Exam 2 Review

1
Exam 2 Review
2
Data referenced throughout review

• An Educational Testing Service (ETS) research
  scientist used multiple regression analysis to
  model y, the final grade point average (GPA) of
  business and management doctoral students
  (Journal of Educational Statistics, Spring 1993).
  Potential independent variables measured for each
  doctoral student in the study include
• Quantitative Graduate Management Aptitude Test
  (GMAT) score
• Verbal GMAT score
• Undergraduate GPA
• First-year graduate GPA
• Student cohort (i.e., year in which the student
  entered doctoral program 1988, 1990, 1992)

3
Interactions, Dummy Variables and Nesting (1)

• _____________ means the smaller number of ßs, the
  better. Simpler models are easier to understand
  and appreciate, and therefore have a "beauty"
  that their more complicated counterparts often
  lack.

4
Interactions, Dummy Variables and Nesting (2)

• What does it mean when two independent variables
  interact?

5
Interactions, Dummy Variables and Nesting (3)

• For Student Cohort (i.e., year in which the
  student entered doctoral program 1988, 1990,
  1992) set up the appropriate dummy variable.

6
Interactions, Dummy Variables and Nesting (4)

• Write a model for final GPA, y, that allows for a
  different slope for each student cohort.
• Graduate Management Aptitude Test (GMAT) score
• Verbal GMAT score
• Undergraduate GPA
• First-year graduate GPA
• Student cohort (i.e., year in which the student
  entered doctoral program 1988, 1990, 1992)

7
Interactions, Dummy Variables and Nesting (5)

• Write a model for final graduate GPA E(y) that
  proposes linear relationships between GPA and the
  two GMAT scores, such that the slopes of the
  lines depend on student cohort but not on the
  other GMAT score.

8
Selecting Variables (1)

• What is the following describing?
• A regression in which a statistical software
  program begins by fitting all possible
  one-variable models to the data. The independent
  variable that produces the largest t value is
  declared the best one-variable predictor of y. A
  new variable is added until the given criteria
  for the t value can no longer be met.

9
Selecting Variables (2)

• Identify the following variables as quantitative
  or qualitative
• Graduate Management Aptitude Test (GMAT) score
• Verbal GMAT score
• Undergraduate GPA
• First-year graduate GPA
• Student cohort (i.e., year in which the student
  entered doctoral program 1988, 1990, 1992)

10
Selecting Variables (3)

• When and why would we use a variable selection
  technique such as stepwise regression?

11
Selecting Variables (4)

• What are the dangers associated with drawing
  inferences from a stepwise model?

12
Selecting Variables (5)

• If I have selected Graduate Management Aptitude
  Test (GMAT) score, Verbal GMAT score and
  Undergraduate GPA as my Independent variables for
  predicting graduate GPA, what would the first
  order model be?
• What are the null and alternative hypotheses
  regarding the global utility of the model?
• What about the hypothesis tests regarding the
  contribution of undergraduate GPA?
• How do I test these hypotheses?

13
Building Models and Avoiding Pitfalls (1)

• To fit a straight line, you need at least_____
  different x values To fit a curve you need at
  least ____.

14
Building Models and Avoiding Pitfalls (2)

• What is extrapolation?

15
Building Models and Avoiding Pitfalls (3)

• What is multicollinearity and how can you detect
  it?

16
Building Models and Avoiding Pitfalls (4)

• Write a first-order model relating final GPA, y,
  to the five independent variables
• Graduate Management Aptitude Test (GMAT) score
• Verbal GMAT score
• Undergraduate GPA
• First-year graduate GPA
• Student cohort (i.e., year in which the student
  entered doctoral program 1988, 1990, 1992)
• Interpret the ßs in the first order model.

17
Building Models and Avoiding Pitfalls (5)

• Write the complete second-order model for the
  final grade point average for doctoral students
  E(y) based on the following variables (Include
  interactions and quadratic terms.)
• Graduate Management Aptitude Test (GMAT) score
• Verbal GMAT score
• Undergraduate GPA
• First-year graduate GPA
• Student cohort (i.e., year in which the student
  entered doctoral program 1988, 1990, 1992)

18
Residual Analysis (1)

• An observation that is larger than 2 or 3s is a/n
  ___________________.

19
Residual Analysis (2)

• What is the difference between homoscedastic and
  heteroscedastic and which is preferable?

20
Residual Analysis (3)

• How can we use residual plots to detect
  departures from the assumption of equal
  variances? (Include a sketch of what you are
  looking for and what indicates a violation of
  this assumption.)

21
Residual Analysis (4)

• What are the assumptions about the random error
  term?

22
Residual Analysis (5)

• What is the purpose of reviewing Standardized
  Residuals, Leverages, Cooks D, and/or DFFITS?
  Select one and tell how you might use it for this
  purpose.