General Knowledge Flashcards

1
Q

Cross-Sectional, Panel Data and Time Series

A

Cross-sectional data is a sample on different entities, for example firms, households, companies, cities, states, and countries that are observed at a given point in time or in a given period.

Time-series is data for a single entity (firms, households, companies, cities, states, countries) collected at multiple time periods.

Panel data, also called longitudinal data, are data for multiple entities in which each entity is observed at two or more periods.

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2
Q

Explain Standard Deviation and Variation

A

Both Standard Deviation and Variation measures the “spread” of s probability distribution. The Variation is measured in squared unites, while standard deviation is the square root of this number.

Std is the square root of the variance. Variance is a measure for how far the actual observation is from the observed one, given in square unites. Hence, we use std since its more easy to interpret

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3
Q

What is the difference between Experimental data and observational data

A

Experimental data comes from an experiment that is designed to investigate the casual effect. Observational data is obtained by measuring actual behaviour outside of an experiment.

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4
Q

Sample Space and events

A

Sample space is the set of all possible outcomes. An event is what gives the outcomes. So one event might have a huge sample space; lots of things can happen from that event

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5
Q

Probability Distribution of a random variable

A

The probability distribution lists all possible values for the variable and the probability that each value will occur. These probabilities sum to 1.

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6
Q

Cumulative probability of a random variable

A

Cumulative probability refers to the likelihood that the value of a random variable is within a given range.

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7
Q

What is Joint probability and distribution

A

Joint probability is the probability of two events happening together (think venn-diagram). The joint distribution is the probability that X and Y take on certain values. Lets say that X is 1 when its raining and 0 when its not. Y is 1 when there is more than 10 degrees outside and 0 otherwise. The joint distribution of this is the probabilities of how these two scenarios happen, with 4 different outcomes. Each outcome has a probability and summed together they give a value of 1.

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8
Q

Marginal probability distribution

A

Just another name for its probability distribution. Term is used to distinguish the distribution of Y alone from the joint distribution.

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9
Q

Conditional Distribution

A

The distribution of a random variable Y conditional on another variable X taking on a specific value.

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10
Q

Conditional Expectation

A

Conditional expectation means that the value of a variable Y is dependent on the value of another variable X.

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11
Q

Law of iterated Expectations

A

The expected outcome of one event can be calculated by finding all the probability and expectation for all variables that affects it.

Intuitively: The mean height of adults is the weighted average of the mean heght for men and the mean height for women, weighted by the proportions of men and women. Mean of Y is the weighted average og the conditional expectation of Y given X.

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12
Q

What is the Standard Error in a regression?

A
  • how accurately your sample data represents the whole population
  • how accurate your regression fits real population
  • mean distance between regression line and the actual observation

Intuitively: Think of a linear regression. For each point, The actual value will probabily not be similar to the expected value. The Standard Error is the mean distance between the observed value and the expected value (regression)

Formula is:
SSR/(n - 2)

n - 2 because it is correcting a bias with two regressor coefficients that were estimated (B0 and B1)

Note:

  • SER measures the mean of the variation
  • sd measures the amount of variation
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13
Q

Kurtosis

A

Kurtosis is how much mass the distribution has in its tails, and is therefore a measure of how much of the variance of Y that arises from extreme values. Extreme values are called outliers. The greater the kurtosis of a distribution is, the more likely it is to have outliers.

The kurtosis of a distribution is a measure of how much mass is in its tails and therefore is a measure of how much of the variance of Y arises from extreme values. BTW: An extreme value of Y is called an outlier.

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14
Q

Skewness

A

Skewness can be quantified as a representation of the extent to which a given distribution varies from a normal distribution. A normal distribution has a skew of zero, represented with equal weight on each tail.

If you are measuring height, you might get a mean of 172 with the tails being equally weighted.

If you are measuring income for people working 100%, few people will have an income under 300K. From 300K to 600K, there will probably be a steep increase. From 600K and to infinity, there will be fewer and fewer people, and the curve will be less and less steep. This means that we get the “long tail” on the right side. “long tail” on right side can be called a “positive skew”, so we can say that the distribution is positively skewed.

If we have an easy exam, and a lot of people get A’s or B’s, we will have a negative skew. The long tail will be on the left side, and slowly increase until it hits C or B. From there it will go steeply up. ‘

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15
Q

I.I.D

A

Independent and Identically distributed

Independent: The result from one event does not have any impact on the other event. So if you roll two dices, the result you got on the first dice does not affect the sum you will get on the second.

Identically: if you flip a coin (heads/tails) each throw gives you a 50/50 chance. The probability does not change over time.

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16
Q

Chi-Squared

A

DISTRIBUTION:
The distribution is asymmetrical, with a mean of zero and a standard deviation of one. It is positively skewed. It can be tested on categorical variables, which are variables that only falls into one category (male vs female etc.)

