Solutions Manual For Categorical and Nonparametric Data
Analysis Choosing the Best Statistical Technique 1st Edition By
E. Michael Nussbaum 9781848726031 ALL Chapters .
what are the 2 types of categorical data? - ANSWER: -nominal: no ordering\n-ordinal: categories are
ordered
what was the original approach to looking at relationships between variables? what were the
problems with this approach? - ANSWER: Treat all variables as categorical, usually dichotomized.
Create contingency tables. Would use chi-square tests of independence\nProblems:\n-loses
information (b/c dichotomizes variables that may be continuous, ignoring variation)\n-complicated
for more than one test variable (if try to control for too many variables, get very small #s)\n-statistical
theory not well developed (e.g. no chi-square test for hypothesis "relationship b/w income and party
preference is same for high school and college grads")
after regression 'discovered,' what was an important limitation of this approach? - ANSWER: -correct
only when dependent variable is at interval or ratio level (not really appropriate for categorical
dependent variables)
what are the 3 different things that the term "multiple regression" is used to describe? - ANSWER: 1.
Model: statistical model for how data were generated\n2. Estimation method: approximate guesses
for unknown parameters in a model\n3. Computing Algorithm: for any given estimation method,
there are often several competing ways of doing the computations, all of which will give same
numerical answers
what are models and what are examples of models? - ANSWER: a set of probabilistic assumptions
(usually expressed as a set of equations and using probabilistic notation) about how the data were
generated\n-often a set of equations expressing what we believe or are willing to assume (usually
deliberately oversimplified)\n-for example, for a dichotomous dependent variable, there are several
alternative models: linear probability model, logit linear probability model, probit model, log-linear
model\n-models usually contain unknown parameters that need to be estimated
what are estimation methods and what are examples of estimation methods? - ANSWER: a way of
using sample data to get an approximation for the unknown parameters\n-for a linear regression
model, we could use ordinary least squares, weighted least squares, maximum likelihood\n-each
method has advantages and disadvantages\n-a given estimation method, like weighted least squares,
can be used for many different kinds of models
what is a computing algorithm and what are examples of computing algorithms? - ANSWER: for any
given estimation method, there are often several competing ways of doing the computations, all of
which will give the same numerical answers\n-for maximum likelihood estimation, for example, we
could use iterative proportional fitting, Newton-Raphson, EM algorithm
what are the 5 assumptions of the linear regression model? - ANSWER: 1. linearity assumption\n2.
mean independence\n3. homoskedasticity\n4. no autocorrelation\n5. normal distribution of the error
term
what is the linearity assumption? - ANSWER: the dependent variable is a linear function of a set of
variables plus an error term (where the error term represents the variables not included)\n-this linear
equation applies to all individuals in the sample
what is the assumption of mean independence? - ANSWER: the x's are unrelated to the random
disturbance (not the same as saying x's are independent of the random disturbance)\n\n-no
correlation between the error term and any of the x's \n\n-the expected value of the error term,
, given a particular value of x, is 0 (i.e. knowing what x's value is doesn't affect the expected value of
the error term, which is always 0)\n-this is important, b/c if there is correlation b/w the error term
and the x's, this would lead to bias (would mean there is a lurking variable that is associated both with
the x's and with the y, leading to a spurious relationship b/w x and y)
what is the assumption of homoskedasticity? - ANSWER: there is constant variance of the error term
across individuals\n-so if you know x, it does not affect the expected variance of the error term, which
is always equal to a constant sigma^2
what is the assumption of no autocorrelation? - ANSWER: for any 2 random errors for any 2
individuals, the covariance (i.e. correlation) is 0\n-no correlation between error terms of individuals in
the sample\n-example of violation: ask a married couple something...there may be a variable not
included in the model that affects their answer and that is the same for both of them
what is the assumption of normally distributed error term? - ANSWER: the error term is Normally
distributed\n-note: this doesn't make any assumptions about distribution of X's (can be non-Normal)
why do we need these 5 assumptions? - ANSWER: The assumptions are plausible approximations in
many cases, and they justify the OLS estimator\n-in other words, the 5 assumptions imply that the
OLS estimator has certain optimal properties\n-if the 5 assumptions are true, OLS will be as good or
better than any estimation method
