Download residual analysis of intercept

*case 1 population with intercept and estimation with intercept
capture program drop testingb
program define testingb, rclass
drop _all
set obs 200
* generating error term u drawn from normal distribution
gen u = rnormal(0,2)
* generating explanatory variable x randomly drawn from uniform distribution
gen x = runiform()
* get population estimator of b in model y = 1 + 2 * x + u
gen y = 1 + 2 * x + u
gen t = _n
tsset t
reg y x
capture predict yhat, xb
sum y
global ymean = r(mean)
sum x
global xmean = r(mean)
* calculate sample b, possible error from deviation operator
gen double beta = [(yhat - $ymean)*(x - $xmean)]/ [(x - $xmean)*(x - $xmean)]
sum beta
return scalar m = r(mean)
return scalar se = r(sd)/sqrt($obs)
gen double e = y - yhat
sum e
return scalar em = r(mean)
return scalar ese = r(sd)* r(sd)
end
global obs 200
* run the sub-program to get sample b for many times
simulate m = r(m) se = r(se) em = r(em) ese = r(ese), reps(1000) : testingb
list m
sum m,detail
sum em,detail
sum ese, detail
* the distribution of b is as betagraph:
hist m, bin(100) normal name(betagraph, replace)
hist em, bin(100) normal xline(0) name(errorgraph, replace)
hist ese, bin(100) normal xline(4) name(evargraph, replace)
graph combine errorgraph evargraph,
///
title("Properties of Sample Error term Case 1")
subtitle("Mean and variance") name(analyse1, replace)
//////////////////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////
*case 2 population with intercept and estimation without intercept
capture program drop testingb
program define testingb, rclass
drop _all
set obs 200
* generating error term u drawn from normal distribution
gen u = rnormal(0,2)
* generating explanatory variable x randomly drawn from uniform distribution
gen x = runiform()
* get population estimator of b in model y = 1 + 2 * x + u
gen y = 1 + 2 * x + u
gen t = _n
tsset t
*intercept less regression
reg y x, nocons
capture predict yhat, xb
sum y
global ymean = r(mean)
sum x
global xmean = r(mean)
* calculate sample b, possible error from deviation operator
gen double beta = [(yhat - $ymean)*(x - $xmean)]/ [(x - $xmean)*(x - $xmean)]
sum beta
return scalar m = r(mean)
///
return scalar se = r(sd)/sqrt($obs)
gen double e = y - yhat
sum e
return scalar em = r(mean)
return scalar ese = r(sd)* r(sd)
end
global obs 200
* run the sub-program to get sample b for many times
simulate m = r(m) se = r(se) em = r(em) ese = r(ese), reps(1000) : testingb
list m
sum m, detail
sum em, detail
sum ese, detail
* the distribution of b is as betagraph:
hist m, bin(100) normal name(betagraph, replace)
hist em, bin(100) normal xline(0) name(errorgraph, replace)
hist ese, bin(100) normal xline(4) name(evargraph, replace)
graph combine errorgraph evargraph,
title("Properties of Sample Error term Case 1")
subtitle("Mean and variance") name(analyse1, replace)
//////////////////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////
*case 3 population without intercept and estimation with intercept
capture program drop testingb
program define testingb, rclass
drop _all
set obs 200
* generating error term u drawn from normal distribution
gen u = rnormal(0,2)
* generating explanatory variable x randomly drawn from uniform distribution
gen x = runiform()
* get population estimator of b in model y = 2 * x + u
gen y = 2 * x + u
gen t = _n
tsset t
reg y x
///
///
capture predict yhat, xb
sum y
global ymean = r(mean)
sum x
global xmean = r(mean)
* calculate sample b, possible error from deviation operator
gen double beta = [(yhat - $ymean)*(x - $xmean)]/ [(x - $xmean)*(x - $xmean)]
sum beta
return scalar m = r(mean)
return scalar se = r(sd)/sqrt($obs)
gen double e = y - yhat
sum e
return scalar em = r(mean)
return scalar ese = r(sd)* r(sd)
end
global obs 200
* run the sub-program to get sample b for many times
simulate m = r(m) se = r(se) em = r(em) ese = r(ese), reps(1000) : testingb
list m
sum m, detail
sum em, detail
sum ese, detail
* the distribution of b is as betagraph:
hist m, bin(100) normal name(betagraph, replace)
hist em, bin(100) normal xline(0) name(errorgraph, replace)
hist ese, bin(100) normal xline(4) name(evargraph, replace)
graph combine errorgraph evargraph,
///
title("Properties of Sample Error term Case 1")
subtitle("Mean and variance") name(analyse1, replace)
///