See the Arc Hints  for help.

1. 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.

2.  Last time, you explored the relationship between TV and weight.  Let's examine this 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?  (Use Dataset: Display Summaries and select both variables)
c) Find the regression equation. (Use Graph&Fit: Fit linear LS)
d) Interpret the regression equation.
e) Look at the residuals; do you see any patterns that suggest the assumptions might not hold? (Check "Rem. Lin. Trnd" on the Scatterplot.)
f) Sometimes a single observation can be very influential:
There is an outlier at (0, 250).  Remove it and repeat b-e.  How do things change? (To remove, select the point and then choose "Case Deletions")
g) By going up to the "Graph&Fit" menu and selecting "Set Marks" you can split the data into two groups.  Do this, and where it says "selection" put in "sex". This will allow you to examine M and F differently.  Now, when you look at the scatterplot, you will see different colors for M and F.  Click on the OLS slider to put up a regression line.  Now when you click on the F down at the bottom, you'll see women only.  When you click on M you'll see men only, and when you click on the words "Mark by sex" you'll see both together.  Is there any evidence that this relationship might be different for men than for women?

3.   A study in England found classified men and their sons into one of five social classes. Class 1 is the lowest and class 5 the highest.  For men in Class 1, they estimated the probability that the son would be in a higher social class:
 

Son's class	1	2	3	4	5
Probability	0.48	0.38	0.08	0.05	0.01

a) Find the probability that the son will end up in one of the top two social classes.
b) Find the probability that the son will NOT end up in the same class as the father.
c) Find the probability that the son will end up in social class 2 or 3.

4. Choose an American worker at random and classify his or her occupation into one of the following classes.  These classes are used in government employment data:
A Managerial and professional
B Technical, sales, administrative support
C Service occupations
D Precision production, craft, and repair
E Operators, fabricators, and laborers
F Farming, forestry, and fishing

The table below gives the probabilities that a randomly chosen worker falls into each of 12 sex-by-occupation clases:
 
 

Class	A	B	C	D	E	F
Male	0.14	0.11	0.06	0.11	0.12	0.03
Female	0.09	0.20	0.08	0.01	0.04	0.01

a) What's the probability a randomly selected worker is female?
b) Given that the worker is in class C, what's the probability she is female?
c) Given that the worker is female, what's the probability she is in class C?
d) What's the probability a worker is in class B OR C?
e) Are the events "worker is in B" and "worker is in C" mutually exclusive?
f) Are the events "worker is in B" and "worker is male" mutually exclusive?  Are they independent?

5. A couple has two children.  What is the probability that both are girls given that the oldest is a girl? What is the probability that both are girls given that one of them is a girl?