ISYE6414 REGRESSION MIDTERM 1
EXAM 2026/ ISYE6414 MIDTERM 1
REAL EXAM QUESTIONS AND 100%
CORRECT ANSWERS/ GRADED A
What are the variables in regression? -CORRECT ANSWER-
1. Response (dependent) variable - one particular variable that we are
interested in understanding or modelling, such as sales of a particular
product.
2. Predicting or Explanatory (independent) variable - set of other
variables that we think might be useful in predicting or modelling the
response variable (like the price of a product)
Which regression variable is a Random variable? -CORRECT
ANSWER- - Response Variable - It varies with changes in the
predictor along with other random changes
Which regression variable is a Fixed variable? -CORRECT ANSWER- -
Predicting Variable - It does not change with the response but it is set
fixed before the response is measured.
What are the objectives in regression analysis? -CORRECT ANSWER- - 1.
Prediction - of the response variable
2. Modelling - the relationship between the response variable and the
explanatory variables
3. Testing - hypotheses of association relationships.
What are the given assumptions when building a linear regression
model? - CORRECT ANSWER-- 1. Linearity/Mean Zero Assumption - it
cannot be true that for certain subgroups in the population, the model is
consistently too low, while for others, it's consistently too high.
2. Constant Variance Assumption - 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.
,3. Independence Assumption are independent random variables - it
cannot be true knowing that the model under-predicts y for one
particular case tells you anything or all about what it does for any other
case. (her language)
4. Normally distributed.
What is the value that is being optimized towards in a linear regression
problem? - CORRECT ANSWER-- Minimizing the sum of squared errors
In terms of model parameter interpretation, how would you interpret a
positive value for B1, negative value, and value close to 0? -CORRECT
ANSWER- - A positive value of B1 is consistent with a direct
relationship between x and y
A negative value of B1 is consistent with an inverse relationship between x
and y
A close to zero value of B1 means that there is not a significant
association between x and y
What are the interpretations of the Least Squares estimated coefficients
(B hat 1 and B hat 0) -CORRECT ANSWER- - B hat 1 is the estimated
expected change in the response variable associated with the unit of
change in the predicting variable
B hat 0 is the estimated expected value of the response variable when the
predicting variable equals zero
What is extrapolation? -CORRECT ANSWER- - When you try to predict a
value using your regression model that is outside of the observed range. It
is unreliable to use extrapolation.
Assuming that the data are normally distributed, under the simple linear
model, the estimated variance has the following sample distribution:
A) Chi-square with n-2 degrees of freedom
B) T-distribution with n-2 degrees of freedom
C) Chi-square with n degrees of freedom
D) T-distribution with n degrees of freedom -CORRECT ANSWER- - A)
Chi- square with n-2 degrees of freedom
, The fitted values are defined as:
EXAM 2026/ ISYE6414 MIDTERM 1
REAL EXAM QUESTIONS AND 100%
CORRECT ANSWERS/ GRADED A
What are the variables in regression? -CORRECT ANSWER-
1. Response (dependent) variable - one particular variable that we are
interested in understanding or modelling, such as sales of a particular
product.
2. Predicting or Explanatory (independent) variable - set of other
variables that we think might be useful in predicting or modelling the
response variable (like the price of a product)
Which regression variable is a Random variable? -CORRECT
ANSWER- - Response Variable - It varies with changes in the
predictor along with other random changes
Which regression variable is a Fixed variable? -CORRECT ANSWER- -
Predicting Variable - It does not change with the response but it is set
fixed before the response is measured.
What are the objectives in regression analysis? -CORRECT ANSWER- - 1.
Prediction - of the response variable
2. Modelling - the relationship between the response variable and the
explanatory variables
3. Testing - hypotheses of association relationships.
What are the given assumptions when building a linear regression
model? - CORRECT ANSWER-- 1. Linearity/Mean Zero Assumption - it
cannot be true that for certain subgroups in the population, the model is
consistently too low, while for others, it's consistently too high.
2. Constant Variance Assumption - 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.
,3. Independence Assumption are independent random variables - it
cannot be true knowing that the model under-predicts y for one
particular case tells you anything or all about what it does for any other
case. (her language)
4. Normally distributed.
What is the value that is being optimized towards in a linear regression
problem? - CORRECT ANSWER-- Minimizing the sum of squared errors
In terms of model parameter interpretation, how would you interpret a
positive value for B1, negative value, and value close to 0? -CORRECT
ANSWER- - A positive value of B1 is consistent with a direct
relationship between x and y
A negative value of B1 is consistent with an inverse relationship between x
and y
A close to zero value of B1 means that there is not a significant
association between x and y
What are the interpretations of the Least Squares estimated coefficients
(B hat 1 and B hat 0) -CORRECT ANSWER- - B hat 1 is the estimated
expected change in the response variable associated with the unit of
change in the predicting variable
B hat 0 is the estimated expected value of the response variable when the
predicting variable equals zero
What is extrapolation? -CORRECT ANSWER- - When you try to predict a
value using your regression model that is outside of the observed range. It
is unreliable to use extrapolation.
Assuming that the data are normally distributed, under the simple linear
model, the estimated variance has the following sample distribution:
A) Chi-square with n-2 degrees of freedom
B) T-distribution with n-2 degrees of freedom
C) Chi-square with n degrees of freedom
D) T-distribution with n degrees of freedom -CORRECT ANSWER- - A)
Chi- square with n-2 degrees of freedom
, The fitted values are defined as:
