Regression Modeling cont''''

1
Regression Modeling (cont.)...

• Look at the next example in Section 1.2 where we
  want to know the relationship between the
  response variable formaldehyde concentration in a
  house (CH2O) and the two explanatory variables
  air tightness of the house (Air) and whether
  the house had urea formaldehyde foam insulation
  installed (UFFI1) or not (UFFI0). This is an
  observational study compared with the previous
  example (Hardness vs. Temp) in which the data was
  obtained from a controlled experiment . Figure
  1.2 on page 8 gives a good idea of what the
  relationship is... the model is
• The random error has the same constraints on mean
  and variance as before ...
• b0 is the average CH2O for x0 (airtight
  houses) and UFFI0 (without UFFI insulation).
• b1 is the average CH2O change for each unit
  increase in air tightness for homes with or
  without UFFI we may introduce interactions
  between Air and UFFI as in model 1.7 on p. 9...
  later...
• b2 is the average CH2O difference, holding Air
  constant, between a house with UFFI and a house
  without UFFI. Show this on p. 9...

2
Now skip over to the gas consumption data in
Table 1.4 (in the data file gasconsumption.txt)...
this represents a random sample of cars from a
larger population of cars. The response variable
is fuel efficiency (a couple of different
measures of this are given) and there are several
explanatory variables given. Well be trying to
find the collection of these variables that best
explain fuel economy... The model 1.9 on page13
assumes they are wt. of the car, engine
displacement, and number of cylinders... As
before, Well be using the double index notation
for the data in these contexts Here, i 1, ...
n, and j 1, ... p (n of observations and p
of explanatory variables). See the General Model
on page 15 and note that the beta parameters have
the interpretation bi the change in m for a
unit change in xi keeping all other explanatory
variables fixed. This model is seen to be linear
in the parameters . See 1.11 on p. 16.