第5章のStataコード
第5章 推測統計の基礎
5.1 統計的仮説検定の考え方
5.1.3 コイン投げの例
clear
display binomial(100, 60, 0.5) - binomial(100, 40, 0.5)
.95395593
5.2 平均値の検定
5.2.5 Rによる例題演習
"distributions.csv", clear
import delimited summarize dista, detail
distA
-------------------------------------------------------------
Percentiles Smallest
1% 1.005143 1.00268
5% 1.071364 1.007606
10% 1.242875 1.027831 Obs 100
25% 1.436728 1.061649 Sum of wgt. 100
50% 2.139604 Mean 2.042323
Largest Std. dev. .6105609
75% 2.566881 2.906963
90% 2.839471 2.909304 Variance .3727846
95% 2.889779 2.940179 Skewness -.1250327
99% 2.947699 2.95522 Kurtosis 1.643932
display sqrt(100) / sqrt(r(Var)) * r(mean)
33.449949
5.2.6 \(p\)値
display 1 - normal(1.250113) + normal(-1.250113)
.21125827
5.3 回帰係数の検定
5.3.2 \(\hat{\beta}_1\)の分布のシミュレーション
clear
set seed 2022
postfile sim beta1 using betahats1000, replace
forvalues i = 1/10000 {
quietly capture drop X Y
quietly set obs 100
quietly generate X = rnormal(0, 1)
quietly generate Y = 1 + 5 * X + rnormal(0, 1)
quietly regress Y X
post sim (e(b)[1, 1])
}
postclose sim
use betahats1000, clear
summarize beta1
beta1
-------------------------------------------------------------
Percentiles Smallest
1% 4.924835 4.876307
5% 4.94757 4.88193
10% 4.959229 4.882976 Obs 10,000
25% 4.978507 4.887352 Sum of wgt. 10,000
50% 5.000195 Mean 4.999877
Largest Std. dev. .0320337
75% 5.021528 5.115664
90% 5.040558 5.115983 Variance .0010262
95% 5.051876 5.117807 Skewness -.0005134
99% 5.074158 5.122896 Kurtosis 3.105771
histogram beta1, frequency bin(12)
5.3.6 Rによる分析例
"wage.csv", clear
import delimited generate lwage = log(wage)
regress lwage educ exper
Source | SS df MS Number of obs = 3,010
-------------+---------------------------------- F(2, 3007) = 333.00
Model | 107.459149 2 53.7295746 Prob > F = 0.0000
Residual | 485.182496 3,007 .161351013 R-squared = 0.1813
-------------+---------------------------------- Adj R-squared = 0.1808
Total | 592.641645 3,009 .196956346 Root MSE = .40169
------------------------------------------------------------------------------
lwage | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
educ | .093168 .0036118 25.80 0.000 .0860863 .1002498
exper | .0406574 .0023344 17.42 0.000 .0360802 .0452346
_cons | 4.666035 .06379 73.15 0.000 4.540958 4.791111
------------------------------------------------------------------------------
display (0.093168 / 0.0036118)
25.795448
5.4 信頼区間
5.4.2 Rによる分析例
regress lwage educ exper
Source | SS df MS Number of obs = 3,010
-------------+---------------------------------- F(2, 3007) = 333.00
Model | 107.459149 2 53.7295746 Prob > F = 0.0000
Residual | 485.182496 3,007 .161351013 R-squared = 0.1813
-------------+---------------------------------- Adj R-squared = 0.1808
Total | 592.641645 3,009 .196956346 Root MSE = .40169
------------------------------------------------------------------------------
lwage | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
educ | .093168 .0036118 25.80 0.000 .0860863 .1002498
exper | .0406574 .0023344 17.42 0.000 .0360802 .0452346
_cons | 4.666035 .06379 73.15 0.000 4.540958 4.791111
------------------------------------------------------------------------------
regress lwage educ exper, level(99)
Source | SS df MS Number of obs = 3,010
-------------+---------------------------------- F(2, 3007) = 333.00
Model | 107.459149 2 53.7295746 Prob > F = 0.0000
Residual | 485.182496 3,007 .161351013 R-squared = 0.1813
-------------+---------------------------------- Adj R-squared = 0.1808
Total | 592.641645 3,009 .196956346 Root MSE = .40169
------------------------------------------------------------------------------
lwage | Coefficient Std. err. t P>|t| [99% conf. interval]
-------------+----------------------------------------------------------------
educ | .093168 .0036118 25.80 0.000 .0838589 .1024772
exper | .0406574 .0023344 17.42 0.000 .0346405 .0466742
_cons | 4.666035 .06379 73.15 0.000 4.501618 4.830451
------------------------------------------------------------------------------