Applied Empirical Methods

• describes Bernoulli-Experiments,

• Binomial distributed random variables result from n-times repetition of a Bernoulli-Experiment

• X ∼ Bin(n, p)) : X ="number of successes after repeating the experiment n times”

• Example: How likely is it to get k-hits at n-tries, wie oft haben 65% oder mehr der Befragten zugestimmt, dass irh Manager biased bei Gehaltserhöhungen ist?

• Random variable X=“number of delayed projects in one year”

when the association between variables is more meaningful on a percentage scale

• on the basis of independent Bernoulli-Experiments

• "Distribution of waiting of the first success"

• mainly used when the frequency of an event over a certain time is considered in a random experiment

• X ∼ P(λ) : X ="number of events that happen in a period of time"

• λ coincides with the expected number of events happening in the specified period of time

• Linear

• x²,y²

• log linear

• log y, 1/y

• log log

• log y, 1/y

• log x, 1/x

• linear log

• log x, 1/x

• used to measure times between events

• (X ∼ Exp(λ))

• when the probability is uniformly distributed within an interval

• (X ∼ U(a, b))

• if they hold you can use X ~ N(mu, se)

q,size,prob

q, lambda

q,prob

q, mean, sd

p, mean, sd

(falls reelle Zahlen benötigt *100)

Student's t-Test Based on Sample Statistics

mean, sd, length(data), “two-sided”, 0.95, mu

two-sided, less, greater

• Mu, sofern es sich um einen Hypotesentest zum Mittelwert handelt

• Ohne mu, beim CI

which(data, <= threshold

<=, =, >=

threshold vorher definieren

• Reduces skewness of our original data

• Improves linearity

• Boosts validity of our data

• Required: origninal data must (approx) follow a log-normal distribution

Heteroscedasticity

if p-value <= 0: Ho verwerfen, Data is heteroscedastic

• Multicollinearity

• VIF > 5 or 10 suggests the variables are highly redundant

• Multicollinearity

• Ho: b0 = b1 = b2…

• H1: Ho stimmt nicht

• Multicollinearity

• After F-Test

• Autocorrelation

• If p-value < 0: There’s autocorrelation, Ho rejected

1. Detect heteroscedasticity (bp)

2. Revise the model

   • rename variables (invheight (x), volumeperft (y)

   • X: 1/x

   • Y: y/x

3. Run regression

4. Check residual plot

5. Regression diagnostic

1. Linearity

2. Strict Exogenity

3. No Corr of X and the Error Term

4. No Corr of Error Terms (Autocorrelation)

5. Homoscedasticity

6. Normality (QQ Plot)

7. No perfect Multicollinearity (only MRM)

Keep it simple

• P(X=a)

P(X<=a)

• indicates how steep the curse of a curve is

• Types

  • Mesokurtic: 3 average

  • Excess Kurtosis

    • Leptokurtic: > 3 indicates flatter tails

    • Platykurtic < 3 indicates larger tails

• dependent

• Effect

• response

• outcome

• Independent

• Cause

• explanatory

• predictor