Final answer:
To understand the relationship between sales volume and miles driven, one must calculate the correlation coefficient using the provided data. If ordinal, a rank correlation coefficient may be more appropriate, but with interval or ratio data, Pearson's r is used. The coefficient of determination (r²) reveals the variance explained by the relationship.
Step-by-step explanation:
Calculating the Correlation Coefficient
To determine if there is a strong correlation between the number of miles driven by a salesperson and the sales volume achieved, we need to calculate the correlation coefficient. With the data provided, we assume that the measurement level is ordinal. However, correlation analysis typically requires interval or ratio data, and for ordinal data, a rank correlation coefficient such as Spearman's rho might be more appropriate. Nevertheless, assuming we proceed with the data given, we would need to carry out a statistical analysis to obtain Pearson's correlation coefficient, r, which quantifies the degree of linear relationship between two variables. Using a statistical software or manual calculation involving the formula for Pearson's r, we would analyze the pairs of data.
Once obtained, the coefficient of determination, r², can also be calculated. This represents the proportion of the variance in the dependent variable that's predictable from the independent variable. For instance, if we had a correlation coefficient of -0.56, squaring it would yield 0.3136, which suggests that approximately 31 percent of the variation in sales could be explained by the number of miles driven. Keep in mind this example is illustrative, and actual calculation for the provided data set is necessary to find the real correlation coefficient.