Final Exam Review

Question 1

steps to calculating a basic regression equation

Answer 1

1. calculate E(x) and E(y)
2. calculate actual minus expected for each variable, each observation
3. square “actual minus expected” for only X
4. for y, take (actual(x) - expected(x))*(actual(y)-expected(y))
5. take the sums of 3 and 4
6. take ratio of these sums with XY on top
   this is your estimator

intercept = E(y) -E(x)*slope

Question 2

interpret:

selling price = 150 + .027(square footage)

Answer 2

for every increase of 1 square foot, we can expect to see the selling price of the house increase by .027

Question 3

Total sum of squares

Answer 3

total actual variation in Y

sum of (Actual Y - expected Y)^2

Question 4

Explained sum of squares

Answer 4

the modeled variation in Y

sum of (estimated y - expected Y)^2

Question 5

steps for an R^2

Answer 5

1. take the actual values of Y, get E(y)
2. take (ACTy - EXPy), square it, add it up
3. thats the actual variation in Y
4. use the results of regression to calculate predicted values of Y for every X
5. take (PREDICTEDy-EXPECTEDy); square it; add it up
6. take the ratio of 5 over 3 (ESS/TSS)

Question 6

r^2

Answer 6

how much of the variance in our data is explained by the regression model

Question 7

Standard Error of OBservations

Answer 7

the standard deviation of the error term

-how far are the actual values from our fitted line

Question 8

What does a t-stat of 1.96 actually mean?

Answer 8

this means you could create an interval of a certain width (1.96 SE above and below our hypothesized mean) and if you repeated your sampling 100 times, 95/100 times that interval would contain the true population mean

Question 9

standard error of the beta hat

Answer 9

remember beta is a random variable

• therefore, it has an expected value and distribution
• that distribution, the sampling distribution, has a spread, measured by the variance and the SD
• the standard error of beta hat is the SD of the sampling distribution…it measures the spread

Question 10

heteroskedastic

Answer 10

variance of the error term changes

Question 11

homoskedastic

Answer 11

variance of the error term is constant

Question 12

why does a smaller standard error of the beta hat usually correlate with a larger t stat?

Answer 12

because as SE decreases, the width of the distribution gets smaller and smaller…decreasing our chances of having an insignificant value…spread is TIGHT

Question 13

F-statistic

Answer 13

-used to test a joint hypothesis that ALL of our betas are really zero

Question 14

formula for an f-statistic

Answer 14

(1-R^2)/(n-k-1)

k is # of IVs

Question 15

whats the formula for testing a subset of variables?

Answer 15

(RSSrestricted-RSSunrestricted)/q
______________________________
RSSunrestricted/n-k-1

Question 16

after running a simple p and q demanded regression, how do we find the elasticity of a product at a certain point?
ex: q = 1147 - 7.93*p, p = 70

Answer 16

(p/q)*coefficient = elasticity at that point

70*-7.93 = 555
1147-555=592

-7.93*(70/592)

Question 17

what’s the most basic way to estimate a curvilinear regression?

Answer 17

convert the data to natural logs, dummy

Question 18

how do we convert an equation BACK from a log?

Answer 18

1. take the exponential of your intercept term
2. take your coefficient (elasticity) and raise your P to it
3. multiply these things

ex: Q demanded = 23,156*p^(-.873)

Question 19

log-log (def and interpretation)

Answer 19

• take the log of both the variables
• changes interpretation to percentages
  ex: a certain % change in X is associated with a certain % change in Y

Question 20

log-linear (def and interpretations)

Answer 20

• convert the DV to logs
• leave IVs just as they are
• changes to the DV are interpreted as percentages, NOT units

Question 21

interpret: Ln(selling price) = 6.21 - .08*(age)

Answer 21

log linear, so:

a one year increase in age of the house translates to an 8% increase in the selling price of the house

Question 22

can you compare the R^2 of a linear regression and a log linear regression?

Answer 22

NO, the DV’s are two very different thigns

Question 23

linear-log (def and interpretation)

Answer 23

convert the IVs to logs

-changes in the IV are interpreted as percentages, not units

Question 24

interpret: # of dining out experiences = -37.9 + 11.33*(LnIncome)

Answer 24

a 1% increase in income translates to a .11 increase in dining out experiences per month
-OR a 9% increase in income translates to a 1 time increase in dining out per month

Question 25

panel data

Answer 25

combination of cross sectional AND time series | -data varies across entities and across time

Question 26

fixed effects regression (time and entity)

Answer 26

- holding constant the effects of different locations or places or times - done using thing specific binary variables and dummy coding

Question 27

how to test for significant of time fixed effect and entity fixed effect

Answer 27

(RSSrestricted-RSSunrestricted)/q ______________________________ RSSunrestricted/n-k-1

Question 28

how do we write in fixed effects on STATA?

