lecture 4 Flashcards
with the 3 least squares assumptions ( along with our line equation)
we know the asymptotic distribution of the OLS estimator
why are normally distributed variables standardized
to learn something about the population - population regression line
learning about a population regression line:
use data from simple random sample
parameters: Bo, B1
estimators: OLS Bcaret o, Bcaret1
determined the distribution of the estimators: asymptotically
calculate confidence interval
(B1 or Bo) +/- critical value (ex: 1.96) x SE(B1 or Bo)
- most commonly the slope
- standard normal critical value comes from normal distribution
critical values to know
1.96 = 95%
1.645 = 90%
how to correctly interpret a confidence interval
our confidence interval estimator contains the true marginal effect of the Y on X 95% of the time, for this sample our estimate of this interval is [>,<] bigger one comes first
hypothesis testing
most often = 0
null hypothesis
no change
alternative hypothesis
trying to prove
we never conclude the null
we just fail to reject
where on the graph is the null
inside the rejection zone, biggest part
where is the alternative hypothesis
in the tails
formula for test statistic (t test)
B1 - (what your test is equal to, usually 0) / standard deviation (root MSE on STATA)
when do we reject a two-tailed test
when the test statistic falls beyond one of the critical values
intercept
Bo
value of Y when x is 0
_cons: 0 is a constant
slope
B1
value of Y for a 1 unit change in x
slope = change
right one-tailed test
when b1 is greater than 0
left one-tailed test
when B1 < 0
null hypothesis is always
equal sign
critical values for 95%
1 tailed = -/+ 1.645
2 tailed = -/+ 1.96
critical values for 90%
1 tailed = -/+ 1.645
2 tailed = -/+ 1.28
p-test how to
calculate the test statistic
compare with p-value
when do we reject using p-value 2-tailed
p-value < significance level
x < 0.05
p-value for 1 tailed
p-value < significance level
x/2 < 0.05
