ISYE 6414 OFFICIAL MIDTERM 1
COMPREHENSIVE STUDY GUIDE 2026 FULL
QUESTIONS AND SOLUTIONS GRADED A+
◍ In ANOVA, when testing for equal means across groups, the alternative
hypothesis is that the means are not equal between two groups for all pairs
of means/groups..
Answer: falseThe alternative is that at least one pair of groups have unequal
means
◍ For a multiple regression model, both the true errors ϵ and the estimated
residuals ϵ-hat have a constant mean and a constant variance..
Answer: False
◍ The statistical inference for linear regression under normality relies on large
size of sample data..
Answer: False. As we are already assuming normality, we do not need to
rely on a large sample size.
◍ If the residuals are not normally distributed, we can model the transformed
response variable instead, where a common transformation for normality is
the Box-Cox transformation..
Answer: trueSee Lesson 3.3.11: Assumptions and DiagnosticsIf the
normality assumption does not hold, we can use a transformation that
normalizes the response variable such as Box-Cox transformation.
◍ In simple linear regression, we can diagnose the assumption of
constant-variance by plotting the residuals against fitted values..
Answer: True
◍ One-way ANOVA is a linear regression model with more than one
qualitative predicting variables..
, Answer: False
◍ The one-way ANOVA is a linear regression model with one qualitative
predicting variable..
Answer: true
◍ Let Y^ be the predicted response at x^ . The variance of Y^ given x^
depends on both the value of x^ and the design matrix..
Answer: True (but the wording was confusing, so everyone got credit no
matter what on this question)
◍ The estimators of the error term variance and of the regression coefficients
are random variables..
Answer: True. The estimators are ̂, ̂^2, and ̂. These estimators are
functions of the response, which is a random variable. Therefore they are
alsorandom.
◍ If the confidence interval for a regression coefficient contains the value
zero, we interpret that the regression coefficient is definitely equal to zero..
Answer: False. The coefficient is plausibly zero, but we cannot be certain
that it is
◍ In a simple linear regression model, the variable of interest is the response
variable..
Answer: True
◍ The prediction of the response variable has higher uncertainty than the
estimation of the mean response..
Answer: True
◍ We can assess the constant variance assumption in linear regression by
plotting the residuals vs. fitted values..
Answer: True
◍ The assumption of normality is not required in linear regression to make
inference on the regression coefficients..
Answer: False (Explanation: is required)
, ◍ In a multiple linear regression model, the R^2 measures the proportion of
total variability in the response variable that is captured by the regression
model..
Answer: true
◍ A partial F-Test can be used to test whether the regression coefficients
associated with a subset of the predicting variables in a multiple linear
regression model are all equal to zero..
Answer: trueSee Lesson 3.7: Testing for Subsets of Regression
ParametersWe use the Partial F-test to test the null hypothesis that the
regression coefficients associated to a subset of the predicting variables are
all equal to zero. The alternative hypothesis is that at least one of these
regression coefficients is not zero.
◍ Multicolinearity in multiple linear regression means that the columns in the
design matrix are (nearly) linearly dependent..
Answer: True. See Unit 3.3.3
◍ If one confidence interval in the pairwise comparison includes zero under
ANOVA, we conclude that the two corresponding means are plausibly
equal..
Answer: true
◍ The ANOVA model with a qualitative predicting variable with k
levels/classes will have k + 1 parameters to estimate..
Answer: True
◍ In multiple linear regression, the estimated regression coefficient
corresponding to a quantitative predicting variable is interpreted as the
estimated expected change in the response variable when there is a change
of one unit in the corresponding predicting variable holding all other
predictors fixed..
Answer: trueSee Lesson 3.4: Model Interpretation"The estimated value for
one of the regression coefficient βi represents the estimated expected change
in y associated with one unit of change in the corresponding predicting
COMPREHENSIVE STUDY GUIDE 2026 FULL
QUESTIONS AND SOLUTIONS GRADED A+
◍ In ANOVA, when testing for equal means across groups, the alternative
hypothesis is that the means are not equal between two groups for all pairs
of means/groups..
Answer: falseThe alternative is that at least one pair of groups have unequal
means
◍ For a multiple regression model, both the true errors ϵ and the estimated
residuals ϵ-hat have a constant mean and a constant variance..
Answer: False
◍ The statistical inference for linear regression under normality relies on large
size of sample data..
Answer: False. As we are already assuming normality, we do not need to
rely on a large sample size.
◍ If the residuals are not normally distributed, we can model the transformed
response variable instead, where a common transformation for normality is
the Box-Cox transformation..
Answer: trueSee Lesson 3.3.11: Assumptions and DiagnosticsIf the
normality assumption does not hold, we can use a transformation that
normalizes the response variable such as Box-Cox transformation.
◍ In simple linear regression, we can diagnose the assumption of
constant-variance by plotting the residuals against fitted values..
Answer: True
◍ One-way ANOVA is a linear regression model with more than one
qualitative predicting variables..
, Answer: False
◍ The one-way ANOVA is a linear regression model with one qualitative
predicting variable..
Answer: true
◍ Let Y^ be the predicted response at x^ . The variance of Y^ given x^
depends on both the value of x^ and the design matrix..
Answer: True (but the wording was confusing, so everyone got credit no
matter what on this question)
◍ The estimators of the error term variance and of the regression coefficients
are random variables..
Answer: True. The estimators are ̂, ̂^2, and ̂. These estimators are
functions of the response, which is a random variable. Therefore they are
alsorandom.
◍ If the confidence interval for a regression coefficient contains the value
zero, we interpret that the regression coefficient is definitely equal to zero..
Answer: False. The coefficient is plausibly zero, but we cannot be certain
that it is
◍ In a simple linear regression model, the variable of interest is the response
variable..
Answer: True
◍ The prediction of the response variable has higher uncertainty than the
estimation of the mean response..
Answer: True
◍ We can assess the constant variance assumption in linear regression by
plotting the residuals vs. fitted values..
Answer: True
◍ The assumption of normality is not required in linear regression to make
inference on the regression coefficients..
Answer: False (Explanation: is required)
, ◍ In a multiple linear regression model, the R^2 measures the proportion of
total variability in the response variable that is captured by the regression
model..
Answer: true
◍ A partial F-Test can be used to test whether the regression coefficients
associated with a subset of the predicting variables in a multiple linear
regression model are all equal to zero..
Answer: trueSee Lesson 3.7: Testing for Subsets of Regression
ParametersWe use the Partial F-test to test the null hypothesis that the
regression coefficients associated to a subset of the predicting variables are
all equal to zero. The alternative hypothesis is that at least one of these
regression coefficients is not zero.
◍ Multicolinearity in multiple linear regression means that the columns in the
design matrix are (nearly) linearly dependent..
Answer: True. See Unit 3.3.3
◍ If one confidence interval in the pairwise comparison includes zero under
ANOVA, we conclude that the two corresponding means are plausibly
equal..
Answer: true
◍ The ANOVA model with a qualitative predicting variable with k
levels/classes will have k + 1 parameters to estimate..
Answer: True
◍ In multiple linear regression, the estimated regression coefficient
corresponding to a quantitative predicting variable is interpreted as the
estimated expected change in the response variable when there is a change
of one unit in the corresponding predicting variable holding all other
predictors fixed..
Answer: trueSee Lesson 3.4: Model Interpretation"The estimated value for
one of the regression coefficient βi represents the estimated expected change
in y associated with one unit of change in the corresponding predicting
