ISYE 6414: MODULES 1 & 2 EXAM
QUESTIONS WITH CORRECT
ANSWERS
Why is the q critical point of the range distribution for the pairwise comparison in
ANOVA used instead of the t critical point? - Answer-to correct for the multiple inference
across all pairs.
In pairwise comparison, how do you know if one variable mean is LARGER than
another? - Answer-confidence levels have only positive values
In pairwise comparison, how do you know if one variable mean is SMALLER than
another? - Answer-confidence levels have only negative values
How many degrees of freedom does the pooled variance estimator (ANOVA) have?
Why? - Answer-n-1
only replacing one parameter- the overall mean
The F-test for equal means is a ___-tailed test with ___ parameters (each one is a
different measure for degrees of freedom). - Answer-one-tailed
two parameters
A ___ interval is always more narrow than its corresponding ___ interval. - Answer-(1)
confidence
(2) prediction
What measures the linear dependence between two variables? - Answer-correlation
mean sum of squared errors (MSE) is a measure of ___ variability - Answer-within-
group
How to check the constant variance assumption of ANOVA - Answer-plot the residuals
by treatment group to assess whether the groups individually have different variability
that contradicts our assumption.
What is the degrees of freedom for the variance estimator in multiple linear regression?
- Answer-n-p-1
In multiple linear regression, the estimator σ2 is the ___. - Answer-Mean Squared Error
, In terms of multilinear regression, how do we quantitatively interpret the meaning of βi
hat? - Answer-The change in the response variable for each one unit change in the
predicting variable, holding all other variables in the model fixed
Marginal relationship - Answer-relationship between the predicting variable and
response variable without consideration of other factors (SLR)
Conditional relationship - Answer-relationship between the predicting variable and
response variable conditional on all other predicting variables in the model (MLR)
For MLR, we evaluate normality using the ___. - Answer-residuals
How do you graphically check the linearity assumption for MLR? - Answer-graph the
residuals against each predictor
How do you graphically check the constant variance and independence assumptions for
MLR? - Answer-graph the standardized residuals against fitted values
Why do residuals need to be standardized in MLR? How do you standardize them? -
Answer-to correct for non-constant variance.
divide ε by σ*sqrt(1-hi,i)
where h is the hat matrix and hi,i is the i-th element on its diagonal
(MLR) If you saw a bimodal distribution of the response variable in a histogram, what
could that indicate? Can you make a conclusion regarding normality/linearity? - Answer-
bimodality in the distribution may indicate that response variable can be explained by a
categorical variable.
does not necessarily mean that there is non-normality (check residuals). If a predicting
variable's distribution is highly skewed, it could indicate non-linearity with respect to that
variable.
(MLR) if there is a non-linear pattern in the residual plot for one of predicting variables,
the linearity assumption for the model as a whole ___. - Answer-does not hold
If the residuals are clustered, ___. - Answer-uncorrelated errors assumption does not
hold
When can't we assess independence assumption? - Answer-In observational data- only
uncorrelated errors can be assessed using residuals
When can we assess independence assumption? - Answer-randomized trial data
(controlled). The independence would be implicit.
Normality transformations:
QUESTIONS WITH CORRECT
ANSWERS
Why is the q critical point of the range distribution for the pairwise comparison in
ANOVA used instead of the t critical point? - Answer-to correct for the multiple inference
across all pairs.
In pairwise comparison, how do you know if one variable mean is LARGER than
another? - Answer-confidence levels have only positive values
In pairwise comparison, how do you know if one variable mean is SMALLER than
another? - Answer-confidence levels have only negative values
How many degrees of freedom does the pooled variance estimator (ANOVA) have?
Why? - Answer-n-1
only replacing one parameter- the overall mean
The F-test for equal means is a ___-tailed test with ___ parameters (each one is a
different measure for degrees of freedom). - Answer-one-tailed
two parameters
A ___ interval is always more narrow than its corresponding ___ interval. - Answer-(1)
confidence
(2) prediction
What measures the linear dependence between two variables? - Answer-correlation
mean sum of squared errors (MSE) is a measure of ___ variability - Answer-within-
group
How to check the constant variance assumption of ANOVA - Answer-plot the residuals
by treatment group to assess whether the groups individually have different variability
that contradicts our assumption.
What is the degrees of freedom for the variance estimator in multiple linear regression?
- Answer-n-p-1
In multiple linear regression, the estimator σ2 is the ___. - Answer-Mean Squared Error
, In terms of multilinear regression, how do we quantitatively interpret the meaning of βi
hat? - Answer-The change in the response variable for each one unit change in the
predicting variable, holding all other variables in the model fixed
Marginal relationship - Answer-relationship between the predicting variable and
response variable without consideration of other factors (SLR)
Conditional relationship - Answer-relationship between the predicting variable and
response variable conditional on all other predicting variables in the model (MLR)
For MLR, we evaluate normality using the ___. - Answer-residuals
How do you graphically check the linearity assumption for MLR? - Answer-graph the
residuals against each predictor
How do you graphically check the constant variance and independence assumptions for
MLR? - Answer-graph the standardized residuals against fitted values
Why do residuals need to be standardized in MLR? How do you standardize them? -
Answer-to correct for non-constant variance.
divide ε by σ*sqrt(1-hi,i)
where h is the hat matrix and hi,i is the i-th element on its diagonal
(MLR) If you saw a bimodal distribution of the response variable in a histogram, what
could that indicate? Can you make a conclusion regarding normality/linearity? - Answer-
bimodality in the distribution may indicate that response variable can be explained by a
categorical variable.
does not necessarily mean that there is non-normality (check residuals). If a predicting
variable's distribution is highly skewed, it could indicate non-linearity with respect to that
variable.
(MLR) if there is a non-linear pattern in the residual plot for one of predicting variables,
the linearity assumption for the model as a whole ___. - Answer-does not hold
If the residuals are clustered, ___. - Answer-uncorrelated errors assumption does not
hold
When can't we assess independence assumption? - Answer-In observational data- only
uncorrelated errors can be assessed using residuals
When can we assess independence assumption? - Answer-randomized trial data
(controlled). The independence would be implicit.
Normality transformations:
