1. Consider the personal
data collected in class. We're going to focus on three variables:
commute time, hours of TV
watched, and weight. For each of these variables, do the following:
a) Classify as quantitative/qualitative, continuous/discrete.
b) Without looking at any graphics, describe the
shape you would expect for the distribution of this variable: symmetric,
skewed? Explain why.
c) What's a typical value for this variable for
students in 110A?
d) Make a histogram or stem and leaf plot of these
variables. Describe the distribution. Are there outliers? Gaps? What
is
the shape?
2. People with short commutes have more time to watch TV.
Do you see any evidence that the length of the commute is
related to the amount of TV watched? What is this evidence?
Can you give an explanation for your conclusion?
3. Are weight and the amount of TV watched related? This is an
ambitious question, so lets make it simpler: is there
evidence that the hours of TV watched and weight are related in
our data set? Use any means you like to answer this
question, but be sure to support your answer with the necessary graphs
or numbers.
4. Is there a relationship between height and income? For men
age 25-34, a large (tens of thousand of people) national study provided
the following
summary statistics:
Average height approximately 70 inches, with SD of 3 inches
Average income $29,800 with SD of $14400 .
The correlation between height and income was r = 0.2
a) What is the regression equation for predicting income from height?
b) Graph it.
c) Generally, people who are one inch taller make how much more?
d) What's the average income of men who are 56 inches tall?
e) True or false and explain: These data show that if you wear elevator
shoes, you can make more money.
5. Let's examine the relation between TV watching and weight in
our data in more detail. Does the amount of TV watched predict
weight?
a) Plot weight (y axis) vs. TV time. (Use the classdata.)
b) What is the correlation? (If you click on the small arrow
in the upper-left corner of the scatterplot, you will get a menu.
Choose the "correlations" option.)
c) Find the regression equation. (Again, use the menu on the upper
left corner of the scatterplot.)
d) Interpret the regression equation.
e) Look at the residuals; do you see any patterns that suggest the
assumptions might not hold? (See the DataDesk
Hints.)
f) Are men and women different with respect to this relationship?
There are several ways of exploring this. See DataDesk
Hints for some hints. Also, you might want to view the
ActivStats tutorial at: 7-2, "Case Study: Fuel Efficiency in Cars".
This is an excellent tutorial for using DataDesk. Does
the women's scatterplot look different than the men's? What
about the regression lines?