If we test a statistical hypothesis, we have the following condition:
Rejecting null hypothesis and accepting alternative hypothesis when null
hypothesis is true. The condition is called (3%)
P-value.
Significance level of test.
Type II error.
Type I error.
If it is known that X has a mean of 25 and a variance of 16, then, which
is the upper bound for P(|X − 25|≥ 12) ? (3%)
1/5
1/4
1/9
1/16
If we collect n observation points, we want to estimate a simple
regression function E(Y ) = β1 X1 from observed data. What is the normal
equation about this regression? (3%)
Breusch-Pagan test.
Goldfeld-Quandt test.
Durbin-Waston test.
Durbin h test.
skew to the left.
skew to the right.
symmetric.
this distribution id skew, but we cannot judge by measure of skewness
directly.
The confidence interval for the sample regression function slope (3%)
can be used to compare the value of the slope relative to that of the
intercept.
adds and subtracts 1.96 from the slope.
can be used to conduct a test about a hypothesized population
regression function slope.
allows you to make statements about the economic importance of your
estimate.
has a standard error that is not normally distributed even in large
samples since D is not a normally distributed variable.
indicates the difference in the slopes of the two regressions.
has no meaning since (Xi ×Di) = 0 when Di =0
indicates the slope of the regression when Di = 1 .
Sample selection bias (3%)
occurs when a selection process influences the availability of data and
that process is related to the dependent variables.
is more important for nonlinear least squares estimation than for OLS.
results in the OLS estimator being biased, although it is still consistent.
is only important for finite sample results.
For the polynomial regression model. (3%)
the critical values from the normal distribution have to be changed to
1.962, 1.963, etc
you can still use OLS estimation techniques, but the t-statistics do not
have an asymptotic normal distribution
you need new estimation techniques since the OLS assumptions do not
apply any longer
the techniques for estimation and inference developed for multiple
regression can be applied
The power of the test (3%)
is the probability that the test actually incorrectly rejects the null
hypothesis when the null is true.
is one minus the size of the test.
is the probability that the test correctly rejects the null when the
alternative is true.
the slopes tell you the effect of a unit increase in X on the probability of
Y.
the β ′ s do not have a simple interpretation
β0 is the probability of observing Y when all X’s are 0.
β0 cannot be negative since probabilities have to lie between 0 and 1.
If the errors are heteroskedastic, then (3%)
the usual formula cannot be used for the OLS estimator
your model becomes overidentified
the OLS estimator is not BLUE
the OLS estimator is still BLUE as long as the regressors are
nonrandom
Consider a competitive market where the demand and the supply depend
on the current price of the good. Then fitting a line through the
quantity-price outcomes will (3%)
estimate neither a demand curve nor a supply curve
give you the exogenous part of the demand in the first stage of TSLS
give you an estimate of the demand curve
enable you to calculate the price elasticity of supply
If you had a two regressor regression model, then omitting one variable
which is relevant (3%)
can result in a negative value for the coefficient of the included variable,
even though the coefficient will have a significant positive effect on Y if
the omitted variable were included.
makes the sum of the product between the included variable and the
residuals different from 0.
will always bias the coefficient of the included variable upwards.
will have no effect on the coefficient of the included variable if the
correlation between the excluded and the included variable is negative.
Let the p.d.f. of X be defined by f (x) = x3 / 4 , 0 < x < 2 . Find the p.d.f. of
Y = X2 . (10%)
Suppose the random variable X has the moment-generating function
M(t) = (1 − t)−2 , t < 1, find E(X) and σ2 . (10%)
The logarithm of the likelihood function (L) for estimating the population
mean and variance for an i.i.d. normal sample is as follows:
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