Final answer:
Without the actual data points, it is not possible to determine which quadratic regression equation best fits the data set. The best-fit quadratic equation would be of the form ŷ = ax² + bx + c, with the constants determined by a regression analysis using the provided data.
Step-by-step explanation:
The subject of the question is to determine which quadratic regression equation best fits the given data set. Quadratic regression is a type of polynomial regression in which the degree of the polynomial is 2, and the general form is â = ax² + bx + c. To find the best-fit equation, you typically would use statistical software or a graphing calculator to input the data points and obtain a quadratic function that minimizes the sum of the squared differences between the observed and predicted values (the least squares method).
Since the information provided includes values of r (correlation coefficient) and the equation of a linear regression line (Ŷ = -173.51 + 4.83x), we can't directly determine the best quadratic regression equation. However, the correct quadratic equation will typically follow the standard format Ŷ = ax² + bx + c, where a, b, and c are constants determined by the regression analysis. It's important to perform the regression with the actual data points, as we don't have enough information to choose between options A, B, C, and D without that data.