In: Statistics and Probability
Examine the computation formula for r, the sample correlation
coefficient.
(a) In the formula for r, if we exchange the symbols x and y, do we
get a different result or do we get the same (equivalent) result?
Explain your answer.
The result is the same because the formula is not dependent on the
symbols.
The result is different because the formula is not dependent on the
symbols.
The result is different because the formula is dependent on the
symbols.
The result is the same because the formula is dependent on the
symbols.
(b) If we have a set of x and y data values and we exchange
corresponding x and y values to get a new data set, should the
sample correlation coefficient be the same for both sets of data?
Explain your answer.
The result is different because the formula is dependent on which
values are the x values and which values are the y values.
The result is different because the formula is not dependent on
which values are the x values and which values are the y
values.
The result is the same because the formula is dependent on which
values are the x values and which values are the y values.
The result is the same because the formula is not dependent on
which values are the x values and which values are the y
values.
(c) Compute the sample correlation coefficient r for each of the
following data sets and show that r is the same for both. (Use 3
decimal places.)
(i) x 6 7 9
y 1 3 5
(ii) x 1 3
5
y 6 7 9
r
(i)
(ii)