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Which is the best estimate of the correlation coefficient for the scatter plot?
4 months ago
Q:
Which is the best estimate of the correlation coefficient for the scatter plot?
Accepted Solution
A:
Answer:Option (4)Step-by-step explanation:Table for the points from the graph attached, x y [tex]x^{2}[/tex] [tex]y^{2}[/tex] xy 2.2 1.8 4.84 3.24 3.96 3.2 1.8 10.24 3.24 5.76 3.6 3 12.96 9 10.8 4.8 3.5 23.04 12.25 16.8 5.2 6.2 27.04 38.44 32.24 6.4 4.5 40.96 20.25 28.8 7.5 7.8 56.25 60.84 58.5 8.5 6.2 72.25 38.44 52.7[tex]\sum x=41.4[/tex][tex]\sum y=34.8[/tex][tex]\sum x^2=247.58[/tex][tex]\sum y^2=185.7[/tex][tex]\sum xy=209.56[/tex]n = 8Formula for the correlation coefficient [tex]r=\frac{n\sum xy-(\sum x)(\sum y)}{\sqrt{[{n\sum x^2-(\sum x)^2][n\sum y^2-(\sum y)^2]}}}[/tex][tex]r=\frac{8(209.56)-(41.4)(34.8)}{\sqrt{[{8(247.58)-(41.4)^2][8(185.7)-(34.8)^2]}}}[/tex]r = [tex]\frac{1676.48-1440.72}{\sqrt{266.52\times 274.56} }[/tex]r = [tex]\frac{235.76}{\sqrt{73175.73}}[/tex]r = [tex]\frac{235.76}{270.51}[/tex]r = 0.87r ≈ 0.9Therefore, Option (4) is the answer.