1. Calculate the linear coefficient r using the table of values.
X Y
43 10
2 19
99 1
86 2
50 8
R=0.326
R=-0992
R=-0.326
R=0.992
R=-0.326
To calculate the linear coefficient r using the table of values, you can use the formula for the correlation coefficient:
r = [nΣXY - (ΣX)(ΣY)] / sqrt([nΣX^2 - (ΣX)^2][nΣY^2 - (ΣY)^2])
where:
- n is the number of data points
- Σ represents the sum of the values
- X and Y are the variables you're comparing
Let's calculate r using the given table of values:
n = 5
ΣX = 43 + 2 + 99 + 86 + 50 = 280
ΣY = 10 + 19 + 1 + 2 + 8 = 40
ΣXY = (43)(10) + (2)(19) + (99)(1) + (86)(2) + (50)(8) = 430 + 38 + 99 + 172 + 400 = 1139
ΣX^2 = (43)^2 + (2)^2 + (99)^2 + (86)^2 + (50)^2 = 1849 + 4 + 9801 + 7396 + 2500 = 22050
ΣY^2 = (10)^2 + (19)^2 + (1)^2 + (2)^2 + (8)^2 = 100 + 361 + 1 + 4 + 64 = 530
Now let's substitute these values into the formula:
r = [5(1139) - (280)(40)] / sqrt([5(22050) - (280)^2][5(530) - (40)^2])
= [5695 - 11200] / sqrt([110250 - 78400][2650 - 1600])
= -5505 / sqrt([31850][1050])
= -5505 / sqrt(33442500)
= -5505 / 5788.62
= -0.951
Therefore, the linear coefficient r is approximately -0.951.