Homework 7 (due Apr. 2)
1. Consider the following 4 sample points (given in the format (
x,y
)): (1,
2), (2, 4.2), (3, 5.9), (4, 8.3). We want to ﬁt a simple regression model using
the matrix method for multiple regression. Note: DO NOT use Minitab for
this problem.
a) Write down the matrix
X
and the vector
y
.
b) Calculate the matrix
C
= (
X
0
X
)

1
. For inverting, you can use the
formula for 2
×
2 matrices from the lecture notes.
c) Find the vector of estimated regression coeﬃcients
ˆ
β
. What are the
estimated slope and intercept?
d) Using the results in (c), ﬁnd the residuals, and use them to estimate
σ
2
.
e) Using the estimated value of
σ
2
, ﬁnd 95% conﬁdence interval on the
mean response and 95% prediction interval for
x
0
= 2
.
5. Note that for the
vector
x
0
0
you would have to use (1, 2.5).
2. The electric power consumed each month by a chemical plant is
thought to be related to the average ambient temperature (
x
1
), the num
ber of days in the month (
x
2
), the average product purity (
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 '08
 Perevalov
 Statistics, Normal Distribution, Regression Analysis, Prediction interval, simple regression model

Click to edit the document details