Statistics 333
Feb 1, 2012
Nordheim
Homework Assignment #2

Due Feb 8
1.
The purpose of this exercise is to explore the meaning of degrees of freedom in regression.
Suppose that you have 5
values of X and Y and you wish to fit a regression of Y on X.
The estimated slope and intercept are
and
ˆ
b
0
=
14.0
respectively.
Below are the data  with 2 of the Y values missing.
Your job is to calculate the sum of
squares for error.
[Hint:
Look at the definitional equations for slope and intercept and use simple algebra to calculate the
missing “Y” values.
Also, notice the simplification that results by considering the value for
x
.]
X:
1
5
6
2
0
Y;
12
18
1
?
?
If there were 20 measurements instead of 5, how many Y values would need to be specified so that you could calculate the
sum of squares for error?
Explain how this relates to degrees of freedom.
2.
An experimenter was interested in the relationship between temperature and heart rate in the common grass frog.
The
temperature was manipulated in 2degree increments ranging from 2 to 16 C with heart rates recorded at each temperature
in beats per minute.
(A different randomly selected frog was used at each temperature.)
temp
2
4
6
8
10
12
14
16
heart rate
4
11
9
13
21
24
29
27
Find (
by hand calculation
) the least squares estimate of slope and intercept viewing heart rate as the dependent variable
(i.e. heart rate as a function of temperature).
Include a plot of heart rate versus temperature.
Are your calculated
estimates consistent with your plot?
Explain.
3.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '11
 Rick
 Statistics, Degrees Of Freedom, Regression Analysis, heart rate, Errors and residuals in statistics

Click to edit the document details