Final answer:
To solve for the least-squares line of the equation ax + b, data is entered into a calculator, a scatter plot is created, and the calculator's regression function is used to find the least-squares regression line, which is then added to the scatter plot.
Step-by-step explanation:
To find a least squares solution of the equation ax + b, you would typically go through two main steps. First, you would enter the data into a calculator and create a scatter plot to visualize the distribution of the data points. Then, you would use your calculator's regression function to calculate the equation of the least-squares regression line. This equation can be added to your scatter plot from part A. The least-squares regression line aims to minimize the sum of the squares of the differences between the observed values and the values predicted by the line.
For a quadratic equation of the form ax² + bx + c = 0, you can find its roots by using the well-known quadratic formula. However, in contexts relating to constructing the normal equations for least squares, the quadratic formula is not directly involved. Instead, the normal equations are derived from partial derivatives of a function representing the sum of squared errors with respect to the coefficients of the regression line.
If the task also requires computing measures like the correlation coefficient to assess the strength of the linear relationship between variables, or the average of an economic indicator such as CPI (Consumer Price Index) for a given year, those would be additional calculations performed after finding the least-squares regression line.