ISYE 6414 FINAL TEST 2026 QUESTIONS
WITH CORRECT ANSWERS GRADED A+
◍ In ANOVA, when we are comparing the means, the alternative hypothesis is
that at least two of the means are different from each other. (T/F).
Answer: True
◍ The estimators for the regression coefficients are:.
Answer: Unbiased regardless of the distribution of the data.
◍ Hat matrix.
Answer: a function of the designmatrix X and thus it depends on the design.
◍ R-square is 1 minus the ratio between the sum of squared errors / sum of
square total. (T/F).
Answer: True
◍ How do we use confidence interval to answer whether ßj is statistically
significant?.
Answer: by checking whether 0 is in the confidence interval. If it is not, we
conclude that ßj is statistically significant.
◍ If we have independent chi-squared random variables, their sum is also a
chi-square distribution. (T/F).
Answer: True
◍ One objective in ANOVA is to determine which groups have statistically
significantly different means from each other. We can compare two groups
at a time, which is called pairwise comparison, and the Tukey method
(TukeyHSD()) will generate all of these for you. (T/F).
Answer: True.
◍ Explanatory variables.
Answer: can be used to explain variability in the response variable. They
, may be included in the model even if other similar variables are in the
model
◍ Prediction.
Answer: We want to see how the response variable behaves in different
settings. For example, for a different location, if we think about a
geographic prediction, or in time, if we think about temporal prediction
◍ controlled.
Answer: Causality statements can only be made in a___ environment such
as randomized trials or experiments. Analysts can change the setting of one
particular factor in the environment, holding others fixed thereby isolating
its effect.
◍ In a general sense, a fitted model is simply the output of minimizing the
errors as measured by a particular criterion. (T/F).
Answer: True. The fitted line is the line that makes the errors as small as
possible given a criterion (like OLS), as shown in the graph on the slide. In
this graph we have two lines, one in red and one in blue. The criterion would
be a function of the deviances of the data from the line, also called error
terms; this function of the error terms will make up the criterion used to
obtain the line.
◍ if x* is one of the observations for the predicting variable, then we use
estimation. (T/F).
Answer: True
◍ In ANOVA with k population samples, the sampling distribution of the
pooled variance is a chi-square distribution with N-2 degrees of freedom.
(T/F).
Answer: False, the sampling distribution of the pooled variance is a
chi-square distribution with N-k degrees of freedom
◍ F-test.
Answer: is the ration of between-group variability and withing-group
variability
, ◍ Residuals.
Answer: are simply the differencebetween observed response and fitted
values, and they are proxies of the error terms inthe regression model
◍ In simple linear regression, the correlation coefficient between the predictor
variable and the response variable is equal to the slope of the regression line.
(T/F).
Answer: False. Correlation Coefficient is a statistic that efficiently
summarizes how well the X's are linearly related to Y is the correlation
coefficient.
◍ predictors.
Answer: The coefficient of multiple regression thus must be interpreted in
the contextof other ___ in the model
◍ The test statistic used in ANOVA for pairwise comparison follows an
F-statistic. (T/F).
Answer: True.
◍ The sampling distribution of the estimated regression coefficients is:.
Answer: Centered at the true regression parameters.The t-distribution
assuming that the variance of the error term is unknown an replaced by its
estimate.Dependent on the design matrix.
◍ If we want to estimate the variance.
Answer: similarly we're going to use the sample variance of the entire
combined response samples. SST / N - 1.Because we are replacing only one
parameter, the overall mean, we're now only losing one degree of freedom.
◍ We do notsee a grouping of the residuals,.
Answer: meaning that the assumption of uncorrelated errorpossibly holds.
◍ independence.
Answer: residual analysis cannot be used to check for the___ assumption
◍ When t-value for a beta value is smaller than our p-threshold, we reject the
null hypothesis which is by default is that the beta value is equal to zero (0).
WITH CORRECT ANSWERS GRADED A+
◍ In ANOVA, when we are comparing the means, the alternative hypothesis is
that at least two of the means are different from each other. (T/F).
Answer: True
◍ The estimators for the regression coefficients are:.
Answer: Unbiased regardless of the distribution of the data.
◍ Hat matrix.
Answer: a function of the designmatrix X and thus it depends on the design.
◍ R-square is 1 minus the ratio between the sum of squared errors / sum of
square total. (T/F).
Answer: True
◍ How do we use confidence interval to answer whether ßj is statistically
significant?.
Answer: by checking whether 0 is in the confidence interval. If it is not, we
conclude that ßj is statistically significant.
◍ If we have independent chi-squared random variables, their sum is also a
chi-square distribution. (T/F).
Answer: True
◍ One objective in ANOVA is to determine which groups have statistically
significantly different means from each other. We can compare two groups
at a time, which is called pairwise comparison, and the Tukey method
(TukeyHSD()) will generate all of these for you. (T/F).
Answer: True.
◍ Explanatory variables.
Answer: can be used to explain variability in the response variable. They
, may be included in the model even if other similar variables are in the
model
◍ Prediction.
Answer: We want to see how the response variable behaves in different
settings. For example, for a different location, if we think about a
geographic prediction, or in time, if we think about temporal prediction
◍ controlled.
Answer: Causality statements can only be made in a___ environment such
as randomized trials or experiments. Analysts can change the setting of one
particular factor in the environment, holding others fixed thereby isolating
its effect.
◍ In a general sense, a fitted model is simply the output of minimizing the
errors as measured by a particular criterion. (T/F).
Answer: True. The fitted line is the line that makes the errors as small as
possible given a criterion (like OLS), as shown in the graph on the slide. In
this graph we have two lines, one in red and one in blue. The criterion would
be a function of the deviances of the data from the line, also called error
terms; this function of the error terms will make up the criterion used to
obtain the line.
◍ if x* is one of the observations for the predicting variable, then we use
estimation. (T/F).
Answer: True
◍ In ANOVA with k population samples, the sampling distribution of the
pooled variance is a chi-square distribution with N-2 degrees of freedom.
(T/F).
Answer: False, the sampling distribution of the pooled variance is a
chi-square distribution with N-k degrees of freedom
◍ F-test.
Answer: is the ration of between-group variability and withing-group
variability
, ◍ Residuals.
Answer: are simply the differencebetween observed response and fitted
values, and they are proxies of the error terms inthe regression model
◍ In simple linear regression, the correlation coefficient between the predictor
variable and the response variable is equal to the slope of the regression line.
(T/F).
Answer: False. Correlation Coefficient is a statistic that efficiently
summarizes how well the X's are linearly related to Y is the correlation
coefficient.
◍ predictors.
Answer: The coefficient of multiple regression thus must be interpreted in
the contextof other ___ in the model
◍ The test statistic used in ANOVA for pairwise comparison follows an
F-statistic. (T/F).
Answer: True.
◍ The sampling distribution of the estimated regression coefficients is:.
Answer: Centered at the true regression parameters.The t-distribution
assuming that the variance of the error term is unknown an replaced by its
estimate.Dependent on the design matrix.
◍ If we want to estimate the variance.
Answer: similarly we're going to use the sample variance of the entire
combined response samples. SST / N - 1.Because we are replacing only one
parameter, the overall mean, we're now only losing one degree of freedom.
◍ We do notsee a grouping of the residuals,.
Answer: meaning that the assumption of uncorrelated errorpossibly holds.
◍ independence.
Answer: residual analysis cannot be used to check for the___ assumption
◍ When t-value for a beta value is smaller than our p-threshold, we reject the
null hypothesis which is by default is that the beta value is equal to zero (0).
