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MAT 3375 Regression Analysis – University of Ottawa
- [6 points] Explain the following procedures/concepts (for sub-questions a, b, c), and give
short answers (for sub-questions d, e, f).
a) What do we mean when we say that the numerical response Y is fit linearly against
the numerical predictor X in the ordinary least squares sense?
b) How does forward stepwise selection work when we attempt to fit a numerical
response Y against a set of numerical predictors {X1, . . . ,Xp}?
c) What do we mean when we say that an observation is a Y −outlier for a dataset?
An X−outlier? An influential observation? Why is it important to identify such
observations?
d) Enumerate the main assumptions of the multiple linear regression model.
e) Name 5 extensions of the SLR model, briefly explaining how these models differ
from SLR.
f) Select all valid answers (no need to justify your choices):
i. It is possible to fit a numerical response Y against a numerical predictor X by
minimizing
Pn
i=1|yi − ˆyi|.
ii. Generally, R2 = r2 in SLR.
iii. The Spearman correlation between two variables always has the same sign as
their Pearson correlation.
iv. We can always determine the linear fit of a dataset {(xi, yi) | i = 1, . . . , n}.
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