ISYE 6414 - All Units Exam Practice Questions and Answers
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Course
ISYE 6414
Institution
ISYE 6414
ISYE 6414 - All Units Exam Practice
Questions and Answers
response (dependent) variables - Answer️️ -one particular variable that we are
interested in understanding or modeling (y)
predicting or explanatory (independent) variables - Answer️️ -a set of other variables
that might be usef...
ISYE 6414 - All Units Exam Practice
Questions and Answers
response (dependent) variables - Answer✔️✔️-one particular variable that we are
interested in understanding or modeling (y)
predicting or explanatory (independent) variables - Answer✔️✔️-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? - Answer✔️✔️-random, because it
varies with changes in the predictor/s along with other random changes.
What kind of variable is a predicting variable and why? - Answer✔️✔️-fixed, because it
does not change with the response but it is fixed before the response is measured.
linear relationship - Answer✔️✔️-a simple deterministic relationship between 2 factors, x
and y
what are three things that a regression analysis is used for? - Answer✔️✔️-1. Prediction
of the response variable, 2. Modeling the relationship between the response and
explanatory variables, 3. Testing hypotheses of association relationships
B0 = ? - Answer✔️✔️-intercept
B1 = ? - Answer✔️✔️-slope
for our linear model where: Y = B0 + B1 + EPSILON (E), what does the epsilon
represent? - Answer✔️✔️-deviance of the data from the linear model (error term)
,what are the 4 assumptions of linear regression? - Answer✔️✔️-Linearity/Mean Zero,
Constant Variance, Independence, Normality
Linearity/Mean zero assumption - Answer✔️✔️-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 - Answer✔️✔️-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 - Answer✔️✔️-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 - Answer✔️✔️-This is needed if we want to do any 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.
what are the 3 parameters we estimated in regression? - Answer✔️✔️-B0, B1, sigma
squared (variance of the one pop.)
What do we mean by model parameters in statistics? - Answer✔️✔️-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,
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,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? - Answer✔️✔️-chi-square with n-1 DF
Why do we lose 1 DF for s^2? - Answer✔️✔️-we replace mu with zbar
what is the relationship between s^2 and sigma^2? - Answer✔️✔️-S^2 estimates sigma^2
What is the estimated sampling distribution of sigma^2? - Answer✔️✔️-chi-square with n-
2 DF (~ equivalent to MSE)
Why do we lose 2 DF for sigma^2? - Answer✔️✔️-we replaced two parameters, B0 and
B1
In SLR, we are interested in the behavior of which parameter? - Answer✔️✔️-B1
If we have a positive value for B1,.... - Answer✔️✔️-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,.... - Answer✔️✔️-is consistent with an inverse
relationship between x and y
When B1 is close to zero... - Answer✔️✔️-we interpret that there is not a significant
association between predicting variables, between the predicting variable x, and the
response variable y.
How do we interpret B1? - Answer✔️✔️-It is the estimated expected change in the
response variable associated with one unit of change in the predicting variable.
How we interpret ^B0? - Answer✔️✔️-It is the estimated expected value of the response
variable, when the predicting variable equals zero.
What is the sampling distribution of ^B1? - Answer✔️✔️-t distribution with N-2 DF
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, What can we use to test for statistical significance? - Answer✔️✔️-t-test
What would we do if the T value is large? - Answer✔️✔️-Reject the null hypothesis 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? - Answer✔️✔️-B1 is statistically different from
zero.
what is the distribution of B1? - Answer✔️✔️-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. - Answer✔️✔️-C
The assumption of normality:
A) It is needed for deriving the estimators of the regression coefficients.
B) It is not needed for linear regression modeling and inference.
C) It is needed for the sampling distribution of the estimators of the regression
coefficients and hence for inference.
D) It is needed for deriving the expectation and variance of the estimators of the
regression coefficients. - Answer✔️✔️-C
What is 'X*'? - Answer✔️✔️-predictor
Where does uncertainty from estimation come from? - Answer✔️✔️-from estimation alone
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