Answer 28

xi: regress y x1 x2 x3 i.x4 i.x5 | - stata will then create dummy variables for all but one of the state or time categories

Question 29

if you ran a regression with a binary variable and your coefficient is -.00377, how do you interpret this?

Answer 29

in states and years where the legal drinking age was 21, the data shows that seat belt usage was, on average, .37% lower than in states and years where the legal drinking age was not 21

Question 30

probit

Answer 30

in a probit model, the model plays the role of z in a cumulative standard normal distribution -estimated beta is the change in the z value associated with a unit change in X it spits out the chance that something is or isn't occurring

Question 31

how does a pro bit work?

Answer 31

when state runs a pro bit, it is choosing values for the parameters that maximize a function -this function is called a likelihood function the likelihood we speak of is the likelihood that we observe the given Y values basked on our given X values

Question 32

time series

Answer 32

used for forecasting, data varies across time periods...not markets or person

Question 33

static or contemporaneous time series variables

Answer 33

an IV that is a statistic from the same time...such as Real GDP and Unemployment for each respective year

Question 34

dynamic time series variable

Answer 34

a statistic from the previous year...ex: REAL GDP and GDP from previous year

Question 35

path order Autoregressive Model

Answer 35

uses Y(T-1) to forecast Yt - there is no rule that says you can only use one lag - you can run a regression where IVs are Yt-1, Yt-2, Tt-3...so on

Question 36

how do you decide on how many lags to include?

Answer 36

Bayes Information Criterion Test | -need RSS, total number of time periods, number of lags

Question 37

BIC method

Answer 37

1. take ln(RSS/periods) 2. take number of (lags + 1)*(Ln(periods)/periods) 3. add both numbers of that - the smallest BIC value is the one you use!

Question 38

why do we want BIC to be the smallest?

Answer 38

1. the BIC has two parts, one part is a function of RSS 2. we know this gets smaller as you add more variables 3. the second part is a function of lags 4. if you add a lag, the second part gets bigger and IF additional lag doesn't do much to reduce RSS, the RSS only gets a little smaller...so overall BIC gets bigger 5. but if you add a lag and it does a lot to make RSS smaller, then the first part gets a lot smaller, the second part gets a little bigger but the overall bic went down 6. lower is better; the benefit you get from adding another lag outweighs the addition of the lag

Question 39

autoregressive distributed lag model

Answer 39

adding an additional variable - ex: past changes in GDP PLUS, say, unemployment - written like: ADL(p,q)

Question 40

BIC for an ADL(p,q) model

Answer 40

ln(RSS(k))/T) + (k)*(Ln(t)/t) where k is the total number of coefficients across all RHS variables

Question 41

granger causality

Answer 41

- a test to see whether an entire series of a RHS variable has useful predictive content - tests whether the estimated coefficients are all distinguishable from zero

Question 42

granger causality formula

Answer 42

(RSSrestricted-RSSunrestricted/q) ---------------------------------------- RSSunrestricted/(n-k-1)

Question 43

how to interpret a LOGIT

Answer 43

e^(result)/(1+e^result) result is a z-score that you can use to find out the likelihood of something occurring

Question 44

what are probits and logits interpreted as?

Answer 44

model is interpreted as probabilities that something occurred! - used for prediction/identification: based on certain factors, what is the probability that a person/observation falls into this group or that ex: the higher a person's income, the greater likelihood he/she owns a car and drives themselves to work

Question 45

what does your beta coefficient represent in a pro bit regression?

Answer 45

- estimated beta is the change in the z-value associated with a unit change in x - -if b is positive, a higher level of X is associated with a higher level of the z-value, therefore associated with a higher prob that y = 1 - -if b is negative, a higher level of X is associated with a lower level of the z-value, and associated with a lower probablitliy that y = 1

Question 46

does STATA use a linear model when coming up with a regression equation for the data?

Answer 46

NO, it uses a maximum likelihood estimation | -likelihood that we observe the given Y values baed on our given X values

Question 47

the impact of a change in x on the z score is linear, but what about the impact on the probability?

Answer 47

IT IS NOT LINEAR. | -marginal effects will tell us the average, but this is misleading

Question 48

why is marginal effects of a probit misleading?

Answer 48

the average change in probability if a variable changed by x units is your MFX...however, this is not representative of the whole group -the increase in probability is drastically effected by the spotting of the change

Question 49

what two different functions do a pro bit and a logit use?

Answer 49

probit: standard normal cumulative density function logit: logistic cumulative density function

Question 50

do probits and log its have R^2?

Answer 50

they have pseudo R^2 | -no sums of squares, can't have R^2