SRaI

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Kartei Details

Karten	125
Sprache	English
Kategorie	Informatik
Stufe	Universität
Erstellt / Aktualisiert	04.10.2019 / 11.10.2019
Weblink	https://card2brain.ch/box/20191004_srai
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Explain the tradeoff between quality and quantity.

What is given? (4)

State the final formular.

Give an example.

What can we conclude?

given
- finite population y1...yN
- g(y) = quantity of interest
- \(\mu_g=E(g(y))\)
- \(\hat\mu_g=\frac{E(R~g(y))}{E(R)}\)
\((\hat\mu_g - \mu_g) = \rho_{Rg}~\sigma_g~\sqrt{(N-n)/n}\)
- accuracy = quality (correlation between availability of data and quantity of interest) * variation (of quantity of interest) * quantity
example: 90% out of 1.000.000 with 5% correlation is equal to 3600 samples without correlation
>> quantity doesnt compensate quality (important in times of big data)

Why is the assumption X (i.e. own price) -> Y (sales) often wrong. Explain.

How to tackle this? (3)

Y depends on X but also on Z (observable, but not available) and U (unobservable)
- \(f_{Y|X,Z,U}=\int f_{Y|X,Z,U}f_{Z,U}~dZdU \neq f_{Y|X}\)
solutions
- extend dataset by Z, U (i.e. competitors price)
- X independent of Z, U (i.e. own price independent of competitor's price)
- find instrumental variable which influcences X (own price) but independent of Z, U (i.e. competitor's price)

Explain the effect of making X independent of Z,U.

How can this be done?

\(\int\frac{f_{Y,X,Z,U}}{f_{X|Z,U}}dZdU = \int\frac{f_{Y,X,Z,U}}{f_{X}}dZdU = f_{Y|X}\)
>> experiment: make X independent / randomly of other influencing effects

What is the main idea of ANOVA? (1)

Name statistics and idea of it (3)

State the F-statistics. (3)

ANOVA = analysis of variance
test in experimental setting (i.e. comparing two versions >> AB-test)
RSS_X = sum of squares residuals = sum of squared deviation of y_jk to group mean y_bar_k .
RSS_zero = sum of squared deviation to overall mean y_bar . .
idea: if RSS_X and RSS_zero are close >> low variance, low difference >> no significant difference/effect
\(F=\frac{\frac{RSS_0-RSS_X}{K-1}}{\frac{RSS_X}{n-K}}\)
- nominator: how much difference normed by number of groups
- denominator: variance of RSS_X (error in groups) bias corrected (# groups)
- >> relates difference of overall RSS_0 to groups RSS_X with the variance within the group

Name elements of the ANOVA table. (6)

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