Answer to Question #245100 in Statistics and Probability for mechanix

Question #245100

For the following data, find the correlation co-efficient. How much š’™ depends on š’š?

Determine and sketch the corresponding regression line. Graphically find the value of š’™

when š’š = šŸšŸ“.


  • š’™: 5 12 18 23 27 30 26 22
  • š’š: 18 16 13 11 9 7 10 13




1
Expert's answer
2021-10-04T16:36:57-0400

Solution:


X Values

āˆ‘ = 163

Mean = 20.375

āˆ‘(X - Mx)2Ā = SSxĀ = 489.875


Y Values

āˆ‘ = 97

Mean = 12.125

āˆ‘(Y - My)2Ā = SSyĀ = 92.875


X and Y Combined

NĀ = 8

āˆ‘(X - Mx)(Y - My) = -208.375


R Calculation

r = āˆ‘((X - My)(Y - Mx)) / "\\sqrt{(SS_x)(SS_y)}"

r = -208.375 / "\\sqrt{(489.875)(92.875)}" = -0.9769

This is a strong negative correlation, which means that high X variable scores go with low Y variable scores (and vice versa).

Sketch of regression line:



From this graph, when y=15, x=13.5



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