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ISYE 6414 - All Units Exam Practice Questions and Answers |100% Pass

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ISYE 6414 - All Units Exam Practice Questions and Answers |100% Pass 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 ...

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  • October 6, 2024
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  • ISYE 6414
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EmillyCharlotte
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ISYE 6414 - All Units Exam Practice
Questions and Answers |100% Pass

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)

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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, but through estimation, we're not identifying the

true parameters. We're just estimating approximations of those parameters.




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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



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