STAT 401 FINAL EXAM CARDS WITH COMPLETE SOLUTIONS!!
If the null hypothesis of the goodness-of-fit F-test associated with data fitted to a simple
linear regression model is not rejected - ANSWER Then there is insufficient evidence to
support the use of the fitted model.
The combined contribution significance of a collection of explanatory variables in
multiple linear regression modeling is best assessed using - ANSWER A partial F-test.
In what way does the adjusted coefficient of multiple determination differ from the
coefficient of multiple determination? - ANSWER The adjusted coefficient of multiple
determination accounts for the number of explanatory variables in the fitted model, the
coefficient of multiple determination does not.
An indication of the need for including a factor (categorical variable) in the proposed
linear regression model is when the plot of the standardized residuals against the fitted
values (or the explanatory variable) clearly exhibits - ANSWER Vertically clustered
plotted points that are symmetrically spread about the horizontal axis.
Which of the following measures should not be used in performing a model selection
from a collection of non-nested candidate models? - ANSWER Mallow's statistic.
An outlying case in the data is considered influential if - ANSWER It has an influence on
one or more of the estimated mean responses and/or parameter estimates.
With respect to remedial measures, the xy-scatterplot of the data in a bivariate sample
can often be helpful in - ANSWER Determining possible transformations of the observed
responses and/or the explanatory variable to remedy a clear nonlinear trend in the
scatterplot.
When it comes to assessing the validity of the assumptions on the error terms for
multiple linear regression through residual analysis, - ANSWER The process is identical
,to that for simple linear regression models, except in that for multiple linear regression
models more plots will be needed because there are more explanatory variables.
What does the statement "do not miss the forest for the trees" translate to? - ANSWER
When analyzing a scatterplot, rather than following individual points in the plot, step
back and visualize the trend that the bulk of the plotted points follow.
Suppose the QQ Normal probability plot of the standardized residuals exhibits a clear
concave-down trend. Then, it is very likely that - ANSWER The error terms have a
left-skewed distribution, and this can often be remedied by applying the transformation
y->y^lambda, lambda greater than 1.
If a particular case in the data is identified as an outlier, then - ANSWER If it is found that
the case is not a result of human error, an analysis of its influence should be conducted.
A useful first step in outlier and influence analysis is to - ANSWER Keep an eye out for
potential outlying cases in the preliminary exploratory and residual analysis plots.
For simple linear regression, the most useful exploratory data analysis plot is - ANSWER
The scatterplot of the observed responses against corresponding values of the
explanatory variable.
The purpose of a partial F-test in multiple linear regression is - ANSWER To test the
combined contribution significance of a collection of explanatory variables to the fitted
model.
A leverage (or hat-value) provides a means of - ANSWER Identifying outlying cases in
the domain space.
The preferred characteristics of a matrix scatterplot of a multivariate sample include -
ANSWER The absence of nonlinear trends in the xjy-scatterplots, and the absence of
linear trends in the xjxk-scatterplots.
, The presence of bias in a fitted model is best assessed by means of - ANSWER Mallow's
statistic.
The quantity DFFITSi is - ANSWER A deletion statistic that provides a measure of the
influence that the ith case has on its corresponding fitted value.
For a multiple linear regression model, a rejection of the null hypothesis in the model
significance test indicates that - ANSWER At least one of the explanatory variables
contributes significantly to explaining variations in the response variable.
In the QQ Normal probability plot of the standardized residuals, the line z = r - ANSWER
Allows an examination of the behavior of the whole set of standardized residuals in
relation to the theoretical (standard Normal probability) quantiles.
The main purpose of the serial-plot of the residuals (or standardized residuals) of a fitted
simple linear regression model is to - ANSWER Determine if there is evidence to suggest
the presence of first order autocorrelation in the data.
The Shapiro-Wilk test is used to assess - ANSWER The validitity of the assumption of
normality on the error terms.
The recommendation for conducting outlier and influence analysis is to - ANSWER Look
for cases that consistently stand out in all, or most of the deletion statistics plots.
When a multivariate sample is fitted to a model containing a factor, the stripcharts of the
residuals (or standardized residuals) against factor levels are used to - ANSWER
Determine if there might be a violation of the constant variances assumption on the
error terms across factor levels.
Suppose the scatterplot of data that is to be used to construct a simple linear regression
model reveals a nonlinear trend. Then - ANSWER Either a transformation of the
underlying variables or a polynomial model may need to be used to construct a fitted
model.
