Problem 21 - College Algebra and Calculus: An Applied Approach

Question

Use the regression capabilities of a graphing utility or a spreadsheet to find the least squares regression quadratic for the given points. Then plot the points and graph the least squares regression quadratic. $$ (0,0),(2,2),(3,6),(4,12) $$

Step-by-Step Solution

Answer

Use your graphing tool or spreadsheet to compute the quadratic least squares regression for the data points (0,0),(2,2),(3,6) and (4,12), providing us a quadratic equation. Plot these points and the obtained quadratic curve on the graph. The curve represents the least squares regression quadratic for the given points.

Step 1: Identify Data Points

Identify the sets of given data points, which are (0,0),(2,2),(3,6) and (4,12). These points will be plotted on the graph.

Step 2: Calculate Quadratic Regression

With the graphing utility or spreadsheet tool of your choice, compute the quadratic least squares regression. It is typically available under the function 'regression' or 'fit data' option in most tools. Be sure to choose the quadratic model in the options. This will give us a quadratic equation in the form \(y = ax^2 + bx + c\), where a, b and c are the parameters that the software calculates.

Step 3: Plot the Points and Graph

After obtaining the quadratic equation, plot the given data points along with the result of the regression. This will show the least squares regression quadratic curve along with the data points. The quadratic curve is the best fit for these points according to the least square regression method.