Pearson eText Business Statistics: First Course -- Instant Access (Pearson+)
8th Edition
ISBN: 9780136880974
Author: David Levine, David Stephan
Publisher: PEARSON+
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4. Suppose that n=100 i.i.d observations for (Y₁, X₁) yield the following results
Ỹ = 32.1 +66.8X, SER=15.1, R² = 0.81
(15.1) (12.2)
Another researcher is interested in the same regression, but he makes an error when he enters the data
in his regression program: He enters each observation twice, so he has 200 observations. Using these
200 observations, what results will be produced by his program? Write it in the following format:
Ỹ
+---X, SER=
(---) (---)
R² =
Suppose that n = 50, i.i.d observations for (Y₁, X₁) yield the following regressions
results:
Ỹ= 49.2 + 73.9 X, SER = 13.4, R²=0.78
(23.5) (16.4)
Another researcher is interested in the same regression, but makes an error when
entering the data into a regression program: The research enters each observation
twice, ending up with 100 observations (with observation 1 entered twice, observation
2 entered twice and so forth).
Using these 100 observations, what results will be produced by the regression
program? Complete the spaces in the equation below. Report the intercept and slope
to one decimal place, but report the R2 to two decimal places.
Ŷ = +
*
X,
R² =
Suppose that n = 100 i.i.d. observations for (Y, X) yield the following
regression results:
Ŷ 32.1 + 66.8X, SER = 15.1, R² = 0.81.
=
(15.1) (12.2)
Another researcher is interested in the same regression, but he makes an
error when he enters the data into his regression program: He enters each
observation twice, so he has 200 observations (with observation 1 entered
twice, observation 2 entered twice, and so forth).
a. Using these 200 observations, what results will be produced by his
regression program? (Hint: Write the "incorrect" values of the sam-
ple means, variances, and covariances of Y and X as functions of the
"correct" values. Use these to determine the regression statistics.)
Ŷ -
X, SER
=
6tc
() ()
b. Which (if any) of the internal validity conditions are violated?
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