If the null hypothesis of the goodness-of-fit F-test associated with data fitted to a simple
linear regression model is not rejected - ANSWER Then there is insufficient evidence to
support the use of the fitted model.
The combined contribution significance of a collection of explanatory variables in
multiple linear regression modeling is best assessed using - ANSWER A partial F-test.
In what way does the adjusted coefficient of multiple determination differ from the
coefficient of multiple determination? - ANSWER The adjusted coefficient of multiple
determination accounts for the number of explanatory variables in the fitted model, the
coefficient of multiple determination does not.
An indication of the need for including a factor (categorical variable) in the proposed
linear regression model is when the plot of the standardized residuals against the fitted
values (or the explanatory variable) clearly exhibits - ANSWER Vertically clustered
plotted points that are symmetrically spread about the horizontal axis.
Which of the following measures should not be used in performing a model selection
from a collection of non-nested candidate models? - ANSWER Mallow's statistic.
An outlying case in the data is considered influential if - ANSWER It has an influence on
one or more of the estimated mean responses and/or parameter estimates.
With respect to remedial measures, the xy-scatterplot of the data in a bivariate sample
can often be helpful in - ANSWER Determining possible transformations of the observed
responses and/or the explanatory variable to remedy a clear nonlinear trend in the
scatterplot.
When it comes to assessing the validity of the assumptions on the error terms for
multiple linear regression through residual analysis, - ANSWER The process is identical
,to that for simple linear regression models, except in that for multiple linear regression
models more plots will be needed because there are more explanatory variables.
What does the statement "do not miss the forest for the trees" translate to? - ANSWER
When analyzing a scatterplot, rather than following individual points in the plot, step
back and visualize the trend that the bulk of the plotted points follow.
Suppose the QQ Normal probability plot of the standardized residuals exhibits a clear
concave-down trend. Then, it is very likely that - ANSWER The error terms have a
left-skewed distribution, and this can often be remedied by applying the transformation
y->y^lambda, lambda greater than 1.
If a particular case in the data is identified as an outlier, then - ANSWER If it is found that
the case is not a result of human error, an analysis of its influence should be conducted.
A useful first step in outlier and influence analysis is to - ANSWER Keep an eye out for
potential outlying cases in the preliminary exploratory and residual analysis plots.
For simple linear regression, the most useful exploratory data analysis plot is - ANSWER
The scatterplot of the observed responses against corresponding values of the
explanatory variable.
The purpose of a partial F-test in multiple linear regression is - ANSWER To test the
combined contribution significance of a collection of explanatory variables to the fitted
model.
A leverage (or hat-value) provides a means of - ANSWER Identifying outlying cases in
the domain space.
The preferred characteristics of a matrix scatterplot of a multivariate sample include -
ANSWER The absence of nonlinear trends in the xjy-scatterplots, and the absence of
linear trends in the xjxk-scatterplots.
, The presence of bias in a fitted model is best assessed by means of - ANSWER Mallow's
statistic.
The quantity DFFITSi is - ANSWER A deletion statistic that provides a measure of the
influence that the ith case has on its corresponding fitted value.
For a multiple linear regression model, a rejection of the null hypothesis in the model
significance test indicates that - ANSWER At least one of the explanatory variables
contributes significantly to explaining variations in the response variable.
In the QQ Normal probability plot of the standardized residuals, the line z = r - ANSWER
Allows an examination of the behavior of the whole set of standardized residuals in
relation to the theoretical (standard Normal probability) quantiles.
The main purpose of the serial-plot of the residuals (or standardized residuals) of a fitted
simple linear regression model is to - ANSWER Determine if there is evidence to suggest
the presence of first order autocorrelation in the data.
The Shapiro-Wilk test is used to assess - ANSWER The validitity of the assumption of
normality on the error terms.
The recommendation for conducting outlier and influence analysis is to - ANSWER Look
for cases that consistently stand out in all, or most of the deletion statistics plots.
When a multivariate sample is fitted to a model containing a factor, the stripcharts of the
residuals (or standardized residuals) against factor levels are used to - ANSWER
Determine if there might be a violation of the constant variances assumption on the
error terms across factor levels.
Suppose the scatterplot of data that is to be used to construct a simple linear regression
model reveals a nonlinear trend. Then - ANSWER Either a transformation of the
underlying variables or a polynomial model may need to be used to construct a fitted
model.
