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Two experts provided subjective lists of Nine school districts that they think are among the best in the
country. For each school district, the average class size, the combined SAT score and the percentage of
students who arrived at a fouryear college were provided.
The following ANOVA table contains information that was generated using the data provided by
these experts on possible linear relationship between the set of variables. Fill the missing
information in the table and answer the questions (a) and (b).
ANOVA
df
SS
MS
F
Regression
1
712.64
712.6
4
Residual
7
98.42*7=688.
94
98.42
7.24
Total
8
a)
What is the value of Rsquare and adjusted Rsquare? Interpret the meaning of adjusted R
square.
Solution:
R Square is given by
= 1 (688.94/ 1401.58) = 1 .49 =
.51
Adjusted R Square is given by
R2 = 1 (1  R2 )((n  1)/(n  k  1))
where: R2 = Coefficient of Determination
_
R2 = Adjusted Coefficient of Determination
n = number of observations
k = number of Independent Variables
Adj R2 = 1 (1.51)(8/7) = 1  .49(1.15) = 1  .56 =
.44
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 Spring '08
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