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ISYE 6414 - Midterm 1 Prep WITH 100- SURE ANSWERS
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ISYE 6414 - Midterm 1 Prep WITH 100- SURE ANSWERS
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10/6/24, 7:59 AMEUNICE
ISYE 6414 - Midterm 1 Prep WITH QUESTIONS AND 100%
SURE ANSWERS
Terms in this set (194)
If λ=1 we do not transform
Regression analysis is one of the simplest ways we have in statistics to investigate the
non-deterministic
relationship between two or more variables in a ___ way
The response variable is a ___ variable, because it varies with changes in the
random
predicting variable, or with other changes in the environment
The predicting variable is a ___ variable. It is set fixed, before the response is
fixed
measured.
regression analysis involving one independent variable and one dependent variable
simple linear regression
in which the relationship between the variables is approximated by a straight line
A statistical method used to model the relationship between one dependent (or
Multiple Linear Regression response) variable and two or more independent (or explanatory) variables by fitting
a linear equation to observed data
a regression model which does not assume a linear relationship; a curvilinear
polynomial regression correlation coefficient is computed (we can think of X and X-squared as two different
predicting variables)
1) Prediction
three objectives in regression 2) Modeling
3) Testing hypothesis
We want to see how the response variable behaves in different settings. For
Prediction example, for a different location, if we think about a geographic prediction, or in
time, if we think about temporal prediction
modeling the relationship between the response variable and the explanatory
Modeling
variables, or predicting variables
Testing hypotheses of association relationships
We do not believe that the linear model represents a true representation of reality.
useful representation of reality
Rather, we think that, perhaps, it provides a ___
β0 intercept parameter (the value at which the line intersects the y-axis)
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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.
pairs of data consisting of a value for the response variable,and a value for the
simple linear regression data structure
predicting variable. And we have n such pairs
modeling framework for the simple linear 1) identifying data structure
regression: 2) clearly stating the model assumptions
1) linearity
linear regression assumptions 2) constant variance assumption
3) independence assumption
mean zero assumption, means that the expected value of the errors is zero.
linearity assumption A violation of this assumption will lead to difficulties in estimating β0, and means that
your model does not include a necessary systematic component.
which means that the variance (σ^2) of the error terms or deviances is constant for
constant variance assumption 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
which means that the deviances are independent random variables.
Independence Assumption Violation of this assumption can lead to misleading assessments of the strength of
the regression.
errors (ε) are normally distributed. This is needed for statistical inference, for
example, confidence or prediction intervals, and hypothesis testing. If this
normality assumption
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 How can we get estimates of the regression coefficients or parameters in linear
squared residuals or errors with respect to regression analysis?
β0 and β1. This translated into finding the
line such that the total squared deviances
from the line is minimum.
to be the regression line where the parameters are replaced
fitted values
by the estimated values of the parameters.
are simply the difference
between observed response and fitted values, and they are proxies of the error
Residuals
terms in
the regression model
The estimator for sigma square is sigma square hat, and is the
MSE
sum of the squared residuals, divided by n - 2.
is chi-squared distribution with n - 2 degrees of freedom (We
σ^2 (sample distribution of the variance lose two degrees of freedom because we replaced the two parameters ß0 and ß1
estimator) with
their estimators to obtain the residuals.)
epsilon i hat proxies for the deviances or the error terms
the estimator of the variance of the error terms (is chi-square with n - 1 degrees of
sample variance estimator (s^2)
freedom)
a direct relationship
positive value for ß1
between the predicting variable x and the response variable y
negative value of ß1 an inverse relationship between x and y.
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