For the following data, find the correlation co-efficient. How much š depends on š?
Determine and sketch the corresponding regression line. Graphically find the value of š
when š = šš.
Solution:
X Values
ā = 163
Mean = 20.375
ā(X - Mx)2Ā = SSxĀ = 489.875
Y Values
ā = 97
Mean = 12.125
ā(Y - My)2Ā = SSyĀ = 92.875
X and Y Combined
NĀ = 8
ā(X - Mx)(Y - My) = -208.375
R Calculation
r = ā((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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