Statistics 528, Summer 2006
Homework #2
1. Dataset “EX02_011.MTP” gives data on the lean body mass and metabolic rate
for 12 women and 7 men.
a. Make a scatterplot. Use different symbols or colors for women and men.
Do you think the correlation will be about the same for men and women or
quite different for the two groups? Why?
b. Find the correlation (r) for women alone and for men alone.
c. Calculate the mean body mass for the women and for the men. Does the
fact that the men are heavier than the women on average influence the
correlations you calculated for (b)? If so, in what way?
d. Lean body mass was measure in kilograms. How would the correlations
change if we measured body mass in pounds? (There are about 2.2
pounds in a kilogram).
2. A mutual fund company’s newsletter says, “A well-diversified portfolio includes
assets with low correlations.” The newsletter includes a table of correlations
between the annual returns on various classes of investments. For example, the
correlation between municipal bonds and large-cap stocks is 0.5, and the
correlation between municipal bonds and small-cap stocks is 0.21.
a. Rachel invests heavily in municipal bonds. She wants to diversity by
adding an investment whose returns do not closely follow the returns on
her bonds. Should she choose large-cap stocks or small-cap stocks for this
purpose? Explain your answer.
b. If Rachel wants an investment that tends to increase when the return on
her bonds drops, what kind of correlation should she look for?
3. Keeping water supplies clean requires regular measurement of levels of
pollutants. The measurements are indirect – a typical analysis involves forming a
dye by a chemical reaction with the dissolved pollutant, then passing light through
the solution and measuring its “absorbance.” To calibrate such measurements, the
laboratory measures known standard solutions and uses regression to relate
absorbance to pollutant concentration. This is usually done every day. Dataset
“EX02_040.MTP” contains one series of data on the absorbance for different
levels of nitrates. Nitrates are measures in milligrams per liter of water.
a. Chemical theory says that these data should lie on a straight line. If the
correlation is not at least 0.997, something went wrong and the calibration
procedure is repeated. Plot the data and find the correlation. Must the
calibration be done again?
b. What is the equation of the least-squares line for predicting absorbance
from concentration? If the lab analyzed a specimen with 500 milligrams
of nitrates per liter, what do you expect the absorbance to be? Based on
your plot and the correlation, do you expect your predicted absorbance to
be very accurate?
