ISYE 6414 - Midterm 1 Prep
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 - CORRECT ANSWER-Multiple Linear 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) - CORRECT ANSWER-polynomial regression
1) Prediction
2) Modeling
3) Testing hypothesis - CORRECT ANSWER-three objectives in regression
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 - CORRECT ANSWER-Prediction
modeling the relationship between the response variable and the explanatory variables,
or predicting variables - CORRECT ANSWER-Modeling
of association relationships - CORRECT ANSWER-Testing hypotheses
We do not believe that the linear model represents a true representation of reality.
Rather, we think that, perhaps, it provides a ___ - CORRECT ANSWER-useful
representation of reality
intercept parameter (the value at which the line intersects the y-axis) - CORRECT
ANSWER-β0
slope parameter (slope of the line we are trying to fit) - CORRECT ANSWER-β1
is the deviance of the data from the linear model - CORRECT ANSWER-epsilon (ε)
to find the line that describes a linear relationship, such that we fit this model. -
CORRECT ANSWER-to find β0 and β1
pairs of data consisting of a value for the response variable,and a value for the
predicting variable. And we have n such pairs - CORRECT ANSWER-simple linear
regression data structure
1) identifying data structure
,2) clearly stating the model assumptions - CORRECT ANSWER-modeling framework
for the simple linear regression:
1) linearity
2) constant variance assumption
3) independence assumption - CORRECT ANSWER-linear regression assumptions
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. - CORRECT
ANSWER-linearity 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 - CORRECT ANSWER-
constant variance 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. - CORRECT ANSWER-Independence 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 -
CORRECT ANSWER-normality assumption
the variance of the error terms (σ^2) - CORRECT ANSWER-third parameter
How can we get estimates of the regression coefficients or parameters in linear
regression analysis? - CORRECT ANSWER-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.
to be the regression line where the parameters are replaced
by the estimated values of the parameters. - CORRECT ANSWER-fitted values
are simply the difference
between observed response and fitted values, and they are proxies of the error terms in
the regression model - CORRECT ANSWER-Residuals
The estimator for sigma square is sigma square hat, and is the
sum of the squared residuals, divided by n - 2. - CORRECT ANSWER-MSE
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.) - CORRECT ANSWER-σ^2 (sample distribution
of the variance estimator)
proxies for the deviances or the error terms - CORRECT ANSWER-epsilon i hat
the estimator of the variance of the error terms (is chi-square with n - 1 degrees of
freedom) - CORRECT ANSWER-sample variance estimator (s^2)
a direct relationship
between the predicting variable x and the response variable y - CORRECT ANSWER-
positive value for ß1
an inverse relationship between x and y. - CORRECT ANSWER-negative value of ß1
there is not a significant association between the predicting variable x, and the response
variable y. - CORRECT ANSWER-ß1 is close to zero.
is the estimated expected change in the response variable associated with
one unit of change in the predicting variable. - CORRECT ANSWER-ß1 hat
is the estimated expected value of the response variable, when the
predicting variable equals zero - CORRECT ANSWER-ß0 hat
when we interpret whether the relationship between x and y is positive, negative, or
there is no relationship. - CORRECT ANSWER-we use ß1 hat
we always have to mention the statistical significance, whether
statistically significantly positive, statistically significantly negative, or no statistical
significance. - CORRECT ANSWER-when we make statistical statements
about the relationship
in model summary, look for Residual standard error - CORRECT ANSWER-estimated
standard deviation
we need to take the square of the residual standard error - CORRECT ANSWER-
estimate of the variance (from output)
not within the range of the observed axis, predicting larger than the values observed -
CORRECT ANSWER-extrapolation
is equal to the linear combination of the expectations. - CORRECT ANSWER-
expectation of a linear combination of random
variables
exactly ß1. ( ß1
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 - CORRECT ANSWER-Multiple Linear 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) - CORRECT ANSWER-polynomial regression
1) Prediction
2) Modeling
3) Testing hypothesis - CORRECT ANSWER-three objectives in regression
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 - CORRECT ANSWER-Prediction
modeling the relationship between the response variable and the explanatory variables,
or predicting variables - CORRECT ANSWER-Modeling
of association relationships - CORRECT ANSWER-Testing hypotheses
We do not believe that the linear model represents a true representation of reality.
Rather, we think that, perhaps, it provides a ___ - CORRECT ANSWER-useful
representation of reality
intercept parameter (the value at which the line intersects the y-axis) - CORRECT
ANSWER-β0
slope parameter (slope of the line we are trying to fit) - CORRECT ANSWER-β1
is the deviance of the data from the linear model - CORRECT ANSWER-epsilon (ε)
to find the line that describes a linear relationship, such that we fit this model. -
CORRECT ANSWER-to find β0 and β1
pairs of data consisting of a value for the response variable,and a value for the
predicting variable. And we have n such pairs - CORRECT ANSWER-simple linear
regression data structure
1) identifying data structure
,2) clearly stating the model assumptions - CORRECT ANSWER-modeling framework
for the simple linear regression:
1) linearity
2) constant variance assumption
3) independence assumption - CORRECT ANSWER-linear regression assumptions
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. - CORRECT
ANSWER-linearity 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 - CORRECT ANSWER-
constant variance 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. - CORRECT ANSWER-Independence 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 -
CORRECT ANSWER-normality assumption
the variance of the error terms (σ^2) - CORRECT ANSWER-third parameter
How can we get estimates of the regression coefficients or parameters in linear
regression analysis? - CORRECT ANSWER-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.
to be the regression line where the parameters are replaced
by the estimated values of the parameters. - CORRECT ANSWER-fitted values
are simply the difference
between observed response and fitted values, and they are proxies of the error terms in
the regression model - CORRECT ANSWER-Residuals
The estimator for sigma square is sigma square hat, and is the
sum of the squared residuals, divided by n - 2. - CORRECT ANSWER-MSE
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.) - CORRECT ANSWER-σ^2 (sample distribution
of the variance estimator)
proxies for the deviances or the error terms - CORRECT ANSWER-epsilon i hat
the estimator of the variance of the error terms (is chi-square with n - 1 degrees of
freedom) - CORRECT ANSWER-sample variance estimator (s^2)
a direct relationship
between the predicting variable x and the response variable y - CORRECT ANSWER-
positive value for ß1
an inverse relationship between x and y. - CORRECT ANSWER-negative value of ß1
there is not a significant association between the predicting variable x, and the response
variable y. - CORRECT ANSWER-ß1 is close to zero.
is the estimated expected change in the response variable associated with
one unit of change in the predicting variable. - CORRECT ANSWER-ß1 hat
is the estimated expected value of the response variable, when the
predicting variable equals zero - CORRECT ANSWER-ß0 hat
when we interpret whether the relationship between x and y is positive, negative, or
there is no relationship. - CORRECT ANSWER-we use ß1 hat
we always have to mention the statistical significance, whether
statistically significantly positive, statistically significantly negative, or no statistical
significance. - CORRECT ANSWER-when we make statistical statements
about the relationship
in model summary, look for Residual standard error - CORRECT ANSWER-estimated
standard deviation
we need to take the square of the residual standard error - CORRECT ANSWER-
estimate of the variance (from output)
not within the range of the observed axis, predicting larger than the values observed -
CORRECT ANSWER-extrapolation
is equal to the linear combination of the expectations. - CORRECT ANSWER-
expectation of a linear combination of random
variables
exactly ß1. ( ß1
