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© 2014 Pacific Crest
339
Step
Explanation
5. Multiply the
z-scores
Multiply the two sets of z-scores to get the product for each point
quiz z-score (z
x
)
test z-score (z
y
)
(z
x
) × (z
y
)
0.768
0.071
0.054
0.949
1.472
1.397
-0.139
0.137
-0.019
0.224
0.204
0.046
-0.320
0.471
-0.151
-0.864
0.137
-0.119
-0.139
0.538
-0.075
1.311
0.538
0.705
-1.589
-2.466
3.917
1.674
1.339
2.241
-0.864
0.137
-0.119
0.949
-0.196
-0.186
-1.045
-0.597
0.624
-1.407
-1.999
2.813
-0.864
-0.463
0.400
0.405
0.671
0.272
0.949
0.004
0.004
sum of third column:
11.80511534
6.
Calculate
r
The correlation coefficient, r, is the sum of the multiplied z-scores divided
by n-1, where n is the number of values in the set of data:
1
x y
z z
r
n
=
−
∑
=
=
11.80511534 0.738
17 - 1
r
7.
Find the strength
of correlation
For a linear regression model to be useful, the correlation coefficient, r,
should be relatively close to 1 or -1.
0.738 is a reasonable value.
7.4 Simple Linear Regression