econometrics introduction

Question 1

what is the probability framework for statistical inference?

Answer 1

a) Population, random variable, and distribution
b) Moments of a distribution (mean, variance, standard deviation, covariance, correlation)
c) Conditional distributions and conditional means
d) Distribution of a sample of data drawn randomly from a population: Y1,…, Yn

Question 2

what is the population?

Answer 2

The group or collection of all possible entities of interest (e.g.school districts, population of workers in the UK etc.)

Question 3

what is the random variable Y?

Answer 3

Numerical summary of a random outcome (e.g. outcome of rolling a die, test score in a district, STR in a district, wage of a person randomly drawn the worker population of the UK)

Question 4

what is the sample space?

Answer 4

all the possible outcomes

Question 5

what is the event?

Answer 5

set of one or more outcomes ie the event that an even number is rolled

Question 6

what is a discrete variable?

Answer 6

Data that can only take certain values ie face of a dice

Question 7

what is continuous variable?

Answer 7

data that can take any value ie time or weight

Question 8

what is the variance?

Answer 8

the measure of the squared spread of the distribution ie E(Y-μ)^2

Question 9

what is the standard deviation?

Answer 9

a measure of how dispersed the data is in relation to the mean. it is the square root of the variance

Question 10

what is skewness?

Answer 10

a measure of assymetry of a distribution. if the skewness is equal to 0 then the dystribution is symmetric

Question 11

what is kurtosis?

Answer 11

measure of the mass in tails, measure of probability of large values

Question 12

what does the postive skew mean about the location of the mode median and mean?

Answer 12

the mode is to the left of the median and the mean is to the right

Question 13

what does negative skew mean about the position of the mode median and mean?

Answer 13

the mode is to the right of the median and the mean is to the left

Question 14

what is the covariance?

Answer 14

covariance is a measure of the linear association between X and Z: its units are units of X x the units of Z. a postive covariance means a postive linear relationship between X and Z

Question 15

what is the correlation coefficient defined in terms of?

Answer 15

it is defined in terms of the covariance

Question 16

what does the correlation coefficient measure?

Answer 16

it measures the linear association

Question 17

what are conditional distributions?

Answer 17

the distribution of Y given values of some other random variable X, for example the distribution of test scores given the STR<20
Pr(Y=y,| X=x) = Pr(X=x, Y=y)/Pr(X=x)

Question 18

what is conditional mean?

Answer 18

mean of the conditional distribution
E(Y| X=x) = Σy_t*Pr(Y=y_t|X=x)

Question 19

what is the law of iterated expectationa?

Answer 19

The mean of Y is the weighted average of the conditional expectation of Y given X, weighted by the probability distribution of X.

Question 20

what is the independence of two random variables?

Answer 20

We say that X and Y are independently distributed (or are independent) if Pr(Y=y|X=x)=Pr(Y=y)

Question 21

if X and Y are independently distributed what is the covariance?

Answer 21

cov(X,Y)=0 but it does not mean if cov(X,Y)=0 they are independent

Question 22

what does random sampling mean for different values of Y?

Answer 22

Y1 and Y2 are independently distributed. they are also identically distributed as they come from the same distribution

Question 23

what are the features of the sampling distribution of Y^_ when n is large>

Answer 23

as n increases the distribution becomes more tightly centered around μ ( the law of large numbers)
moreover, the distribution of Ῡ - μ_Y becomes normal (central limit theorem

Question 24

what is the definition of the consistent estimator

Answer 24

An estimator is consistent if the probability that its falls within an interval of the true population value tends to one as the sample size increases

Question 25

what is the hypothesis testing problem?

Answer 25

make a provisional decision based on the evidence at hand whether a null hypothesis is true, or instead that some alternative hypothesis is true