ISYE6414 Regression Midterm 1 Exam Questions
And Answers Verified 100% Correct
The estimated versus predicted regression line for a given x*:
A) Have the same variance
B) Have the same expectation
C) Have the same variance and expectation
D) None of the above -ANSWER-- B) Have the same expectation
The variability in the prediction comes from:
A) The variability due to a new measurement
B) The variability due to estimation
C) The variability due to a new measurement and due to estimation
D) None of the above -ANSWER-- C) The variability due to a new measurement
and due to estimation
What are residuals? -ANSWER-- The differences between the
observed responses and the fitted responses
What are the assumptions in residual analysis? -ANSWER-- 1.
Linearity assumption - if there is a nonlinear shape to the data.
2. Constant variance assumptions. - the residuals increase with the X variable
3. Independence assumption - if there are clusters of residuals
4. Normality assumption - using a normal probability plot (if it has a curviture then
it is showing non-normality)
In residual analysis, if some of the assumptions do not hold, what is the
interpretation? -ANSWER-- We interpret that the model fit is inadequate, but it
does not mean that the regression is not useful.
For example, if the linearity does not hold, then we could transform Y or X to
improve the linear assumption.
,What is an outlier? -ANSWER-- Any data point that is far from the
majority of the data (in both x and y) is called an outlier.
What are leverage points? -ANSWER-- Data points that are far from
the mean of the x's are called leverage points.
What are influential points? -ANSWER-- A data point that is far from the mean of
both the y's and the x's are influential points and can change the values of the
estimated parameters significantly.
What is a coefficient that can efficiently summarize how well the X's can be used
to predict Y? -ANSWER-- R**2
1 - SSE / SST
What is the correct way to interpret R**2 -ANSWER-- R**2 =
Proportion of total variability in Y that can be explained by the regression (that
uses X)
What is the correlation coefficient? -ANSWER-- A statistic that efficiently
summarizes how well the X's are linearly related to Y is the correlation
coefficients.
The square of the correlation coefficient is the R**2.
Which one is correct?
A) Independence assumption can be assessed using the residuals vs fitted values.
B) Independence assumption can be assessed using the normal probability plot.
C) Residual analysis can only be used to assess uncorrelated errors.
D) None of the above -ANSWER-- C) Residual analysis can only be used to assess
uncorrelated errors.
We detect departure from the assumption of constant variance
A) When the residuals vs fitted values are larger in the ends but smaller in the
middle.
, B) When the residuals vs fitted are scattered randomly around the zero line.
C) When the histogram does not have a symmetric shape.
D) All of the above -ANSWER-- A) When the residuals vs fitted values are larger
in the ends but smaller in the middle.
Which one is correct?
A) If a departure from normality is detected, we transform the predicting variable
to improve upon the normality assumption.
B) If a departure from the independence assumption is detected, we transform the
response variable to improve upon this assumption.
C) The Box-Cox transformation is commonly used to improve upon the linearity
assumption.
D) None of the above -ANSWER-- D) None of the above
In evaluating a simple linear model
A) There is a direct relationship between coefficient of variation and the
correlation between the predicting and response variables.
B) The coefficient of variation is interpreted as the percentage of variability in the
response variable explained by the model.
C) Residual analysis is used for goodness of fit assessment.
D) All of the above -ANSWER-- D) All of the above
What does ANOVA stand for? -ANSWER-- Analysis of variance
What is the overarching objective of ANOVA? -ANSWER-- To
compare the means of multiple samples.
What is one visual method to perform ANOVA? -ANSWER-- Side by
side box plot comparisons
What are the primary objectives of ANOVA? -ANSWER-- 1. Analysis of the
variance in the data 2. Testing for equal means
3. Estimation of simultaneous confidence intervals for the mean difference
The 2nd and 3rd objective are statistical inference problems
And Answers Verified 100% Correct
The estimated versus predicted regression line for a given x*:
A) Have the same variance
B) Have the same expectation
C) Have the same variance and expectation
D) None of the above -ANSWER-- B) Have the same expectation
The variability in the prediction comes from:
A) The variability due to a new measurement
B) The variability due to estimation
C) The variability due to a new measurement and due to estimation
D) None of the above -ANSWER-- C) The variability due to a new measurement
and due to estimation
What are residuals? -ANSWER-- The differences between the
observed responses and the fitted responses
What are the assumptions in residual analysis? -ANSWER-- 1.
Linearity assumption - if there is a nonlinear shape to the data.
2. Constant variance assumptions. - the residuals increase with the X variable
3. Independence assumption - if there are clusters of residuals
4. Normality assumption - using a normal probability plot (if it has a curviture then
it is showing non-normality)
In residual analysis, if some of the assumptions do not hold, what is the
interpretation? -ANSWER-- We interpret that the model fit is inadequate, but it
does not mean that the regression is not useful.
For example, if the linearity does not hold, then we could transform Y or X to
improve the linear assumption.
,What is an outlier? -ANSWER-- Any data point that is far from the
majority of the data (in both x and y) is called an outlier.
What are leverage points? -ANSWER-- Data points that are far from
the mean of the x's are called leverage points.
What are influential points? -ANSWER-- A data point that is far from the mean of
both the y's and the x's are influential points and can change the values of the
estimated parameters significantly.
What is a coefficient that can efficiently summarize how well the X's can be used
to predict Y? -ANSWER-- R**2
1 - SSE / SST
What is the correct way to interpret R**2 -ANSWER-- R**2 =
Proportion of total variability in Y that can be explained by the regression (that
uses X)
What is the correlation coefficient? -ANSWER-- A statistic that efficiently
summarizes how well the X's are linearly related to Y is the correlation
coefficients.
The square of the correlation coefficient is the R**2.
Which one is correct?
A) Independence assumption can be assessed using the residuals vs fitted values.
B) Independence assumption can be assessed using the normal probability plot.
C) Residual analysis can only be used to assess uncorrelated errors.
D) None of the above -ANSWER-- C) Residual analysis can only be used to assess
uncorrelated errors.
We detect departure from the assumption of constant variance
A) When the residuals vs fitted values are larger in the ends but smaller in the
middle.
, B) When the residuals vs fitted are scattered randomly around the zero line.
C) When the histogram does not have a symmetric shape.
D) All of the above -ANSWER-- A) When the residuals vs fitted values are larger
in the ends but smaller in the middle.
Which one is correct?
A) If a departure from normality is detected, we transform the predicting variable
to improve upon the normality assumption.
B) If a departure from the independence assumption is detected, we transform the
response variable to improve upon this assumption.
C) The Box-Cox transformation is commonly used to improve upon the linearity
assumption.
D) None of the above -ANSWER-- D) None of the above
In evaluating a simple linear model
A) There is a direct relationship between coefficient of variation and the
correlation between the predicting and response variables.
B) The coefficient of variation is interpreted as the percentage of variability in the
response variable explained by the model.
C) Residual analysis is used for goodness of fit assessment.
D) All of the above -ANSWER-- D) All of the above
What does ANOVA stand for? -ANSWER-- Analysis of variance
What is the overarching objective of ANOVA? -ANSWER-- To
compare the means of multiple samples.
What is one visual method to perform ANOVA? -ANSWER-- Side by
side box plot comparisons
What are the primary objectives of ANOVA? -ANSWER-- 1. Analysis of the
variance in the data 2. Testing for equal means
3. Estimation of simultaneous confidence intervals for the mean difference
The 2nd and 3rd objective are statistical inference problems
