The
purpose of this assignment is to develop models that can be used to predict the
specific variable:frequency of going to
a fast food restaurant (FFR), q2, which we shall treat as interval scale [even
though it is, technically, merely ordinal] with values ranging from 1 to 5.
(I.e., q2 is back to its original form on the questionnaire).

A reasonable strategy is to first
run (stepwise) regressions including
as (eligible) independent variables the questions in each noted “block of
variables.” Particularly relevant “blocks “ might be thought of as (1) Product
attributes/ benefits, q16 – q26; (2) Restaurant scripts – ideas in your mind
about fast food restaurants, q69 – q84; (3) Usage/occasion, q85 – q102, (4)
Demographics, q136 – q148. Then note which variables are statistically
significant[1],
and the R-squared values from the model using the variables. Call this “phase
1.”

Q1) What is the
R² for each of the four blocks of variables? Which block of
variables is the most predictive of q2?

Next (call this “phase 2”), you
should run a stepwise regression using the variables that were identified in
phase 1 as being important (i.e., “survived” phase 1 stepwise – the “winners”
from each block). This is your “final model.”

Q2) For your
final model, explain the impact of each independent variable on the dependent
variable in terms of the variable’s coefficient; do not focus on the actual
numerical value, but, rather, on the sign of the coefficient. A typical answer
for the variable, Income, would be something like, “Assuming other variables in
the model are held constant, if a person has a higher income, he/she will visit
FFR’s more (less) often.” Also, along
with this explanation, indicate if the sign of the coefficient makes sense
to youand why.

Q3) a) In your
final model, suppose that each of the independent variables takes on a value of
its respective mean (average) in the dataset of n = 402. What do you predict as
the value for q2?

Q3) b) Find a 90%
confidence interval for the prediction in Q3a) for a hypothetical “average” individual
person with that set of values for the independent variables.

In addition to building your phase
2, “final” model, there is a particular interest in the relationship of the
dependent variable (q2) to the importance the respondent gives to “popularity
with children,” q18, and “the number of children 15 and under,” q138.

4) For each of the 2 variables, q18 and q138, is it in the final model? If it is, describe its exact
relationship to q2 after adjusting for other variables in the final model[2].
If it isn’t, is it because the variable is redundant or because it is
irrelevant? (Please make sure I can tell whether your answer is “redundant” or
if it is “irrelevant,” by typing a boldfaceredundant or a boldfaceirrelevant somewhere in your answer). Also,provide your
reasoning for your conclusion.

Technical
note: Some of the
questions toward the end of the data set (i.e., questionnaire) are nominal scale
variables with more than two categories: specifically, 144 and 145. These need
to be converted to dummy variable form. (If there are only two categories to
begin with [e.g., Male, Female], then the variable is “already in dummy variable
form,” and does not need conversion.)

At the end of
the database, various dummy variables have been constructed for your
convenience. The category of the housing variable, Duplex, which had a very low
frequency, was combined with one of the other categories, Apartment, resulting
in the variable having only 2 categories (and, correspondingly, one variable).

[1]
I.e., remain in the stepwise regression at the end of the stepwise process.

[2]
Note: its “relationship” to q2 concerns its coefficient/slope (not
something to do with R or R²).