Direct and indirect effects in OLS regression

sysuse auto, clear

eststo clear

// Bivariate relationship:
eststo: regress price mpg
// Accounting for confounding variable:
eststo: regress price mpg displacement

// Accounting for confounding variable in three steps:
  // 1
quietly regress mpg displacement
predict u, residuals
  // 2
quietly regress price displacement
predict v, residuals
  // 3
eststo: regress v u

// Table:
esttab, rename(u mpg) se nomtitle label varwidth(30)

Random graphs (122): Specification checks of OLS regression

// Simulate data set
clear
set obs 1000
set seed 1
generate x = runiform()
generate z = runiform()
generate u = rnormal()
generate y1 =      0 +      x   + 0 * z + u
generate y2 =      0 + 10 * x^2 + 0 * z + u
generate y3 = exp(-1 +      x   + 0 * z + u)

// Correctly specified model
regress y1 x z
rvfplot,   name(rvf1, replace)  title(Fitted values vs. residuals) nodraw
rvpplot x, name(rvpx1, replace) title(Predictor variable x vs. residuals) nodraw
rvpplot z, name(rvpz1, replace) title(Predictor variable z vs. residuals) nodraw
graph combine rvf1 rvpx1 rvpz1, col(3) xsize(7) ysize(2) /// 
                                title(Residual plots of correctly specified model) ///
                                name(correct, replace) nodraw

// Missing out on quadratic relationship
regress y2 x z
rvfplot,   name(rvf2, replace)  title(Fitted values vs. residuals) nodraw
rvpplot x, name(rvpx2, replace) title(Predictor variable x vs. residuals) nodraw
rvpplot z, name(rvpz2, replace) title(Predictor variable z vs. residuals) nodraw
graph combine rvf2 rvpx2 rvpz2, col(3) xsize(7) ysize(2) ///
                                title(Residual plots of model missing quadratic term) ///
                                name(quadractic, replace) nodraw

// Missing out on exponential relationship
regress y3 x z
rvfplot,   name(rvf3, replace)  title(Fitted values vs. residuals) nodraw
rvpplot x, name(rvpx3, replace) title(Predictor variable x vs. residuals) nodraw
rvpplot z, name(rvpz3, replace) title(Predictor variable z vs. residuals) nodraw
graph combine rvf3 rvpx3 rvpz3, col(3) xsize(7) ysize(2) ///
                                title(Residual plots of model missing exponential shape) ///
                                name(exponential, replace) nodraw

graph combine correct quadractic exponential, col(1) xsize(7) ysize(6) altshrink