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