what do the various assumptions imply about the OLS estimator b (i.e. the slope coefficient)? -
ANSWER: -assumptions 1 and 2 imply that b is unbiased (linearity and mean independence -->
unbiased)\n-assumptions 3 and 4 imply that OLS b is BLUE \n\n-assumption 5 implies that OLS b is
normally distributed across repeated samples (so we can use a normal table for significance tests and
confidence intervals), b is MVUE, and b is MLE
what does it mean to say assumptions 3 and 4 imply that OLS b is BLUE? - ANSWER: best linear
unbiased estimator\n-i.e. among all linear unbiased estimators, b has minimum sampling variance\n-
ensures that usual standard error estimates are approximately unbiased, i.e. consistent
what does it mean to say assumption 5 implies that OLS b is MVUE? - ANSWER: minimum variance
unbiased estimator\n-stronger than BLUE\n-among all unbiased estimators (both linear and
nonlinear), b has minimum sampling variance
what does it mean to say assumption 5 implies that OLS b is the maximum likelihood estimator? -
ANSWER: means that using b as our estimate would lead to the same estimation method as using the
maximum likelihood estimator
which of the assumptions are part of the Gauss-Markov Theorem? - ANSWER: Assumptions 1-4\n-
linearity, mean independence, homoskedasticity, and no autocorrelation\n-same assumptions that
make b BLUE
which of the 5 assumptions of the linear regression model is the least important and why? - ANSWER:
assumption 5 (error term is Normally distributed) \n\n-if sample is reasonably large, Central Limit
Theorem will ensure that distribution of b is approximately Normal, regardless (so could go ahead and
use Normal distribution for significance tests, etc.)
what is the expected value of a dichotomous/dummy variable ? - ANSWER: the expected value of a
dichotomous variable is equal to the probability that the variable (πi) = 1
how does this affect the interpretation of a linear regression model where the dependent variable is
dichotomous? - ANSWER: since the model implies that the expected value of the dependent variable
is a linear function of the x's, this is the same as saying the probability of an event is a linear function
of the x's\n-this leads to the "linear probability model"
Analysis Choosing the Best Statistical Technique 1st Edition By
E. Michael Nussbaum 9781848726031 ALL Chapters .
what are the 2 types of categorical data? - ANSWER: -nominal: no ordering\n-ordinal: categories are
ordered
what was the original approach to looking at relationships between variables? what were the
problems with this approach? - ANSWER: Treat all variables as categorical, usually dichotomized.
Create contingency tables. Would use chi-square tests of independence\nProblems:\n-loses
information (b/c dichotomizes variables that may be continuous, ignoring variation)\n-complicated
for more than one test variable (if try to control for too many variables, get very small #s)\n-statistical
theory not well developed (e.g. no chi-square test for hypothesis "relationship b/w income and party
preference is same for high school and college grads")
after regression 'discovered,' what was an important limitation of this approach? - ANSWER: -correct
only when dependent variable is at interval or ratio level (not really appropriate for categorical
dependent variables)
what are the 3 different things that the term "multiple regression" is used to describe? - ANSWER: 1.
Model: statistical model for how data were generated\n2. Estimation method: approximate guesses
for unknown parameters in a model\n3. Computing Algorithm: for any given estimation method,
there are often several competing ways of doing the computations, all of which will give same
numerical answers
what are models and what are examples of models? - ANSWER: a set of probabilistic assumptions
(usually expressed as a set of equations and using probabilistic notation) about how the data were
generated\n-often a set of equations expressing what we believe or are willing to assume (usually
deliberately oversimplified)\n-for example, for a dichotomous dependent variable, there are several
alternative models: linear probability model, logit linear probability model, probit model, log-linear
model\n-models usually contain unknown parameters that need to be estimated
what are estimation methods and what are examples of estimation methods? - ANSWER: a way of
using sample data to get an approximation for the unknown parameters\n-for a linear regression
model, we could use ordinary least squares, weighted least squares, maximum likelihood\n-each
method has advantages and disadvantages\n-a given estimation method, like weighted least squares,
can be used for many different kinds of models
what is a computing algorithm and what are examples of computing algorithms? - ANSWER: for any
given estimation method, there are often several competing ways of doing the computations, all of
which will give the same numerical answers\n-for maximum likelihood estimation, for example, we
could use iterative proportional fitting, Newton-Raphson, EM algorithm
what are the 5 assumptions of the linear regression model? - ANSWER: 1. linearity assumption\n2.
