Question
What is the correlation coefficient, r , for this data? x & y 34 & 59 57 & 53 62 & 55 73 & 58 96 & 32 97 & 48 Round your answer to the nearest tenth. [ r= ] square
Answer
3.8
(344 Votes)
Riley
Advanced · Tutor for 1 years
Answer
# ExplanationTo find the correlation coefficient,
, for the given data, we will use the Pearson correlation coefficient formula. The formula for
is given by:
where:-
is the number of data points,-
is the sum of the product of each pair of
and
values,-
and
are the sums of
and
values respectively,-
and
are the sums of the squares of
and
values respectively.Given data:
First, we calculate the necessary sums:-
-
-
- \( \sum xy = (34 \times 59) + (57 \times 53) + (62 \times 55) + (73 \times 58) + (96 \times 32) + (97 \times 48) = 2006 + 3021 + 3410 + 4234 + 3072 + 4656 = 20399 \)-
-
Now, substitute these values into the formula:
Rounding to the nearest tenth,
.# Answer