Stat 104 – Homework 3
Due Tuesday September 25, 2007
Reading:
September 11 – September 20
September 25 – September 27
Chapter 3
Chapter 4
Assignment:
1. Complete the following problems from the text: 3.8, 3.16, 3.36, 3.40, and 3.60.
2. The October 2005 issue of Consumer Reports (CR) has an article on the difference
between Environmental Protection Agency (EPA) mileage ratings (miles per gallon) and
mileage results (miles per gallon) obtained by Consumer Reports in test-track driving.
The EPA mileage ratings are the ones posted on new car sales stickers. Below are
mileage values for 10 different vehicle types.
Vehicle type
EPA mileage, x
CR mileage, y
1
15
9
2
21
13
3
13
8
4
48
26
5
22
11
6
17
10
7
20
12
8
13
8
9
26
17
10
18
11
Note: SS(x) = 944.1, SS(y) = 266.5, SS(xy) = 493.5
a) Plot the data. Use EPA mileage as the explanatory variable, x, and CR mileage
as the response, y.
b) Compute the mean and standard deviation for the EPA mileage. Round final
answers to 2 decimal places.
c) Compute the mean and standard deviation for the CR mileage. Round final
answers to 2 decimal places.
d) The correlation between the EPA mileage and the CR mileage is r=0.9839.
Explain in words what this correlation means.
e) Compute the estimate of the slope for the least squares regression line. Round
final answer to 4 decimal places.
f) Give an interpretation of the estimated slope within the context of the problem.
g) Compute the estimate of the intercept for the least squares regression line.
Round final answer to 4 decimal places.
h) Give the equation of the least squares regression line. Use this equation to
predict the Consumer Reports mileage for a vehicle the EPA rates at 30 miles per
gallon.
3. Data were collected on the selling price of homes ($100) and the living area of the home
(ft2)
for
a
sample
of
50
homes.
The
data
are
available
at
http://www.public.iastate.edu/~wrstephe/stat104.html. Follow the instructions in the
JMP Guide to download/open the data set. Use JMP to look at the distribution of selling
price and the relationship between living area and selling price. Use the JMP output to
help you answer the questions below. Be sure to attach the JMP output to your
assignment.
a. Describe the distribution of selling price of homes. Make sure to include in your
description the five number summary, the mean and standard deviation, and the
shape of the histogram. Are there any outliers? If so, what are the selling prices?
b. Describe the scatter plot of selling price of homes versus living area. Give the
regression equation for predicting the selling price of homes from living area.
Give an interpretation of the estimated slope. Give the value of R2 and an
interpretation of this value. Finally, describe the plot of residuals versus living
area and make note of any potential problems with the regression.
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