ISYE 6414 - All Units 4 Exam Questions With Correct Verified Answers A+ Graded
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Course
ISYE 6414
Institution
ISYE 6414
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 ...
,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
K
random, because it varies with changes in the predictor/s along with
other random changes.
C
What kind of variable is a predicting variable and why? - ANS fixed,
LO
because it does not change with the response but it is fixed before the
response is measured.
linear relationship - ANS a simple deterministic relationship between
YC
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
D
between the response and explanatory variables, 3. Testing
hypotheses of association relationships
U
B0 = ? - ANS intercept
ST
B1 = ? - ANS slope
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
K
Constant variance assumption - ANS Means that it cannot be true
that the model is more accurate for some parts of the population, and
C
less accurate for other parts of the populations. This can result in less
accurate parameters and poorly-calibrated prediction intervals.
LO
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)
YC
This can result in very misleading assessments of the strength of
regression.
Normality assumption - ANS This is needed if we want to do any
D
confidence or prediction intervals, or hypothesis test, which we usually
do. If this assumption is violated, hypothesis test and confidence and
U
prediction intervals and be very misleading.
ST
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 those parameters.
What is the estimated sampling distribution of s^2? - ANS chi-square
with n-1 DF
Why do we lose 1 DF for s^2? - ANS we replace mu with zbar
K
what is the relationship between s^2 and sigma^2? - ANS S^2
estimates sigma^2
C
What is the estimated sampling distribution of sigma^2? - ANS
LO
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
YC
In SLR, we are interested in the behavior of which parameter? - ANS
B1
D
If we have a positive value for B1,.... - ANS then that's consistent
with a direct relationship between the predicting variable x and the
U
response variable y.
ST
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 association between predicting variables, between the
predicting variable x, and the response variable y.
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