Math 151, Homework problems with SPSS files from Activstats For SPSS
Sievers' comments in purple. Click the link
to open the SPSS data file. MRA-81-4: Metabolic Rates MRA_81_4Metab.sav
Metabolic rate, the rate at which the body consumes energy, is
important in studies of weight gain, dieting, and exercise. The
table below gives data on the lean body mass and resting metabolic rate
for 12 women and 7 men who are subjects in a study of dieting.
Lean body mass, given in kilograms, is a person's weight leaving out
all fat.
Metabolic rate is measured in calories burned per 24 hours, the same
calories used to describe the energy content of foods. The
researchers believe that lean body mass is an important influence on
metabolic rate.
Make a scatterplot of the data, using different symbols or colors for
men and women. It is often helpful to use different plot symbols
to distinguish different groups in a scatterplot.
Is the association between these variables positive or negative?
What is the form of the relationship? How strong is the
relationship? Does the pattern of relationship differ for women
and men? How do the male subjects as a group differ from the
female subjects as a group? Based on Active Practice of Statistics, Moore, p. 81 MRA-83-8: Educational Spending
vs. Teacher Salaries MRA_83_8EdSal.sav
The SAT datafile gives educational data for the states. We are
interested in the relationship between how much states spend on
education (dollars per pupil) and how much they pay their teachers
(median teacher salaries, in thousands of dollars).
Explain why you expect a positive association between these variables.
We think that education spending helps explain teachers' pay.
Make a scatterplot to display this relationship.
Describe the relationship. Is there a positive association?
Is the relationship approximately linear?
On the plot, identify a state where teacher salaries are unusually high
relative to the state's education spending. (This state is an
outlier, though not an extreme outlier.) What state is this?
How do the Mountain states compare with the rest of the country in
education spending and teacher salaries? Mark the points for
states in the MTN region with a different color on your
scatterplot. Based on the plot, briefly answer the question. Based on Active Practice of Statistics, Moore, p. 83 MRA-80-2: Speed vs. Fuel
Consumption MRA_80_2Speed.sav
How does the fuel consumption of a car change as its speed increases?
Here are data for a British Ford Escort. Speed is measured in
kilometers per hour, and fuel consumption is measured in liters of
gasoline used per 100 kilometers traveled.
Make a scatterplot. (Which variable should go on the x axis?)
Describe the form of the relationship. Why is it not
linear? Explain why the form of the relationship makes sense.
It does not make sense to describe the variables as either positively
associated or negatively associated. Why?
Is the relationship reasonably strong or quite weak? Explain your
answer. Based on Active Practice of Statistics, Moore, p. 80 TRE-58-26: Bear Neck/Weight
TRE_58_26Bear.sav
Consider the relationship between the size of a bear's neck and the
bear's weight. Use the distances around bear necks for the
horizontal scale and use the bear weights for the vertical scale.
Based on the result, what is the relationship between a bear's neck
size and its weight?
Why might this be the better choice of which variable to plot on the x
and which on the y-axes?
ALSO Make a plot with
the M&F bears marked differently. What if any sex differences
do you see here?
Based on Elementary Statistics, Triola, 9th ed., p. 58 MRB-95-13: How Many Corn Plants
Are Too Many? MRB_95_13Corn.sav Corn plants. This is a first
introduction
to the idea of predicting or estimating a "typical" y for a given x
value.
Ch. 8 will do an important special case of that.
How much corn per acre should a farmer plant to obtain the
highest yield? Too few plants will give a low yield. On the other
hand, if there are too many plants, they will compete with each other
for moisture and nutrients, and yields will fall. To find the
best planting rate, plant at different rates on several plots of ground
and measure the harvest. (Be sure to treat all the plots the same
except for the planting rate.) Attatched are data from such an
experiment.
Is yield or planting rate the explanatory variable?
Make a scatterplot of yield and planting rate.
Describe the overall pattern of the relationship. Is it
linear? Is there a positive or negative association, or neither?
Find the mean yield for each of the five planting rates. [Use your calculator] Plot each mean
yield against its planting rate on your scatterplot and connect these
five points with lines [with pen or pencil].
This combination of numerical description and graphing makes the
relationship clearer. What planting rate would you recommend to a
farmer whose conditions were similar to those in the experiment? Based on Basic Practice of Statistics, Moore, p. 95 MRA-89-4: Gas Mileage vs.
Speed MRA_80_2Speed.sav
A previous exercise (
MRA-80-2) gave data on gas mileage versus speed for a small car.
Make a scatterplot and find the correlation r. Explain why r is
close to zero despite a strong relationship between speed and gas
used. Based on Active Practice of Statistics, Moore, p. 89