Question

For the following data, find the correlation co-efficient. How much 𝒙 depends on 𝒚?

Determine and sketch the corresponding regression line. Graphically find the value of 𝒙

when 𝒚 = 𝟏𝟓.

• 𝒙: 5 12 18 23 27 30 26 22
• 𝒚: 18 16 13 11 9 7 10 13

Answer 1

Solution:

X Values

∑ = 163

Mean = 20.375

∑(X - M_x)² = SS_x = 489.875

Y Values

∑ = 97

Mean = 12.125

∑(Y - M_y)² = SS_y = 92.875

X and Y Combined

N = 8

∑(X - M_x)(Y - M_y) = -208.375

R Calculation

r = ∑((X - M_y)(Y - M_x)) / $\sqrt{(SS_x)(SS_y)}$

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