ISYE 6414 - All Units of THE COURSE COMPLETELY COVERED AND QUESTIONS ANSWERED CORRECTLY!
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Course
ISYE 6414
Institution
ISYE 6414
ISYE 6414 - All Units of THE COURSE COMPLETELY COVERED AND QUESTIONS ANSWERED CORRECTLY!
response (dependent) variables - ANS one particular variable that we are interested in understanding or modeling (y)
predicting or explanatory (independent) variables - ANS a set of other variables th...
THE COURSE
COMPLETELY COVERED
AND QUESTIONS
ANSWERED CORRECTLY!
,response (dependent) variables - ANS one particular variable that we are
interested in understanding or modeling (y)
predicting or explanatory (independent) variables - ANS a set of other
variables that might be useful in predicting or modeling the response
variable (x1, x2)
What kind of variable is a response variable and why? - ANS random,
because it varies with changes in the predictor/s along with other random
changes.
M
What kind of variable is a predicting variable and why? - ANS fixed,
because it does not change with the response but it is fixed before the
response is measured.
AO
linear relationship - ANS a simple deterministic relationship between 2
factors, x and y
what are three things that a regression analysis is used for? - ANS 1.
Prediction of the response variable, 2. Modeling the relationship between
the response and explanatory variables, 3. Testing hypotheses of
association relationships
N
B0 = ? - ANS intercept
B1 = ? - ANS slope
JP
for our linear model where: Y = B0 + B1 + EPSILON (E), what does the
epsilon represent? - ANS deviance of the data from the linear model (error
term)
what are the 4 assumptions of linear regression? - ANS Linearity/Mean
Zero, Constant Variance, Independence, Normality
Linearity/Mean zero assumption - ANS Means that the expected value
(deviances) of errors is zero. This leads to difficulties in estimating B0 and
means that our model does not include a necessary systematic component
,Constant variance assumption - ANS Means that it cannot be true that
the model is more accurate for some parts of the population, and less
accurate for other parts of the populations. This can result in less accurate
parameters and poorly-calibrated prediction intervals.
Assumption of Independence - ANS Means that the deviances, or in fact
the response variables ys, are independently drawn from the
data-generating process. (this most often occurs in time series data) This
can result in very misleading assessments of the strength of regression.
Normality assumption - ANS This is needed if we want to do any
M
confidence or prediction intervals, or hypothesis test, which we usually do.
If this assumption is violated, hypothesis test and confidence and
prediction intervals and be very misleading.
AO
what are the 3 parameters we estimated in regression? - ANS B0, B1,
sigma squared (variance of the one pop.)
What do we mean by model parameters in statistics? - ANS Model
parameters are unknown quantities, and they stay unknown regardless
how much data are observed. We estimate those parameters given the
model assumptions and the data, but through estimation, we're not
identifying the true parameters. We're just estimating approximations of
N
those parameters.
What is the estimated sampling distribution of s^2? - ANS chi-square with
JP
n-1 DF
Why do we lose 1 DF for s^2? - ANS we replace mu with zbar
what is the relationship between s^2 and sigma^2? - ANS S^2 estimates
sigma^2
What is the estimated sampling distribution of sigma^2? - ANS
chi-square with n-2 DF (~ equivalent to MSE)
Why do we lose 2 DF for sigma^2? - ANS we replaced two parameters, B0
and B1
, In SLR, we are interested in the behavior of which parameter? - ANS B1
If we have a positive value for B1,.... - ANS then that's consistent with a
direct relationship between the predicting variable x and the response
variable y.
If we have a negative value for B1,.... - ANS is consistent with an inverse
relationship between x and y
When B1 is close to zero... - ANS we interpret that there is not a significant
M
association between predicting variables, between the predicting variable
x, and the response variable y.
How do we interpret B1? - ANS It is the estimated expected change in the
AO
response variable associated with one unit of change in the predicting
variable.
How we interpret ^B0? - ANS It is the estimated expected value of the
response variable, when the predicting variable equals zero.
What is the sampling distribution of ^B1? - ANS t distribution with N-2 DF
N
What can we use to test for statistical significance? - ANS t-test
What would we do if the T value is large? - ANS Reject the null hypothesis
JP
that β1 is equal to zero. If the null hypothesis is rejected, we interpret this
that β1 is statistically significant.
what does 'statistical significance' mean? - ANS B1 is statistically different
from zero.
what is the distribution of B1? - ANS Normal
The estimators for the regression coefficients are:
A) Biased but with small variance
B) Unbiased under normality assumptions but biased otherwise.
C) Unbiased regardless of the distribution of the data. - ANS C
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