Question

500450400350300Cups25020015010050G510153540455020 25 30Temperature (°F)Does this scatter plot show a positive association, a negative association, or no association?positive associationnegative associationno association

Answer 1

To find asociation , must be calculated

R= [ Sum of xy ]/ √(sum of x^2)• (sum of y^2)

Then first calculate median for X= (10 + 20 + 4•25 + 30 + 2•35 + 40 )/ 10

median for X= 270/10= 27

Now find median for Y = ( 400 + 2•200 + 2•150 + 100 + 75 + 3•50 )/ 10

median for Y = 142.5

Then now find differences for X = X - median = X - 27

and differences for Y = Y - median

Differences X= ( -17, -7, 4•-2, 3, 2•8, 13 )

Differences Y= ( 257.5 , 2•57.5, 2•7.5 , -42.5 , - 67.5 , 3• -92.5)

NOW multiply pairs similar , and add results

( -17•257.5 ) + ( -7•2•57.5)+ ( -8•2•7.5)+ (3•-42.5) + (16•-67.5) + (13•-92.5)

All THIS added is equal to

= -7712 .5

NOW find denominator of R

√(sum of x^2)• (sum of y^2)=

Then

Sum of x^2 = -17^2 + -7^2+ -8^2 + 3^2 +16^2 + 13^2 = 836

Sum of y^2 = 66306.25 +13225 + 225 + 1806.25 + 4556.25 + 77006.25= Sum of y^2 = 163125

Now calculate

√(sum of x^2)• (sum of y^2)=√ (836)•(163125)= 11677.9

So then finally divide both results

numerator/ denominator= -7712 .5/ 11677.9= -0.66

THEN ANSWER IS -0.66

Is a negative association