ISYE 6414 Midterm 1 Prep Questions And Answers Well Illustrated.
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ISYE 6414 Midterm 1 Prep Questions And Answers Well Illustrated.
If λ=1 - correct answer. we do not transform
non-deterministic - correct answer. Regression analysis is one of the simplest ways we have in statistics to investigate the relationship between two or more variables ...
ISYE 6414 Midterm 1 Prep Questions And
Answers Well Illustrated.
If λ=1 - correct answer. we do not transform
non-deterministic - correct answer. Regression analysis is one of the simplest ways
we have in statistics to investigate the relationship between two or more variables in a
___ way
random - correct answer. The response variable is a ___ variable, because it varies
with changes in the predicting variable, or with other changes in the environment
fixed - correct answer. The predicting variable is a ___ variable. It is set fixed, before
the response is measured.
simple linear regression - correct answer. regression analysis involving one
independent variable and one dependent variable in which the relationship between the
variables is approximated by a straight line
Multiple Linear Regression - correct answer. A statistical method used to model the
relationship between one dependent (or response) variable and two or more
independent (or explanatory) variables by fitting a linear equation to observed data
polynomial regression - correct answer. a regression model which does not assume a
linear relationship; a curvilinear correlation coefficient is computed (we can think of X
and X-squared as two different predicting variables)
Prediction - correct answer. We want to see how the response variable behaves in
different settings. For example, for a different location, if we think about a geographic
prediction, or in time, if we think about temporal prediction
Modeling - correct answer. modeling the relationship between the response variable
and the explanatory variables, or predicting variables
Testing hypotheses - correct answer. of association relationships
useful representation of reality - correct answer. We do not believe that the linear
model represents a true representation of reality. Rather, we think that, perhaps, it
provides a ___
β0 - correct answer. intercept parameter (the value at which the line intersects the y-
axis)
β1 - correct answer. slope parameter (slope of the line we are trying to fit)
epsilon (ε) - correct answer. is the deviance of the data from the linear model
to find β0 and β1 - correct answer. to find the line that describes a linear relationship,
such that we fit this model.
simple linear regression data structure - correct answer. pairs of data consisting of a
value for the response variable,and a value for the predicting variable. And we have n
such pairs
modeling framework for the simple linear regression: - correct answer. 1) identifying
data structure
2) clearly stating the model assumptions
linearity assumption - correct answer. mean zero assumption, means that the
expected value of the errors is zero.
A violation of this assumption will lead to difficulties in estimating β0, and means that
your model does not include a necessary systematic component.
constant variance assumption - correct answer. which means that the variance (σ^2)
of the error terms or deviances is constant for the given population. A violation of this
, assumption means that the estimates are not as efficient as they could be in estimating
the true parameters
Independence Assumption - correct answer. which means that the deviances are
independent random variables.
Violation of this assumption can lead to misleading assessments of the strength of the
regression.
normality assumption - correct answer. errors (ε) are normally distributed. This is
needed for statistical inference, for example, confidence or prediction intervals, and
hypothesis testing. If this assumption is violated, hypothesis tests and confidence and
prediction intervals can be misleading.v
third parameter - correct answer. the variance of the error terms (σ^2)
One approach is to minimize the sum of squared residuals or errors with respect to β0
and β1. This translated into finding the line such that the total squared deviances from
the line is minimum. - correct answer. How can we get estimates of the regression
coefficients or parameters in linear
regression analysis?
fitted values - correct answer. to be the regression line where the parameters are
replaced
by the estimated values of the parameters.
Residuals - correct answer. are simply the difference
between observed response and fitted values, and they are proxies of the error terms in
the regression model
MSE - correct answer. The estimator for sigma square is sigma square hat, and is the
sum of the squared residuals, divided by n - 2.
σ^2 (sample distribution of the variance estimator) - correct answer. is chi-squared
distribution with n - 2 degrees of freedom (We
lose two degrees of freedom because we replaced the two parameters ß0 and ß1 with
their estimators to obtain the residuals.)
epsilon i hat - correct answer. proxies for the deviances or the error terms
sample variance estimator (s^2) - correct answer. the estimator of the variance of the
error terms (is chi-square with n - 1 degrees of freedom)
positive value for ß1 - correct answer. a direct relationship
between the predicting variable x and the response variable y
negative value of ß1 - correct answer. an inverse relationship between x and y.
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