Chapter 8 Regression and Correlation 349during 1991. INC90 is the percentage
net income for 1990, and similarly,
INC91 is the percentage net income for
- CAPRET90 is the percentage capi-
tal gain for 1990, and CAPRET91 is the
percentage capital gain for 1991.
a. Open the Fidelity workbook from
the Chapter08 folder and save it as
Fidelity Financial Analysis.
b. What is the correlation between the
percentage capital gains for 1990 and
1991? Do your analysis using both the
Pearson and Spearman correlations,
calculating the p value for both. Is
there evidence to support the sup-
position that the percentage capital
gains from 1990 are highly correlated
with the percent capital gains for
1991?
c. What is the correlation between the
percentage net income for 1990 and
1991? Use both the Pearson and
Spearman correlation coeffi cents and
include the p values. Is net income
from 1990 highly correlated with net
income from 1991?
d. Create a scatter plot for the two cor-
relations in parts a and b. Label each
point on the scatter plot with labels
from the Sector column.
e. You should get a stronger correlation
for income than for capital gains. How
do you explain this?
f. Calculate the correlation between the
percentage increase in net asset value
in 1990 to 1991 using the NAV90 and
NAV91 variables and then generate
the scatter plot, labeling the points
with the sector names. Note that the
Biotechnology Fund stands out in the
plot. It was the only fund that per-
formed well in both years.
g. Compare the Pearson and Spearman
correlation values for NAV90 and
NAV91. Are they the same sign? What
could account for the different corre-
lation values? Which do you think is
more representative of the scatter plot
you created?
h. If the correlation is this weak, what
does it suggest about using fund per-
formance in one year as a guide to
fund performance in the following
year?
i. Save your changes to the workbook
and write a report summarizing your
observations.- The Draft workbook contains information
on the 1970 military draft lottery. Draft
numbers were determined by placing
all 366 possible birth dates in a rotating
drum and selecting them one by one. The
fi rst birth date drawn received a draft
number of 1 and men born on that date
were drafted fi rst, the second birth date
entered received a draft number of 2, and
so forth. Is there any relationship between
the draft number and the birth date?
a. Open the Draft workbook from the
Chapter08 folder and save it as Draft
Correlation Analysis.
b. Using the values in the Draft Numbers
worksheet, calculate the Pearson and
Spearman correlation coeffi cients and
p value between the Day_of_the_Year
and the Draft number. Is there a sig-
nifi cant correlation between the two?
Using the value of the correlation,
would you expect higher draft num-
bers to be assigned to people born ear-
lier in the year or later?
c. Create a scatter plot of Number versus
Day_of_the_Year. Is there an obvious
relationship between the two in the
scatter plot?
d. Add a trend line to your scatter plot
and include both the regression equa-
tion and the R^2 value. How much
of the variation in draft number is
explained by the Day_of_the_Year
variable?
e. Calculate the average draft number
for each month and then calculate