Chi-squared tests can be used when we:

1) Need to estimate how closely an observed distribution matches an expected one
2) need to estimate if two random variables are independent.

GOODNESS OF FIT:
When you have one independent variable, and you want to compare and observed frequency to a theoretical. For example, does age and car accidents have a relation?

H0: no relation between age and var accidents
HA: There is a relation between age and car accidents

Chi-Squared value that’s greater than our critical value implies that there is a relation between age and car accident, hence reject the hull hypothesis. It means that there most likely is a relation, but does not tell us how large that relation is.

Another example is if you flip a coin 100 times. You would expect it to get 50/50 head/tails. The further away from 50/50, the less goodness of fit.

Tests how well a sample of a data matches the known characteristics at the larger population that the sample is trying to represent. For example, the x^2 tells us how well the actual results from 100 coin flips compare to the theoretical model which assumes 50/50. The further away from 50/50, the less goodness of fit (and more likely to conclude that this is not a representative coin).

TEST FOR INDEPENDENCE:

Categorical data for two independent variables, and you want to see if there is an association between them.

Does gender have any significance on Driving test outcome? Is there a relation between student gender and course choice? Reasearcher collect data and compare the frequencies at which rate male and female students select among the different classes. The x^2 for independence tells us how likely it is that random chance can explain the observed difference.

P-value smaller than 0,05: Chi-square value bigger than critical: there is some relation in gender and driving test scores. Reject H0.

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17
Q

Normal Distribution

A
  • bell shape
  • both sides equally weighted
  • mean of 0
  • std of 1
  • kurtosis of 3
  • no skewness
  • symmetrical
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18
Q

Student t

A

Similar to the normal distribution which has […..]. The difference is that this one got heavier tails, or in other words, a greater kurtosis. This leads to more variance of Y from outliers.

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19
Q

F Distribution + Statistics

A

F-distribution

  • Divide one chi-squared variable by another = F-distribution
  • Used specially in analysis of variance
  • Function of ratio between two independent variables, each which has a chi-squared distribution

F-Statistics:
- Group A, B and C put on 10 mg, 5 mg and placebo.
- Mean Square Between (MSB) = Mean square between these groups
- Mean Square Error (MSE) = Mean Variance of all these groups added together
F-stat = MSB/MSE
- A large F-stat might indicate that the population means are not equal

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20
Q

The central limit theorem

A
  • Each variable themselves can be random
  • But as the sample increases, it will go towards a normal distribution
  • The more we add, the closer we get to the real population distribution
  • Higher N gives higher probability of having Normality and Consistency
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21
Q

Explain R2, ESS, SSR, TSS

A

R2

  • How much variance of y is explained by the regressors
  • 0 to 1
  • Increase when adding more regressors
  • Adjusted will penalize adding regressors
  • If B1=0, X explains nothing of var in Y, and R2 = 0

Explained Sum of Squares (ESS)
- Difference between predicted value and the mean of the dependent variable
Sum of Squared
Residuals (SSR)
- Difference between predicted and observed value at squared level.

Total Sum of Squares

  • Difference between observed dependent variable and its mean
  • TSS = SSR + ESS
22
Q

Explain what the standard error of the regression is

A
  • std of its sampling distribution
  • average distance between observed values and the regression line
  • mean distance between observed value and reg line
  • can be used to make confident intervalls
23
Q

What is goodness of fit/measures of fit?

A

When you have estimated a linear regression, you will wonder how good the regression line describes the data. The R2 and the standard error measure how well the OLS regression line fits the data.

The R-squared (R^2) represents the proportion of the variance for a dependent variable. It ranges between 0 and 1, but will usually fall in some place in between the extreme values.

If β1=0, X explains nothing of the variance in Y, and R-squared should be 0.

The Explained Sum of Squares (ESS) is the sum of the differences between the predicted value and the mean of the dependent variable

The Sum of Squared Residuals (SSR) is the difference between the observed value and the predicted value. We can interpret the residual as the remaining, or the unexplained.

The Total Sum of Squares is the difference between the observed dependent variable, and its mean.

24
Q

What is the Standard error of the regression?

A
  • Standard deviation of the residuals
  • Mean distance between observed value and predicted value
  • Can be used to make confident intervals.

SSR/(n-2)

n-2 because it is correcting a bias with two regressor coefficients that were estimated (β_1 and β_0 )

25
Q

What is estimator bias?

A

Difference between expected value of estimator and true value of parameter

26
Q

What is estimator consistency?

A

Is consistent if:

• It converges in probability to the true value if the sample increases

27
Q

What is the point of the F-statistic?

A

To find out if the means between two populations are significantly different.

28
Q

What is meant by estimator consistency?

A

An estimator converges in probability to the correct population value as the
sample size increases (the normal distribution gets tighter and tighter)

29
Q

What is meant by estimator efficiency?

