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ISYE 6414 STATISTICAL MODELLING AND REGRESSION ANALYSIS ACTUAL EXAM LATEST 2024/2025 QUESTIONS AND VERIFIED CORRECT ANSWERS/ALREADY GRADED A++

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ISYE 6414 STATISTICAL MODELLING AND REGRESSION ANALYSIS ACTUAL EXAM LATEST 2024/2025 QUESTIONS AND VERIFIED CORRECT ANSWERS/ALREADY GRADED A++ ISYE 6414 STATISTICAL MODELLING AND REGRESSION ANALYSIS ACTUAL EXAM LATEST 2024/2025 QUESTIONS AND VERIFIED CORRECT ANSWERS/ALREADY GRADED A++

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ISYE 6414 STATISTICAL MODELLING AND REGRESSION
ANALYSIS ACTUAL EXAM LATEST 2024/2025 QUESTIONS
AND VERIFIED CORRECT ANSWERS/ALREADY GRADED
A++
Which variable type is considered "random"? -ANSWER response
variable - it varies with changes in the predicting variables

Which variable type is considered "fixed"? -ANSWER predicting variables-
the predicting variables are set before the response variable is measured

A regression model tries to explain/predict the ___ of the response variable
by using the predicting variables (x). Some explained by x and some due to
____. -ANSWER (1) total variability, (2) random error

What are the 3 objectives in regression? -ANSWER (1) Prediction-
predicting how the response variable behaves in different settings
(2) Modeling the relationship
(3) Testing hypotheses of association relationships

Y = β0 + β1x + ε -ANSWER Simple linear regression equation

What is β1 in the simple linear regression equation? -ANSWER Slope. The
expected (average) change in Y associated with a 1- unit increase in the
value of x.

What is β0 in the simple linear regression equation? -ANSWER Intercept.
The average value of Y when x is zero.

What is ε in the simple linear regression equation? -ANSWER
Deviance/error

Define what it means for a model to be non-deterministic? -ANSWER the
outcome cannot be predicted with certainty, even if the inputs are known.
The model behaves differently each time it is run

Is ε considered random or fixed? -ANSWER random

,What are the assumptions of a simple linear regression model? -ANSWER
(1) linearity/mean zero assumption
(2) constant variance assumption
(3) Independence assumption
(4) Normal distribution of error terms

Assumption of linearity -ANSWER Expectation of the deviances is 0

Assumption of constant variance -ANSWER The variance (σ2) of the error
terms (ε) is constant for the given population

Assumption of independence -ANSWER Deviances (ε) are independent,
random variables

T or F: Parameters β1, β0, and ε in statistical modeling are observed in the
data and therefore fixed, known quantities. -ANSWER False. These
parameters are considered unknown regardless of how much data is
observed. Approximate values are estimated.

In simple linear regression, the fitted line ____. -ANSWER makes the
errors as small as possible given a criterion (function of error terms)

To estimate β1 and β0, we find values that minimize the ___. -ANSWER
sum of squared residuals or errors.

or in other words:
total squared deviances from the line

What does the "hat" ("^") symbolize? -ANSWER Differentiates estimated
parameters from the true, unknown values

Median or robust regression -ANSWER Replace squared error criterion
used in the standard regression model with the absolute value of errors

Sxx, Sxy and Syy -ANSWER Sum of Square terms

Define what it means for a model to be deterministic? -ANSWER Given the
same input values, the model will consistently return the same output

Residual -ANSWER difference between the observed and fitted values

,Mean squared error (MSE) in SLR -ANSWER Sum of the squared
residuals divided by n-2
SSE/(n-2)

What is the sampling distribution of the estimator of the variance parameter
in SLR? -ANSWER Chi-square with n-2 degrees of freedom

sample variance estimator equation -ANSWER sum of the Zi minus their
average, squared, divided by n-1

Σxi yi - (Σxi )(Σyi )/n -ANSWER Sxy

Σxi^2 - (Σxi )^2/n -ANSWER Sxx

When β1 is positive, it is consistent with a ___ relationship between x and
y. -ANSWER direct

When β1 is negative it is consistent with a ___ relationship between x and
y. -ANSWER inverse

When β1 is close to 0, it is consistent with a ___ relationship between x and
y. -ANSWER insignificant

How do you find the variance from residual standard error? -ANSWER take
the square of the residual standard error (also called the standard deviation
of the error terms)

Define extrapolation. -ANSWER When the regression equation is used to
produce a y value from an x value that is outside the range of the observed
x values

Why does the MSE divide by (n-2) instead of (n-1)? -ANSWER an
additional degree of freedom is lost because both β0 and β1 are estimates

Define unbiasedness -ANSWER The expectation that the parameter's
estimated value is exactly the true value

, T or F: β1 hat is normally distributed -ANSWER True. β1 hat is a linear
combination of normally distributed variables and thus is also normally
distributed.

β1 hat is a ___ distribution with ___ degrees of freedom -ANSWER (1) t
(2) n-2

Data points that are far from the mean of the x's -ANSWER leverage points

Data point that is far from the mean of the x's and/or y's -ANSWER
influential point

When do you use adjusted R-squared? -ANSWER when comparing
models

When do you use R-squared? -ANSWER when evaluating the model
performance in terms of variability explained

Box-Cox Transformation -ANSWER a power transformation of y that
normalizes or variance-stablizes the response variable

What is overarching objective of ANOVA? -ANSWER Compare the means
across k number of populations

in ANOVA, we compare the ___ to the ___of the response data -ANSWER
(1) within-variability
(2) between variability

The only difference in assumptions from the linear regression model is the
___ assumption not needed in ANOVA. -ANSWER linearity

Do you use ANOVA or linear regression when the predicting factor is either
a categorical or qualitative variable? -ANSWER ANOVA

degree of freedom in the estimation in the pooled variance estimator -
ANSWER N-k

MSE = SSE/N-k -ANSWER within-group variability

MSST= SSTr/k-1 -ANSWER between-group variability

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ISYE 6414 STATISTICAL MODELLING AND REGRESSION ANALYSIS ACTUAL EXAM LATEST 2024/2025 QUESTIONS AND VERIFIED CORRECT ANSWERS/ALREADY GRADED A++

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