Gebruiker:Pjetter/klad: verschil tussen versies
Verwijderde inhoud Toegevoegde inhoud
Regel 327:
and
:<math> {Var} \left( aX + b \right) = a^2 Var (X)</math>
this will be used:
:<math>V \left( \widehat{\beta} \right) = V \left( \frac{\sum_i^{n} ( \beta x_i^2 + \varepsilon_i x_i)}{\sum_i^{n} x_i^2} \right)</math>
:<math>V \left( \widehat{\beta} \right) = V \left( \frac{\sum_i^{n} \beta x_i^2}{\sum_i^{n} x_i^2} + \frac{\sum_i^{n} \varepsilon_i x_i}{\sum_i^{n} x_i^2} \right)</math>
:<math>V \left( \widehat{\beta} \right) = V \left( \frac{\sum_i^{n} \beta x_i^2}{\sum_i^{n} x_i^2} + \frac{\sum_i^{n} \varepsilon_i x_i}{\sum_i^{n} x_i^2} \right)</math>
:<math>V \left( \widehat{\beta} \right) = V \left( \beta + \frac{\sum_i^{n} \varepsilon_i x_i}{\sum_i^{n} x_i^2} \right)</math>
:<math>V \left( \widehat{\beta} \right) = x_i^2 V \left( \frac{\sum_i^{n} \varepsilon_i}{\sum_i^{n} x_i^2} \right)</math>
Using the definition given for Variance of epsilon:
:<math>Var \left( {\varepsilon_i} \right) = \sigma^2</math>
:<math>V \left( \widehat{\beta} \right) = \frac{\sigma^2} {\sum_i^{n} x_i^2}</math>
==Nav==
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