Section Problems #4
1.
When
y
is regressed on
x
, the OLS regression line goes through the points (1,2) and (3,6).
The
equation of the OLS regression line is
y_hat
=
b
0
+
b
1
x
.
What is
b
0
?
What is
b
1
?
2.
The points (1,1), (2,7), and (3,1) are plotted in a scatterplot.
In this example, when
y
is
regressed on
x
, the equation of the OLS regression line is
y
ˆ
=
b
0
, where
b
0
is a constant.
What is
b
0
?
3.
Suppose we measure two variables
x
and
y
on each of several subjects.
We standardize both
variables and compute the leastsquares regression line of
y
on
x
for these standardized values.
The fraction of the variation in
y
explained by the leastsquares regression of
y
on
x
is 0.16.
What is
b
0
?
What is
b
1
?
4.
A researcher wishes to determine whether the rate of water flow (in liters per second) over an
experimental soil bed can be used to predict the amount of soil washed away (in kilograms).
The researcher measures the amount of soil washed away for various flow rates, and from these
data calculates the leastsquares regression line to be:
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 Fall '08
 ABDUS,S.
 Least Squares, Regression Analysis, researcher, OLS regression line, 0.7 liters, 0.8 kilograms

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