PS 233 – Intermediate Statistical Analysis
Homework 1
(Due 2/1/2002)
Exercise 1
Show that:
xx
yy
i
n
i
i
S
S
y
y
ErrorSS
2
1
2
1
ˆ
)
ˆ
(
β

=

=
∑
=
where
2
1
)
(
y
y
S
n
i
i
yy

=
∑
=
,
2
1
)
(
x
x
S
n
i
i
xx

=
∑
=
, and
1
ˆ
β
is the slope of the
regression line in a Linear Regression Model.
Exercise 2
If the errors in the Linear Regression Model are NOT normally distributed, the
OLS estimator is still unbiased, but it is no longer the most efficient. Is this statement
true, false, or undetermined? Explain.
Exercise 3
Table 1 presents data on economic growth and education for 11 East Asian
countries. Ecgrowth measures the average annual growth of GDP per capita during 1965
90. SecSch measures the log of the average number of years of secondary school in the
population in 1965. We are interested in estimating the impact of education on economic
growth.
a)
Find “by hand” the least squares line for the data in Table 1;
b) Find “by hand” a 95% confidence interval for
1
ˆ
β
, the regression slope;
c)
Check the results in Stata and plot the data and the regression line.
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
 Staff
 Statistics, Econometrics, Regression Analysis, Media, regression line, linear regression model, SecSch

Click to edit the document details