STA 3024: Homework 5 (due Friday July 30)
Total: 30 points
Since its implementation in 2005, the essay portion of the SAT writing test has been severely
criticized by those who claim that students’ scores are based almost exclusively on factors
such as the length of the essay and the use of long words, without regard to reasoning,
organization, or precise use of language. Suppose we want to investigate this claim. We
record the number of words (
X
1
), proportion of words that are eight or more letters (
X
2
),
and score (
Y
) for a random sample of 31 essays from diﬀerent students. (The essays are
graded in whole numbers on a scale of 1–12.) The multiple regression equation, standard
errors of the regression coeﬃcients, and multiple regression ANOVA table are shown below.
ˆ
Y
(
X
1
,X
2
) = 1
.
82 + 0
.
0162
X
1
+ 6
.
19
X
2
(SE of
a
) = 1
.
32
(SE of
b
1
) = 0
.
00259
(SE of
b
2
) = 10
.
47
Source
df
SS
MS
Regression
2
59.217
29.609
Residual
28
42.267
1.510
Total
30
101.484
1. (a) Calculate the value of
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 Spring '08
 TA
 Statistics, Regression Analysis, test statistic value

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