General Knowledge

Question 1

Cross-Sectional, Panel Data and Time Series

Answer 1

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.

Question 2

Explain Standard Deviation and Variation

Answer 2

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

Question 3

What is the difference between Experimental data and observational data

Answer 3

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.

Question 4

Sample Space and events

Answer 4

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

Question 5

Probability Distribution of a random variable

Answer 5

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

Question 6

Cumulative probability of a random variable

Answer 6

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

Question 7

What is Joint probability and distribution

Answer 7

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.

Question 8

Marginal probability distribution

Answer 8

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

Question 9

Conditional Distribution

Answer 9

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

Question 10

Conditional Expectation

Answer 10

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

Question 11

Law of iterated Expectations

Answer 11

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.

Question 12

What is the Standard Error in a regression?

Answer 12

• 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

Question 13

Kurtosis

Answer 13

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.

Question 14

Skewness

Answer 14

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. ‘

Question 15

I.I.D

Answer 15

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.

Question 16

Chi-Squared

Answer 16

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.

Question 17

Normal Distribution

Answer 17

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

Question 18

Student t

Answer 18

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.

Question 19

F Distribution + Statistics

Answer 19

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

Question 20

The central limit theorem

Answer 20

• 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

Question 21

Explain R2, ESS, SSR, TSS

Answer 21

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

Question 22

Explain what the standard error of the regression is

Answer 22

• 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

Question 23

What is goodness of fit/measures of fit?

Answer 23

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.

Question 24

What is the Standard error of the regression?

Answer 24

• 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 )

Question 25

What is estimator bias?

Answer 25

Difference between expected value of estimator and true value of parameter

Question 26

What is estimator consistency?

Answer 26

Is consistent if:

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

Question 27

What is the point of the F-statistic?

Answer 27

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

Question 28

What is meant by estimator consistency?

Answer 28

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

Question 29

What is meant by estimator efficiency?

Answer 29

• The “best possible” estimator

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

Question 30

What is the Central Limit Theorem

Answer 30

• 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

Question 31

How can you get rid of outliers?

Answer 31

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.

Question 32

What is a dummy trap?

Answer 32

• 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

Question 33

log-level what does β mean

Answer 33

1 unit change in X gives B1 change in Y

Question 34

log-log what is β

Answer 34

if we change x by one percent,

we’d expect y to change by β1 percent”

Question 35

level-log what is β

Answer 35

If we increase x by one percent,

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

Question 36

unbiased estimators conditions

Answer 36

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

Question 37

when is a dummy variably useful?

Answer 37

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

Question 38

What is the residual?

Answer 38

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

Question 39

The smaller the residuals…

Answer 39

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

Question 40

What is the difference between regression residuals and errors?

Answer 40

• 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

Question 41

What is standard error?

Answer 41

• 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

Question 42

What is a continuous random variable?

Answer 42

A varable that in theory can go towards infinity

Question 43

What is the F-distribution?

Answer 43

• 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%

Question 44

What is the shape of the F distribution?

Answer 44

• 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.

Question 45

How do we interpret variance and correlation?

Answer 45

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

Question 46

What does endogeneity mean? what is the opposite?

Answer 46

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

Question 47

Why is a random walk model nonstationary?

Answer 47

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

Question 48

What are the three properties of estimators?

Answer 48

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

Question 49

Yi - Ŷ is….

Answer 49

The residual (prediction mistake)

Question 50

What is a correlation?

What is its particularty compared to covariance?

Answer 50

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

Question 51

What is the Conditional expectation of Y given X?

Answer 51

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

Question 52

What is a random sample?

Answer 52

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 → ∞).