mean independence\n3. homoskedasticity\n4. no autocorrelation\n5. normal distribution of the error
term
what is the linearity assumption? - ANSWER: the dependent variable is a linear function of a set of
variables plus an error term (where the error term represents the variables not included)\n-this linear
equation applies to all individuals in the sample
what is the assumption of mean independence? - ANSWER: the x's are unrelated to the random
disturbance (not the same as saying x's are independent of the random disturbance)\n\n-no
correlation between the error term and any of the x's \n\n-the expected value of the error term,
, given a particular value of x, is 0 (i.e. knowing what x's value is doesn't affect the expected value of
the error term, which is always 0)\n-this is important, b/c if there is correlation b/w the error term
and the x's, this would lead to bias (would mean there is a lurking variable that is associated both with
the x's and with the y, leading to a spurious relationship b/w x and y)
what is the assumption of homoskedasticity? - ANSWER: there is constant variance of the error term
across individuals\n-so if you know x, it does not affect the expected variance of the error term, which
is always equal to a constant sigma^2
what is the assumption of no autocorrelation? - ANSWER: for any 2 random errors for any 2
individuals, the covariance (i.e. correlation) is 0\n-no correlation between error terms of individuals in
the sample\n-example of violation: ask a married couple something...there may be a variable not
included in the model that affects their answer and that is the same for both of them
what is the assumption of normally distributed error term? - ANSWER: the error term is Normally
distributed\n-note: this doesn't make any assumptions about distribution of X's (can be non-Normal)
why do we need these 5 assumptions? - ANSWER: The assumptions are plausible approximations in
many cases, and they justify the OLS estimator\n-in other words, the 5 assumptions imply that the
OLS estimator has certain optimal properties\n-if the 5 assumptions are true, OLS will be as good or
better than any estimation method
what do the various assumptions imply about the OLS estimator b (i.e. the slope coefficient)? -
ANSWER: -assumptions 1 and 2 imply that b is unbiased (linearity and mean independence -->
unbiased)\n-assumptions 3 and 4 imply that OLS b is BLUE \n\n-assumption 5 implies that OLS b is
normally distributed across repeated samples (so we can use a normal table for significance tests and
confidence intervals), b is MVUE, and b is MLE
what does it mean to say assumptions 3 and 4 imply that OLS b is BLUE? - ANSWER: best linear
unbiased estimator\n-i.e. among all linear unbiased estimators, b has minimum sampling variance\n-
ensures that usual standard error estimates are approximately unbiased, i.e. consistent
what does it mean to say assumption 5 implies that OLS b is MVUE? - ANSWER: minimum variance
unbiased estimator\n-stronger than BLUE\n-among all unbiased estimators (both linear and
nonlinear), b has minimum sampling variance
what does it mean to say assumption 5 implies that OLS b is the maximum likelihood estimator? -
ANSWER: means that using b as our estimate would lead to the same estimation method as using the
maximum likelihood estimator
which of the assumptions are part of the Gauss-Markov Theorem? - ANSWER: Assumptions 1-4\n-
linearity, mean independence, homoskedasticity, and no autocorrelation\n-same assumptions that
make b BLUE
which of the 5 assumptions of the linear regression model is the least important and why? - ANSWER:
assumption 5 (error term is Normally distributed) \n\n-if sample is reasonably large, Central Limit
Theorem will ensure that distribution of b is approximately Normal, regardless (so could go ahead and
use Normal distribution for significance tests, etc.)
what is the expected value of a dichotomous/dummy variable ? - ANSWER: the expected value of a
dichotomous variable is equal to the probability that the variable (πi) = 1
how does this affect the interpretation of a linear regression model where the dependent variable is
dichotomous? - ANSWER: since the model implies that the expected value of the dependent variable
is a linear function of the x's, this is the same as saying the probability of an event is a linear function
of the x's\n-this leads to the "linear probability model"
