \textrm{tenure}+v_2.$$
Finally, I regress the second residual on the first residual
$$v_2=\rho_0+\rho_1v_1+\epsilon.$$
 ─────────────────────────────────────────────────────────────
                            Model 1             Model 2       
                     ─────────────────────────────────────────
   (Intercept)                1.623 ***           0           
                             (0.01922)           (0.01919)    
   educ                       0.2548 ***                      
                             (0.0203)                         
   exper                      0.05593 *                       
                             (0.02339)                        
   tenure                     0.1594 ***                      
                             (0.02235)                        
   xtilde                                         0.2416 ***  
                                                 (0.0192)     
                     ─────────────────────────────────────────
   N                        526                 526           
   R2                         0.316               0.2319      
 ─────────────────────────────────────────────────────────────
   All continuous predictors are mean-centered and            
   scaled by 1 standard deviation.  *** p < 0.001; **         
   p < 0.01; * p < 0.05.                                      

Column names: names, Model 1, Model 2


According to Frisch-Waugh theorem, which states that multiple regression estimate is supposed to be equal to that of partitioned regression (as described step by step above), it must hold the following: $\hat\beta_1=\hat\rho_1$. However, the following results of estimates on educ and xtilde are slightly different ($0.2548$ vs. $0.2416$). I wonder if I made a mistake or whether there is some source of gap in my understanding of the theory.
For your reference, I ran the regressions using R with the data wage1 embedded in the package called wooldridge.
{r}
library{wooldridge}
wage <- lm(lwage~educ+exper+tenure, data = wage1)

# Regress educ on exper, tenure
step.1 <- lm(educ~exper+tenure, data = wage1)
xtilde <- step.1$residuals

# Regress lwage on exper, tenure
step.2 <- lm(lwage~exper+tenure, data = wage1)
ytilde <- step.2$residuals
wage_fwt <- lm(ytilde~xtilde)

summary(wage, wage_fwt)


Turning comment to answer.

FWL theorem has not been violated; it survives the day. A quick run in $\mathsf R$ with the following script
 wage <- lm(lwage ~ educ + exper + tenure, data = wage1)
 educ_res <- lm(educ ~ exper + tenure, data = wage1)$residuals
 wage_res <- lm(lwage ~ exper + tenure, data = wage1)$residuals
 summary(lm(wage_res ~ educ_res)) 
 summary(wage) 

shows that the required estimated coefficients are respectively $9.023\mathrm{e}-02$ and $0.092029.$
