Final answer:
The question involves calculating the covariance and correlation coefficient from a set of data points which represent the strength and direction of their linear relationship.
Step-by-step explanation:
The student's question is about computing the covariance and the correlation coefficient for a given set of data pairs. To compute the covariance, one must first calculate the mean of the x-values and the y-values separately, then multiply the differences from the respective means for each pair, summing those products, and finally divide by the number of pairs minus one. For the correlation coefficient, the formula involves a more complex calculation, taking the product of the number of data points and the sum of the x-y products, subtracting the product of the sum of x-values and the sum of y-values, and then dividing by the square root of several other calculated values.
Calculating the covariance and correlation coefficient helps in understanding the strength and direction of a linear relationship between two variables. Examples of how to compute these measurements are given in the provided sample cases and summaries, such as in example 12.5 and 12.9.