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Note that the number ‘‘1’’ along the diagonal of the correlation matrix means
that the correlation of each variable with itself is a perfect, positive correlation
Correlation coefﬁcients are always expressed in just two decimal places.
You are now ready to read the correlation between the six pairs of variables:
The correlation between READING SCORE and FROSH GPA is:
The correlation between WRITING SCORE and FROSH GPA is:
The correlation between MATH SCORE and FROSH GPA is:
The correlation between WRITING SCORE and READING SCORE is:
The correlation between MATH SCORE and READING SCORE is:
The correlation between MATH SCORE and WRITING SCORE is:
This means that the best predictor of FROSH GPA is the MATH SCORE with a
correlation of +0.77. Adding the other two predictor variables, READING SCORE
and WRITING SCORE, improved the prediction by only 0.03 to 0.80, and was,
therefore, only slightly better in prediction. MATH SCORES are an excellent
predictor of FROSH GPA all by themselves.
If you want to learn more about the correlation matrix, see Levine et al. ( 2011 ).
7.5 End-of-Chapter Practice Problems
1. The Graduate Record Examinations (GRE) are a standardized test that is an
admissions requirement for many U.S. graduate schools. The test is intended to
measure general academic preparedness, regardless of specialization ﬁeld. The
General GRE test produces three subtest scores: (1) GRE Verbal Reasoning
(scale 200–800), (2) GRE Quantitative Reasoning (scale 200–800), and (3)
Analytical Writing (scale 0–6).
Suppose that you have been asked by the Chair of the Biology Department at a
selective graduate university to see how well the GRE predicts GPA at the end of
the ﬁrst-year of graduate study for Biology majors. The Chair has asked you to use
the three subtest scores of the GRE as predictors, and, in addition, to use the GRE
Biology Test score (score range 200–990) as an additional predictor of this GPA.
The Chair would like your recommendation as to whether or not the Biology Test
should become an admissions requirement in addition to the GRE for admission to
the program in Biology. The GRE Biology Test includes descriptions of laboratory
and ﬁeld situations, diagrams, and experimental results.
You have decided to use a multiple correlation and multiple regression analysis,
and to test your Excel skills, you have collected the data of a random sample of 12
Biology students who have just ﬁnished their ﬁrst-year of study at this university.
These hypothetical data appear in Fig. 7.10 :
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