ISYE 6414 COMPREHENSIVE EXAM 2026 QUESTIONS AND
SOLUTIONS RATED A+
✔✔If one confidence interval in the pairwise comparison includes zero under ANOVA,
we conclude that
the two corresponding means are plausibly equal. - ✔✔True. See Unit 2.2.1
✔✔We do not need to assume normality of the response variable for making inference
on the
regression coefficients. - ✔✔False. The sampling distributions we use for inference rely
on normality of the response.
✔✔Assuming the model is a good fit, the residuals in simple linear regression have
constant variance - ✔✔True. Goodness of fit refers to whether the model assumptions
hold, one of which is constant variance.
✔✔We cannot estimate a multiple linear regression model if the predicting variables are
linearly independent. - ✔✔False. We cannot if they are linearly dependent.
✔✔If a predicting variable is categorical with 5 categories in a linear regression model
without intercept, we will include 5 dummy variables in the model. - ✔✔True. See Unit
2.2.3
✔✔In the ANOVA, the number of degrees of freedom of the chi-squared distribution for
the variance estimator is N-k-1 where k is the number of groups. - ✔✔False. This
variance estimator has N-1 degrees of freedom.
✔✔If the non-constant variance assumption does not hold in multiple linear regression,
we apply a transformation to the predicting variables. - ✔✔False. We apply a
transformation on the response.
✔✔The prediction of the response variable has higher uncertainty than the estimation of
the mean response. - ✔✔True. We have additional uncertainty from the newness of the
observation (see Unit 3.2.4).
✔✔In linear regression, outliers do not impact the estimation of the regression
coefficients. - ✔✔False. Outliers can impact estimation, especially if they are also
influential points.
✔✔Multicolinearity in multiple linear regression means that the columns in the design
matrix are (nearly) linearly dependent. - ✔✔True. See Unit 3.3.3
, ✔✔The statistical inference for linear regression under normality relies on large size of
sample data. - ✔✔False. As we are already assuming normality, we do not need to rely
on a large sample size.
✔✔ We can assess the constant variance assumption in linear regression by plotting
the residuals vs. fitted values. - ✔✔True
✔✔If one confidence interval in the pairwise comparison in ANOVA includes zero, we
conclude that the two corresponding means are plausibly equal. - ✔✔True
✔✔The assumption of normality is not required in linear regression to make inference
on the regression coefficients. - ✔✔False (Explanation: is required)
✔✔We cannot estimate a multiple linear regression model if the predicting variables are
linearly independent. - ✔✔False (Explanation: linearly dependent)
✔✔If a predicting variable is a categorical variable with 5 categories in a linear
regression model without intercept, we will include 5 dummy variables. - ✔✔True
✔✔If the normality assumption does not hold for a regression, we may use a
transformation on the response variable. - ✔✔True
✔✔The prediction of the response variable has higher uncertainty than the estimation of
the mean response. - ✔✔True
✔✔Statistical inference for linear regression under normality relies on large sample size.
- ✔✔False (Explanation: small sample size is fine)
✔✔A nonlinear relationship between the response variable and a predicting variable
cannot be modeled using regression. - ✔✔False (Explanation: Nonlinear relationships
can often be modeled using linear regression by including polynomial terms of the
predicting variable, for example.)
✔✔Assumption of normality in linear regression is required for confidence intervals,
prediction intervals, and hypothesis testing. - ✔✔True
✔✔If the confidence interval for a regression coefficient contains the value zero, we
interpret that the regression coefficient is plausibly equal to zero. - ✔✔True
✔✔The smaller the coefficient of determination or R-squared, the higher the variability
explained bythe simple linear regression. - ✔✔False (Explanation: The larger the R-
squared)
SOLUTIONS RATED A+
✔✔If one confidence interval in the pairwise comparison includes zero under ANOVA,
we conclude that
the two corresponding means are plausibly equal. - ✔✔True. See Unit 2.2.1
✔✔We do not need to assume normality of the response variable for making inference
on the
regression coefficients. - ✔✔False. The sampling distributions we use for inference rely
on normality of the response.
✔✔Assuming the model is a good fit, the residuals in simple linear regression have
constant variance - ✔✔True. Goodness of fit refers to whether the model assumptions
hold, one of which is constant variance.
✔✔We cannot estimate a multiple linear regression model if the predicting variables are
linearly independent. - ✔✔False. We cannot if they are linearly dependent.
✔✔If a predicting variable is categorical with 5 categories in a linear regression model
without intercept, we will include 5 dummy variables in the model. - ✔✔True. See Unit
2.2.3
✔✔In the ANOVA, the number of degrees of freedom of the chi-squared distribution for
the variance estimator is N-k-1 where k is the number of groups. - ✔✔False. This
variance estimator has N-1 degrees of freedom.
✔✔If the non-constant variance assumption does not hold in multiple linear regression,
we apply a transformation to the predicting variables. - ✔✔False. We apply a
transformation on the response.
✔✔The prediction of the response variable has higher uncertainty than the estimation of
the mean response. - ✔✔True. We have additional uncertainty from the newness of the
observation (see Unit 3.2.4).
✔✔In linear regression, outliers do not impact the estimation of the regression
coefficients. - ✔✔False. Outliers can impact estimation, especially if they are also
influential points.
✔✔Multicolinearity in multiple linear regression means that the columns in the design
matrix are (nearly) linearly dependent. - ✔✔True. See Unit 3.3.3
, ✔✔The statistical inference for linear regression under normality relies on large size of
sample data. - ✔✔False. As we are already assuming normality, we do not need to rely
on a large sample size.
✔✔ We can assess the constant variance assumption in linear regression by plotting
the residuals vs. fitted values. - ✔✔True
✔✔If one confidence interval in the pairwise comparison in ANOVA includes zero, we
conclude that the two corresponding means are plausibly equal. - ✔✔True
✔✔The assumption of normality is not required in linear regression to make inference
on the regression coefficients. - ✔✔False (Explanation: is required)
✔✔We cannot estimate a multiple linear regression model if the predicting variables are
linearly independent. - ✔✔False (Explanation: linearly dependent)
✔✔If a predicting variable is a categorical variable with 5 categories in a linear
regression model without intercept, we will include 5 dummy variables. - ✔✔True
✔✔If the normality assumption does not hold for a regression, we may use a
transformation on the response variable. - ✔✔True
✔✔The prediction of the response variable has higher uncertainty than the estimation of
the mean response. - ✔✔True
✔✔Statistical inference for linear regression under normality relies on large sample size.
- ✔✔False (Explanation: small sample size is fine)
✔✔A nonlinear relationship between the response variable and a predicting variable
cannot be modeled using regression. - ✔✔False (Explanation: Nonlinear relationships
can often be modeled using linear regression by including polynomial terms of the
predicting variable, for example.)
✔✔Assumption of normality in linear regression is required for confidence intervals,
prediction intervals, and hypothesis testing. - ✔✔True
✔✔If the confidence interval for a regression coefficient contains the value zero, we
interpret that the regression coefficient is plausibly equal to zero. - ✔✔True
✔✔The smaller the coefficient of determination or R-squared, the higher the variability
explained bythe simple linear regression. - ✔✔False (Explanation: The larger the R-
squared)
