Find a 95 % confidence interval for b 2 . As part of a study at a large universi
ID: 3065400 • Letter: F
Question
Find a 95 % confidence interval for b2.
As part of a study at a large university (Communication of the ACM, Vol. 27, 1984), data were collected on n= 224 freshmen computer science (CS) majors in a particular year. The researchers were interested in modeling y, a student’s grade point average (GPA) after three semesters, as a function of the following independent variables (recorded at the time the students enrolled in the university):
x1 = average high school grade in mathematics (HSM)
x2 = average high school grade in science (HSS)
x3 = average high school grade in English (HSE)
x4 = SAT mathematics score (SATM)
x5 = SAT verbal score (SATV)
The first-order model below was fit to data with the following results:
SOURCE
DF
SS
MS
F VALUE
PROB > F
MODEL
5
28.64
5.73
11.69
.0001
ERROR
218
106.82
0.49
TOTAL
223
135.46
ROOT MSE
0.700
R-SQUARE
0.211
DEP MEAN
4.635
ADJ R-SQ
0.193
PARAMETER
STANDARD
T FOR 0:
VARIABLE
ESTIMATE
ERROR
PARAMETER = 0
PROB > |T|
INTERCEPT
2.327
0.039
5.817
0.0001
X1 (HSM)
0.146
0.037
3.718
0.0003
X2 (HSS)
0.036
0.038
0.950
0.3432
X3 (HSE)
0.055
0.040
1.397
0.1637
X4 (SATM)
0.00094
0.00068
1.376
0.1702
X5 (SATV)
-0.00041
0.00059
-0.689
0.4915
SOURCE
DF
SS
MS
F VALUE
PROB > F
MODEL
5
28.64
5.73
11.69
.0001
ERROR
218
106.82
0.49
TOTAL
223
135.46
Explanation / Answer
Find a 95 % confidence interval for b2.
Here 95% confidence interval = b2^ +- t218,0.05 se(b2) = 0.036 +- 1.971 * 0.038
= (-0.039, 0.111)
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