//Gabarito

use "C:\Users\fcs\Downloads\votoeconUS.dta" 

//a.

//b.
sum growth votes
*ou
sum growth votes, detail

//c.
scatter growth votes, mlabel(year) || lfit growth votes

//d.
scatter growth votes, mlabel(year) yline(.3793939) xline(52.07112)

//e.
*Gerar variaveis constantes com as medias
qui sum growth, detail
gen mean_growth = r(mean)

qui sum votes, detail
gen mean_votes = r(mean)

*Gerar variavel - media
gen xi_xbar = growth-mean_growth
gen yi_ybar = votes-mean_votes

*Multiplicar as variaveis de x e y
gen cov_xy = xi_xbar*yi_ybar

*Obter covariância de x e y
egen covariance = sum(cov_xy)
replace covariance = covariance / (_N-1)
sum covariance
*Covariância é o único valor de `covariance`

//f.
format cov_xy %9.2f
scatter growth votes, mlabel(cov_xy) yline(.3793939) xline(52.07112)


//g. 
reg votes growth
//ou
egen sum_xi_xbar = sum(xi_xbar^2)
scalar beta = sum_xi_xbar / cov_xy

//h.

//i.
reg votes growth
predict voteshat

scatter votes voteshat || lfit votes voteshat

//j.
kdensity votes, addplot(kdensity voteshat)

//k.

//l.
gen uhat = votes - voteshat
sum uhat
kdensity uhat

//m.
reg uhat voteshat