Final answer:
The correlation coefficient, r, is calculated using a formula that incorporates the sums of the x and y variables and their products. For the given data, the formula is applied to determine the strength and direction of the relationship between miles traveled and sales volume. The coefficient of determination, r², can also be computed to understand the percentage of variation in sales explained by miles traveled.
Step-by-step explanation:
The correlation coefficient, r, is a statistical measure that calculates the strength of the relationship between the independent variable x (miles traveled) and the dependent variable y (sales). The formula to calculate r involves finding the sum of the product of the x and y values, the sum of the x values, the sum of the y values, the sum of the x values squared, and the sum of the y values squared. For the given data points, we would compute each of these sums, substitute these values into the correlation coefficient formula, and then solve for r.
The formula for the correlation coefficient is:
r = (n(\u03A3xy) - (\u03A3x)(\u03A3y)) / √[(n\u03A3x^2 - (\u03A3x)^2)(n\u03A3y^2 - (\u03A3y)^2)]
Where n is the number of paired scores, \u03A3 denotes the sum of the variables, and x and y represent the individual variables in the dataset. After performing the calculation, the result will yield the correlation coefficient, which can be any value between -1 and +1. An r close to +1 or -1 indicates a strong linear relationship, while an r close to 0 indicates a weak relationship.
Once r is found, the coefficient of determination, r², can also be computed to determine the percentage of variation in sales explained by the variation in miles traveled by the sales representatives using the best-fit regression line.