data table: left side: 0,2,4,6,8,10
right side: 3,6,9,12,15,18
Estimate the correlation coefficient based on the data.
A. 0.9
B. 1
C. -0.9
D. −1
The correlation coefficient can be estimated by calculating the covariance and the standard deviation of both sets of data.
The covariance formula is:
cov(X,Y) = Σ((xᵢ - x̄)(yᵢ - ȳ)) / (n-1)
The standard deviation formula is:
s(X) = √(Σ(xᵢ - x̄)² / (n-1))
After calculating the covariance and standard deviation for the given data, the correlation coefficient can be found using the formula:
r = cov(X,Y) / (s(X)*s(Y))
Based on the data provided in the table, the correlation coefficient is expected to be close to 1 as the data sets on the left and right side of the table appear to have a strong positive linear relationship. Therefore, the answer is:
B. 1