Six statements about what you can learn from the correlation coefficient are lis

Question

Six statements about what you can learn from the correlation coefficient are listed below. Label each statement, choosing from A (can always tell), N (can never tell), or S (can sometimes tell). For each statement you label S for sometimes, explain briefly when you can tell and when you cannot.

(a) Whether there is a systematic relationship between x and y.

(b) Whether the relationship between x and y is linear or curved

(c) Whether the least squares line has a positive or negative slope

(d) How closely the points fall near a line

(e) Whether there are outliers or influential points

(f) How steep the least squares line is

Explanation / Answer

Correlation coefficient:

a) a sysyematic relationship between x and y - A (can always tell)

b) the relationship between x and y is linear or curved - N(can never tell)

we can tell if relationship is linear or curved from graph

c) the least squares line has a positive or negative slope - A(can always tell)

if slope is positive then correlation coefficient is positive

d) how closely the points fall near a line - N(can never tell)

e) there are outliers or influential points -S(can sometimes tell)

if there are extreme observations correlation coefficient is significantly affected

f) how steep the least squares line is - N(can never tell)

we can tell this from the graph

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