Multiple Choice: For each of the following data sets, choose the most appropriat

Question

Multiple Choice: For each of the following data sets, choose the most appropriate response from the choices below the table. Data Set #1 Data Set #2 x y x y 0 19 10 19 1 15 14 15 2 13 18 13 3 18 24 12 4 23 27 7 5 14 32 0 6 9 36 -3 7 13 40 -4 8 27 45 -7 A. A strong positive linear relation exists A. A strong positive linear relation exists B. A strong negative linear relation exists B. A strong negative linear relation exists C. A curvilinear relation exists C. A curvilinear relation exists D. No linear relation exists D. No linear relation exists Multiple Choice: For each of the following data sets, choose the most appropriate response from the choices below the table. Data Set #1 Data Set #2 x y x y 0 19 10 19 1 15 14 15 2 13 18 13 3 18 24 12 4 23 27 7 5 14 32 0 6 9 36 -3 7 13 40 -4 8 27 45 -7 A. A strong positive linear relation exists A. A strong positive linear relation exists B. A strong negative linear relation exists B. A strong negative linear relation exists C. A curvilinear relation exists C. A curvilinear relation exists D. No linear relation exists D. No linear relation exists

Explanation / Answer

FOR BOTH THE SETS WE HAVE TO CALCULATE THE CORRELATION COEFFICIENT FOR BOTH

DATA 1

XY , X2 and Y2 as it was done in the table below.

the sum of every column to get:

X=36 , Y=151 , XY=618 , X2=204 , Y2=2783

r = 0.1144

as its closer to 0 therefore no kinear relation

option d is correct

b) data 2

XY , X2 and Y2 as it was done in the table below.

the sum of every column to get:

X=246 , Y=52 , XY=528 , X2=7870 , Y2=1022

r = -0.9824

therefore strong negative linear relation

X Y XY XX YY   0 19 0 0 361 1 15 15 1 225 2 13 26 4 169 3 18 54 9 324 4 23 92 16 529 5 14 70 25 196 6 9 54 36 81 7 13 91 49 169 8 27 216 64 729

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