STAT 501 � Final Exam � Spring 2015
A final exam testing knowledge of statistical concepts and hypothesis testing.
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STAT 501 – Final Exam – Spring 2015
1) (5x2 = 10 points) State which of the following statements are true and which are false. For
the statements that are false, explain why they are false.
a) In a logistic regression analysis where Y=1 represents survival and Y=0 represents death,
the logit of the survival probability is the negative of the logit of death probability.
b) In regression analysis, the method of ordinary least squares can be used in the presence
of non-normal errors.
c) In multiple linear regression analysis, the width of a prediction interval for a future
response of Y based on a single predictor X increases with the value of X.
d) The error terms in an AR(1) model have zero mean.
e) In model selection, the MSE (or S) criterion minimizes confidence/prediction interval
widths, while the PRESS criterion evaluates model unbiasedness.
2) (7x2 = 14 points) Fill in the blanks with terms from the list: non-normality, multicollinearity,
heteroscadasticity, confidence intervals, prediction intervals. [Note: there are 7 blanks but
only 5 terms, so you’ll have to use some terms more than once and there may be some
terms you don’t use at all.]
a) A small p-value for the Ryan-Joiner test indicates non-normality.
b) A residual vs. fits plot with a non-random pattern around a horizontal line at zero
indicates heteroscedasticity.
c) A large sample size ensures the validity of a confidence interval for a mean response
even when errors exhibit non-normality
d) Multicollinearity among predictors will lead to unreliable confidence intervals for
regression coefficients.
e) Weighted least squares estimation can be used in the presence of error
heteroscadasticity and non-normality.
3) (4x3 = 12 points) The following ANOVA table is abstracted from a regression fit to the
model: Y = β0 + β1 X1 + β2 X2 + β3 X3 + … + β10 X10 + ε.
Source DF SS
Regression 10 110.53
Residual
Error 28 39.47
Total 38 150
STAT 501 – Final Exam – Spring 2015
1) (5x2 = 10 points) State which of the following statements are true and which are false. For
the statements that are false, explain why they are false.
a) In a logistic regression analysis where Y=1 represents survival and Y=0 represents death,
the logit of the survival probability is the negative of the logit of death probability.
b) In regression analysis, the method of ordinary least squares can be used in the presence
of non-normal errors.
c) In multiple linear regression analysis, the width of a prediction interval for a future
response of Y based on a single predictor X increases with the value of X.
d) The error terms in an AR(1) model have zero mean.
e) In model selection, the MSE (or S) criterion minimizes confidence/prediction interval
widths, while the PRESS criterion evaluates model unbiasedness.
2) (7x2 = 14 points) Fill in the blanks with terms from the list: non-normality, multicollinearity,
heteroscadasticity, confidence intervals, prediction intervals. [Note: there are 7 blanks but
only 5 terms, so you’ll have to use some terms more than once and there may be some
terms you don’t use at all.]
a) A small p-value for the Ryan-Joiner test indicates non-normality.
b) A residual vs. fits plot with a non-random pattern around a horizontal line at zero
indicates heteroscedasticity.
c) A large sample size ensures the validity of a confidence interval for a mean response
even when errors exhibit non-normality
d) Multicollinearity among predictors will lead to unreliable confidence intervals for
regression coefficients.
e) Weighted least squares estimation can be used in the presence of error
heteroscadasticity and non-normality.
3) (4x3 = 12 points) The following ANOVA table is abstracted from a regression fit to the
model: Y = β0 + β1 X1 + β2 X2 + β3 X3 + … + β10 X10 + ε.
Source DF SS
Regression 10 110.53
Residual
Error 28 39.47
Total 38 150
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Document Details
University
Pennsylvania State University
Subject
Statistics