ISYE 6414 - Midterm 1 Prep Exam Study Questions and Answers Graded A 2024
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ISYE 6414
If λ=1 - we do not transform
non-deterministic - 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 - The response variable is a ___ variable, because it varies with changes in the predicting...
ISYE 6414 - Midterm 1 Prep Exam Study
Questions and Answers Graded A 2024
If λ=1 - we do not transform
non-deterministic - 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 - The response variable is a ___ variable, because it varies with changes in the
predicting variable, or with other changes in the environment
fixed - The predicting variable is a ___ variable. It is set fixed, before the response is
measured.
simple linear regression - 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 - 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 - 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 - 1) Prediction
2) Modeling
ISYE 6414 - Midterm 1 Prep
,ISYE 6414 - Midterm 1 Prep
3) Testing hypothesis
Prediction - 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 - modeling the relationship between the response variable and the
explanatory variables, or predicting variables
Testing hypotheses - of association relationships
useful representation of reality - We do not believe that the linear model represents a
true representation of reality. Rather, we think that, perhaps, it provides a ___
β0 - intercept parameter (the value at which the line intersects the y-axis)
β1 - slope parameter (slope of the line we are trying to fit)
epsilon (ε) - is the deviance of the data from the linear model
to find β0 and β1 - to find the line that describes a linear relationship, such that we fit
this model.
simple linear regression data structure - 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: - 1) identifying data structure
2) clearly stating the model assumptions
linear regression assumptions - 1) linearity
2) constant variance assumption
ISYE 6414 - Midterm 1 Prep
, ISYE 6414 - Midterm 1 Prep
3) independence assumption
linearity assumption - 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 - 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 - 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 - 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 - 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. - How can we get estimates of the regression coefficients or
parameters in linear
regression analysis?
fitted values - to be the regression line where the parameters are replaced
by the estimated values of the parameters.
ISYE 6414 - Midterm 1 Prep
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