Stat S100 Homework 5 Assignment

1. Some
believe that individuals with a constant sense of time urgency (often called
Type-A behavior) are more susceptible to heart disease than the more relaxed
individuals. Although most studies of
this issue have focused on individuals, some psychologists have investigated
geographical areas. They considered the
relationship of city-wide heart disease rates and general measures of the pace
of life in the city.
For
each region of the United States (NE, Midwest, South, West) they selected three
large metropolitan areas, three medium size cities and three smaller
cities. In each city they measured three
indicators of pace of life. The variable
walk is the walking speed of pedestrians over a distance of 60 feet during
business hours on a clear summer day along a main downtown street. Bank is the average time a sample of bank
clerks takes to make change for two $20 bills or to give $20 bills for
change. The variable talk is obtained by
recording responses of postal clerks explaining the difference between regular,
certified and insured mail and by dividing the total number of syllables by the
time of their response. The researchers
also obtained the age-adjusted death rates from ischemic heart disease (a decreased
flow of blood to the heart) for each city (heart). The variables have been standardized so there
are no units of measurement involved.

Row BANK WALK
TALK HEART
1 31
28 24 24
2 30
23 23 29
3 29
24 18 31
4 28
28 23 26
5 27
22 30 26
6 26
25 24 20
7 30
26 24 17
8 28
30 21 19
9 33
22 18 26
10 33
22 22 24
11 22
23 23 26
12 30
25 20 25
13 32
23 23 14
14 29
18 25 11
15 25
27 27 19
16 24
22 14 24
17 27
23 24 20
18 26
22 24 13
19 24
23 25 20
20 31
12 19 18
21 27
23 17 16
22 28
20 18 19
23 21
20 17 23
24 19
22 18 11
25 34
14 22 27
26 24
20 23 18
27 25
17 19 15
28 25
26 19 20
29 20
19 22 18
30 22
23 23 21
31 26
13 22 11
32 29
16 21 14 continued on next page
33 25
17 18 19
34 22
17 15 15
35 24
16 10 18
36 13
20 12 16

a. Develop three
separate scatterplots with heart as y and bank, walk and talk as x. Interpret the plots.

b. Run a regression of bank, walk and talk (x) with heart
(y) and analyze the results.

c. Drop the least
significant variable and rerun the model.
Analyze the new output.

d. Using only the
“best” variable, run another model and interpret your results.

e. Run a correlation
table for these four variables. Do the
correlations support the analyses you have made?

f. What are some of
the limitations of this study and your conclusions?

2. Evolutionary
biologists are keenly interested in the characteristics that enable a species
to withstand the selective mechanisms of evolution. An interesting variable in this respect is
brain size. One might expect that bigger
brains are better, but certain penalties seem to be associated with large
brains, such as the need for longer pregnancies and fewer offspring. To shed some light on this issue, it is
helpful to determine exactly which characteristics are associated with large
brains. Data for this problem are in a
file on Blackboard.

a. Create
scatterplots for brain size and each of the independent variables (body,
gestation and litter.) Interpret the
plot.

b. Construct a
correlation matrix and interpret the results.

c. Regress brain size
(y) on the other three variables (x1, x2, x3) and interpret the results.
3. You have
just been hired by Dubuque, a hot dog manufacturer that produces Dubuque brand
hot dogs for the retail market. On your
first day at work you receive a disturbing memo indicating that Ball Park, a
competing brand, may substantially reduce the price of its hotdog. Dubuque is concerned about the negative
impact this might have on its market share.
Ball
Park produces two kinds of hotdogs. One
is regular and the other is a special all-beef hotdog. The current prices are $1.79 and $1.89 per
package. Dubuque’s current price is
$1.49 and Oscar Mayer’s is $1.55.
According
to the memo, Ball Park intends to reduce the price of the regular hot dog to
$1.45 and the all beef to $1.55.
You
want to predict Dubuque’s market share under these different scenarios. Some data are available from a scanner study
conducted at grocery stores located in the western suburbs of Chicago (on
Blackboard). The data are compiled on a
weekly level and consist of information on Dubuque’s market share (MKTDUB)
along with its price (pdub), as well as Oscar Mayer’s prices (poscar) and Ball
Park’s prices (pbpreg) and (pbpbeef).
Prices are given in cents and market share is in decimal form.

a. To begin the
analysis, create scatterplots of all x
variables with market share. What do you
see as potential relationships?

b. Construct a
correlations table and interpret the results.

c. Run a regression
of marketshare on the four price variables and interpret the results.

d. Rerun the
regression with an improved model and interpret.

e. Run a residuals
graph. Is there a problem with
residuals?

f. Going back to the
original question, what is the impact on market share by changing the prices of
Ball Park from $1.79 for regular and $1.89 for beef to $1.45 and $1.55? Remember that Dubuque’s and Oscar Mayer’s are
to remain constant at $1.49 and $1.69.

g. What are the
effects on market share of lowering the prices (one at a time) for each of the
hotdogs?