A
  • The “best possible” estimator

- Efficiency: how close it is to the true population estimator

30
Q

What is the Central Limit Theorem

A
  • if you have a large sample, the mean and std will be close to its true paramters
  • goes towrds normal distribution
  • gets closer when N gets higher
31
Q

How can you get rid of outliers?

A

Transform & Delete

Winzoring: Transforming extreme values.

Triming: deleting extreme values

For example, you can winzorize/trim at 5% interval. This will affect 2,5% of the empirical distribution to the right and left.

32
Q

What is a dummy trap?

A
  • add dummy for each chategorical variable, eg. male and female
  • when the number of dummys is equal to each category it can take on
  • leads to multicollinearity
33
Q

log-level what does β mean

A

1 unit change in X gives B1 change in Y

34
Q

log-log what is β

A

if we change x by one percent,

we’d expect y to change by β1 percent”

35
Q

level-log what is β

A

If we increase x by one percent,

we expect y to increase by (β1/100) units of y.

36
Q

unbiased estimators conditions

A

linear in parameters,
random sampling,
sample variation in explanatory variable,
zero conditional mean (E(u|x)=0)

37
Q

when is a dummy variably useful?

A

when we want to quantify a concept thats qualitative (like gender)

38
Q

What is the residual?

A

It is the difference between the estimated value of the dependent variable and the actual value of the dependent variable

39
Q

The smaller the residuals…

A

the better the fit, and the closer estimated Ys will be to the observed Ys.

40
Q

What is the difference between regression residuals and errors?

A
  • error –> is the difference between the data observed and the population regression line using the actual values of α and β
  • residual –> is the difference between the data and the sample regression line using the parameter estimates: α(hat) and β(hat)
  • residual can be referred to as an estimation of the errors
41
Q

What is standard error?

A
  • sometime referred to as standard error of the mean, it is the variability of the mean of data from different samples taken from a single population
  • this is the most basic version but in general, if you have multiple sets of data e.g. medians, and found the standard deviations of of them, you would have found the standard error
  • it is the standard deviation of multiple sample moments taken from one population
  • standard error, in the standard deviation of sample statistics
42
Q

What is a continuous random variable?

A

A varable that in theory can go towards infinity

43
Q

What is the F-distribution?

A
  • Suppose we have two random variables each of which follows a chi-squared distribution
  • A variable follows an F-distribution if it is constructed as the ratio of two Chi-squared distributed variables each of which is divided by its degrees of freedom:

let X{1] ~ χ{k{1}}^2 and X{2}~χ{k{2}}^2

X = (X{1}/k{1})/(X{2}/k{2}) = (X{1}/X{2}) * (k{2}/k{1}) ~ F{k{1},k{2}}

  • The F-distribution arises naturally in econometric analysis when we consider the ratios of variables which are constructed as the sum of squared random variables
  • comparing the s.d. or variance of two sets of data to see if they are statistically different to each other - more variation in errors from the theortical values
  • the value given in the table give you F values which if are greater than the critical value (usually 5%) it is rejected
  • Note that the order of these degrees of freedom is important:
    F{k{1},k{2}}^5% ≠ F{k{2},k{1}}^5%
44
Q

What is the shape of the F distribution?

A
  • For k{1}>4 the F distribution has a similar shape to the chi-squared distribution.
  • The F distributions with k{1} less than 4 does not have the typical shape:
  • For k{1}= 3 –> f(0) >0 while for χ= 1 or 2, f(χ) –> ∞ as χ –> 0 - rather like we saw for the chi-squared distribution –> again similar shape.
  • Another similarity with the chi-squared distribution is that as both k{1} and k{2} become large, the shape of the F distribution becomes symmetric.
45
Q

How do we interpret variance and correlation?

A

Variance: squared unit measure of the standard variance/difference bewteen an observation and the mean. Correlation: linear relationship between two variables, will always be between -1 and 1

46
Q

What does endogeneity mean? what is the opposite?

A

That a regressor is correlated with the error term. Exogeneity, when the variable is uncorrelated to the error term.

47
Q

Why is a random walk model nonstationary?

A

The distribution of Y will vary over time, making the variance NOT being constant

48
Q

What are the three properties of estimators?

A
  1. Unbiasedness: The estimator is correct (on avg.)
  2. Consistency: increased sample will increase the efficiency
  3. Efficiency: estimator is precise
49
Q

Yi - Ŷ is….

A

The residual (prediction mistake)

50
Q

What is a correlation?

What is its particularty compared to covariance?

A

Correlation (ρ) is a measure of the linear association between 2 variables.

The correlation doesn’t depend on the unit of measurement, whereas covariance does

51
Q

What is the Conditional expectation of Y given X?

A

It is a weighted average of possible values of Y, but the weights reflect the fact tha X has taken on a specific value.

52
Q

What is a random sample?

A

Subset of individuals chosen from a population such that:

Each individual is chosen randomly and entierly by chance.
Each subset of k individuals has the same chance to be chosen.
It can be done with or without replacement (n → ∞).