Final answer:
The statistical method that best fits a set of data points and is used to predict values within the data set is regression analysis, specifically using the least-squares regression line. Therefore, the correct option is C.
Step-by-step explanation:
The statistical method used for obtaining the unique cost-estimating equation that best fits a set of data points is regression analysis. This involves plotting data points on a scatter plot and then finding the least-squares regression line, which is the line that minimizes the sum of the squared errors (SSE) between the actual data points and the predicted values on the line. The regression line equation, typically in the form ŷ = a + bx, where 'a' is the y-intercept and 'b' is the slope, helps in predicting values within the given data set. The significance of the correlation coefficient, 'r', depicts the strength of the relationship between the independent and dependent variables.
For example, if you were trying to predict a person's height based on the length of their pinky finger, you would collect data, plot it on a graph, and then calculate the least-squares regression line. This calculated line can be used to predict heights based on pinky finger lengths within the scope of the collected data. Thus, if your equation were ŷ = a + bx, and you wanted to predict the height for a pinky length of 2.5 inches, you would substitute 'x' with 2.5 in your equation to get the predicted height.