Regression (ISYE 6414) - Module 2 Test Questions and Answers Already Passed Latest
Update 2025-2026
multiple linear regression (MLR) - Answers a generalization of both ANOVA and simple linear
regression
has 1 response variable and multiple (n) quantitative and qualitative predicting variables
What is the relationship captured in MLR? - Answers the linear relationship between the
response variable and the predicting variables
What are 3 uses of a regression Analysis? - Answers 1) Prediction of the response variable
2) Modeling the relationship between the response variable and the explanatory variables
3) Testing hypotheses of association relationships
Deviances - Answers Also called epsilons or error terms
the difference between the response variable and the linear function in the x's
Assumptions of MLR - Answers The same as for SLR
1) Linearity/mean zero - the error terms have a mean of 0, also implies that the linearity
assumption holds
2) Constant variance - cannot be true that the model is more accurate for some parts of the
population and less accurate for other parts
3) Independence - the response variables are independently drawn from the data generating
process
4) Normality - error terms are normally distributed
,What does violation of the constant variance assumption result in for MLR? - Answers The
same as for SLR
estimates are not as efficient in estimating the true parameters resulting in poorly calibrated
confidence intervals
What does violation of the independence assumption result in for MLR? - Answers The same as
for SLR
can lead to misleading assessments of the strength of the regression
What does violation of the normality assumption result in for MLR? - Answers The same as for
SLR
can lead to misleading hypothesis tests and confidence/prediction intervals
What are the parameters in MLR? - Answers The regression coefficients beta_0 through beta_p
The variance of the squared errors (sigma squared)
What are the names of the 4 matrices used to write the data for MLR and what data do they
contain? - Answers 1) Y - response matrix
2) Design Matrix - columns of predicting variables, including a column of 1s corresponding to
the intercept
3) Beta - the regression parameters
4)Epsilon - the error terms
What Are the 4 Basic Approaches to MLR - Answers 1) First Order Model
2) Second Order Model
, 3) First Order Interaction Model
4) Second Order Interaction Model
Contour Plot MLR - Answers A graphic representation of the relationships among 3 numeric
variables in 2 dimensions
plotting a 3D surface by plotting constant z slices called contours
Used to display the relationship between 2 independent variables and a dependent variable -
show values of the z variable for combinations of x and y variables
What is the generic formula for a first order MLR model with 2 predicting variables? How would
you explain what the formula means? - Answers Y = beta_0 + beta_1 * x_1 + beta_2 * x_2 +
epsilon
When you fix one of the variables, for example x_1, the expected value of Y is a linear function
other variable x_2
What do we get when we graph a first order MLR model with 2 predicting variables? - Answers
the graph is a function of only one variable for several values of the fixed variables
we get contours of the regression function as a collection of lines
What is the generic formula for a second order MLR model with 2 predicting variables? How
would you explain what the formula means? - Answers Y = beta_0 + beta_1 * x_1 + beta_2 * x_2
+ beta_3 * x_1_squared + beta_4 * x_2_squared + epsilon
The relationship in the individual predictors doesn't have to be linear, we can include the square
of the predictors
beta_3 - the coefficient for the square of x_1
Update 2025-2026
multiple linear regression (MLR) - Answers a generalization of both ANOVA and simple linear
regression
has 1 response variable and multiple (n) quantitative and qualitative predicting variables
What is the relationship captured in MLR? - Answers the linear relationship between the
response variable and the predicting variables
What are 3 uses of a regression Analysis? - Answers 1) Prediction of the response variable
2) Modeling the relationship between the response variable and the explanatory variables
3) Testing hypotheses of association relationships
Deviances - Answers Also called epsilons or error terms
the difference between the response variable and the linear function in the x's
Assumptions of MLR - Answers The same as for SLR
1) Linearity/mean zero - the error terms have a mean of 0, also implies that the linearity
assumption holds
2) Constant variance - cannot be true that the model is more accurate for some parts of the
population and less accurate for other parts
3) Independence - the response variables are independently drawn from the data generating
process
4) Normality - error terms are normally distributed
,What does violation of the constant variance assumption result in for MLR? - Answers The
same as for SLR
estimates are not as efficient in estimating the true parameters resulting in poorly calibrated
confidence intervals
What does violation of the independence assumption result in for MLR? - Answers The same as
for SLR
can lead to misleading assessments of the strength of the regression
What does violation of the normality assumption result in for MLR? - Answers The same as for
SLR
can lead to misleading hypothesis tests and confidence/prediction intervals
What are the parameters in MLR? - Answers The regression coefficients beta_0 through beta_p
The variance of the squared errors (sigma squared)
What are the names of the 4 matrices used to write the data for MLR and what data do they
contain? - Answers 1) Y - response matrix
2) Design Matrix - columns of predicting variables, including a column of 1s corresponding to
the intercept
3) Beta - the regression parameters
4)Epsilon - the error terms
What Are the 4 Basic Approaches to MLR - Answers 1) First Order Model
2) Second Order Model
, 3) First Order Interaction Model
4) Second Order Interaction Model
Contour Plot MLR - Answers A graphic representation of the relationships among 3 numeric
variables in 2 dimensions
plotting a 3D surface by plotting constant z slices called contours
Used to display the relationship between 2 independent variables and a dependent variable -
show values of the z variable for combinations of x and y variables
What is the generic formula for a first order MLR model with 2 predicting variables? How would
you explain what the formula means? - Answers Y = beta_0 + beta_1 * x_1 + beta_2 * x_2 +
epsilon
When you fix one of the variables, for example x_1, the expected value of Y is a linear function
other variable x_2
What do we get when we graph a first order MLR model with 2 predicting variables? - Answers
the graph is a function of only one variable for several values of the fixed variables
we get contours of the regression function as a collection of lines
What is the generic formula for a second order MLR model with 2 predicting variables? How
would you explain what the formula means? - Answers Y = beta_0 + beta_1 * x_1 + beta_2 * x_2
+ beta_3 * x_1_squared + beta_4 * x_2_squared + epsilon
The relationship in the individual predictors doesn't have to be linear, we can include the square
of the predictors
beta_3 - the coefficient for the square of x_1
