2. (Problem 4.14, Page 120). Consider fitting the model to the same data set as that of the first 2 problems. Now let u be the residuals obtained from regressing Y on X1 and X2, and v be

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Problems of Tutorial 9

• (Problem 4.12, Page 120) Download the Data for
  Exercise 4.12-4.14 from the class website. The
  data consist of 1 response variable and 6
  predictor variables. Consider fitting a linear
  model relating Y to all predictor variables.
• a). What least squares assumptions (if
  any) seem to be violated?
• b). Compute
  
• c). Construct the index plots of
  as
  well as the Potential-Residual plot.
• d). Identify all unusual observations
  in the data and classify each according to type
  (outlier, high leverage observation, influential
  observation)

2. (Problem 4.14, Page 120). Consider
fitting the model
to the same data set
as that of the first 2 problems. Now let u be
the residuals obtained from regressing Y on X1
and X2, and v be the residuals obtained from
regressing X3 on X1 and X2. Show (or verify
using the above data set as an example) that
a). b). The standard error of
is .
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3 (4.4, page 116) In an attempt to find
unusual points in a regression data set, a data
analyst examines the P-R plot as in the
right-hand side. Classify each of the unusual
points in this plot according to type.
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4. Download the Data for Exercise 4.12-4.14
from the class website. The data consist of 1
response and 6 predictor variables. Suppose we
fit a linear model relating Y to the first three
X-variables. Justify your answer to each of the
following questions with the appropriate
added-variable plot a). Should we add
X4 to the above model? If yes, keep X4 in the
model. b). Should we add X5 to the
above model? If yes, keep X5 in the model.
c). Should we add X6 to the above model?
d). What model would you recommend as the
best possible description of Y? Use the above
results and /or perform additional analysis if
needed.