Final answer:
To find the correlation coefficient for the given data set, calculate the means of both x and y values, find the sum of the products of their deviations, and the sums of squared deviations, then apply the correlation coefficient formula.
Step-by-step explanation:
To compute the correlation coefficient (r) for the given data set, we must first recognize that the correlation coefficient measures the strength and direction of a linear relationship between two variables. Here are the steps we would take to calculate r:
- Compute the mean of the x-values and the mean of the y-values.
- Subtract the mean of x from each x-value (X), and the mean of y from each y-value (Y), creating a list of deviations.
- Multiply each pair of deviations together and sum them up to get ΣXY.
- Square the deviations for x and y separately, sum them up to get ΣX2 and ΣY2.
Use the correlation coefficient formula:
r = ΣXY / √(ΣX2 ΣY2)
Finding the values for these sums and then using the formula will give us the correlation coefficient for this data set.