Statistics 512: Problem Set No. 5
Due October 2, 2009
For the following problems use the computer science data that we have been discussing
in class.
You can get a copy of the data set
csdata.dat
from the class website.
The
variables are:
id
, a numerical identifier for each student;
GPA
, the grade point average
after three semesters;
HSM
;
HSS
;
HSE
;
SATM
;
SATV
, which were all explained in class; and
GENDER
, coded as 1 for men and 2 for women.
1. In this exercise you will illustrate some of the ideas described in Chapter 7 of the text related
to the extra sums of squares.
(a) Create a new variable called
SAT
which equals
SATM + SATV
and run the following two
regressions:
i. predict
GPA
using
HSM
,
HSS
, and
HSE
;
ii. predict
GPA
using
SAT
,
HSM
,
HSS
, and
HSE
.
Calculate the extra sum of squares for the comparison of these two analyses. Use it to
construct the
F
statistic – in other words, the general linear test statistic – for testing
the null hypothesis that the coefficient of the
SAT
variable is zero in the model with all
four predictors. What are the degrees of freedom for this test statistic?
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 Fall '08
 Staff
 Statistics, Regression Analysis, Null hypothesis, Statistical hypothesis testing, Type I and type II errors, explanatory variable

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