ISYE 6414 MIDTERM 2 PART 1 EXAM
SCRIPT WITH VERIFIED ANSWERS
◉ non-deterministic
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
Answer: The response variable is a ___ variable, because it varies
with changes in the predicting variable, or with other changes in
the environment
◉ fixed
Answer: The predicting variable is a ___ variable. It is set fixed,
before the response is measured.
◉ simple linear regression
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
,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
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)
◉ three objectives in regression
Answer: 1) Prediction
2) Modeling
3) Testing hypothesis
◉ Prediction
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
Answer: modeling the relationship between the response variable
and the explanatory variables, or predicting variables
◉ Testing hypotheses
,Answer: of association relationships
◉ useful representation of reality
Answer: We do not believe that the linear model represents a true
representation of reality. Rather, we think that, perhaps, it
provides a ___
◉ β0
Answer: intercept parameter (the value at which the line
intersects the y-axis)
◉ β1
Answer: slope parameter (slope of the line we are trying to fit)
◉ epsilon (ε)
Answer: is the deviance of the data from the linear model
◉ to find β0 and β1
Answer: to find the line that describes a linear relationship, such
that we fit this model.
◉ simple linear regression data structure
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:
Answer: 1) identifying data structure
2) clearly stating the model assumptions
◉ linear regression assumptions
Answer: 1) linearity
2) constant variance assumption
3) independence assumption
◉ linearity assumption
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
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
SCRIPT WITH VERIFIED ANSWERS
◉ non-deterministic
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
Answer: The response variable is a ___ variable, because it varies
with changes in the predicting variable, or with other changes in
the environment
◉ fixed
Answer: The predicting variable is a ___ variable. It is set fixed,
before the response is measured.
◉ simple linear regression
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
,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
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)
◉ three objectives in regression
Answer: 1) Prediction
2) Modeling
3) Testing hypothesis
◉ Prediction
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
Answer: modeling the relationship between the response variable
and the explanatory variables, or predicting variables
◉ Testing hypotheses
,Answer: of association relationships
◉ useful representation of reality
Answer: We do not believe that the linear model represents a true
representation of reality. Rather, we think that, perhaps, it
provides a ___
◉ β0
Answer: intercept parameter (the value at which the line
intersects the y-axis)
◉ β1
Answer: slope parameter (slope of the line we are trying to fit)
◉ epsilon (ε)
Answer: is the deviance of the data from the linear model
◉ to find β0 and β1
Answer: to find the line that describes a linear relationship, such
that we fit this model.
◉ simple linear regression data structure
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:
Answer: 1) identifying data structure
2) clearly stating the model assumptions
◉ linear regression assumptions
Answer: 1) linearity
2) constant variance assumption
3) independence assumption
◉ linearity assumption
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
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
