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Samenvatting les 2 colleges

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Samenvatting les 2 colleges

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  • December 28, 2021
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LES 2


Multiple (=meervoudige) regressie (H3)

Y i= β^ 0 + β^ 1 X 1 i+ β^ 1 X 1 i+ …+ ^β k X ki + u^ i

1. Deriving OLS estimators  argmin
β
SSR Minimaliseren door bèta’s te
n 2 veranderen
 argmin (Σ i=1 u^ i )
β



Y ˆ1 
ˆ 2 
ˆ 0 
Coef. Std. Err. t P>|t| [95% Conf. Interval]

X1 .3318305 .1721011 1.93 0.067 -.0250853 .6887462
X2 .1257858 .037688 3.34 0.003 .0476257 .2039458
_cons 36.79008 17.29449 2.13 0.045 .9235081 72.65665



Voorbeeld: consumptie of 25 Households
 Data on 25 households
 Impact of income (X1) and wealth in stocks (X2) on private consumption (Y) (in
€1000)
 Yi = 0 + 1X1i + 2X2i + ui
 Coefficients measure the impact of a 1 unit increase of an X-variable on
the mean value of Y, holding the values of the other X-variables
constant
 It measures the net or direct effect of an X on Y

Short results OLS-estimation




1

, 2
2 σu
2. Precision of OLS estimators  σ β = 2 2
σ X ( 1−r X )


Y Coef. Std. Err. t P>|t| [95% Conf. Interval]

X1 en X2 moeten X1 .3318305 .1721011 1.93 0.067 -.0250853 .6887462
onafhankelijk zijn
X2 .1257858 .037688 3.34 0.003 .0476257 .2039458
van elkaar =
ceteris paribus _cons 36.79008 17.29449 2.13 0.045 .9235081 72.65665

Hoe > spreiding rond X: hoe zekerder we zijn van de parameters


Goodness-of-fit?

 Do we have a good model?
2 SSM SSR
 R-squared R = =1−
SST SST
 Do we have a better model? (comparing)
 3 important conditions on using R-squared
1. Sample (size) must be the same
2. Dependent variable must be the same
3. Number of estimated parameters must be the same

. reg Y X1 X2

Source SS df MS Number of obs = 25
F(2, 22) = 42.71
Model 126186.655 2 63093.3276 Prob > F = 0.0000
Residual 32501.9575 22 1477.36171 R-squared = 0.7952
Adj R-squared = 0.7766
Total 158688.613 24 6612.02553 Root MSE = 38.436

SSR
N−k ( N−1 )
2 2
 Adjusted R-squared Adj . R =R =1− =1−( 1−R 2)
SST N −k
N −1
 Corrects (penalizes) for the number of estimated parameters: zorgt ervoor
dat je niet oneindig parameters opneemt: hoe > k hoe < adjusted r²
 Conditions
1. Sample (size) must be the same
2. Dependent variable must be the same

How to work with STATA

 Import  first row as variable names
 Data editor
 Sum
. sum

Variable Obs Mean Std. Dev. Min Max

household 25 13 7.359801 1 25
Y 25 163.2936 81.31436 45.73 373
X1 25 163.204 83.23113 36.4 312
X2 25 575.164 380.0727 26 1536.6




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