/* Regress 1 - Bivariate Regression
*/

clear all
set seed 210312

scalar b0 = 1                  // intercept
scalar b1 = 0.5                // slope
scalar sigma = 0.75            // residual standard deviation

set obs 25

generate x = runiform(0,5)
sort x  // for graphing
generate mu_y = b0 + b1*x

generate eps = rnormal(0, sigma)
generate y = mu_y + eps

graph twoway (scatter y x) (line mu_y x, lpattern(dash) lcolor(red)) (pcspike y x mu_y x, lcolor(black)), ///
  title(Data Generating Process) legend(label(2 "true E(y)") label(3 "epsilon")) ///
  name(datagen)
  
twoway (scatter y x) (line mu_y x, lpattern(dash) lcolor(red)) (lfit y x, lcolor(black)), ///
  title(Estimation Result) legend(label(2 "true E(y)") label(3 "estimated E(y)")) ///
  name(estimation)

regress y x

test x

test x = 0.5