Question

Use the regression capabilities of a graphing utility or a spreadsheet to find the least squares regression line for the given points. $$ (-4,-1),(-2,0),(2,4),(4,5) $$

Short answer

To find the least squares regression line for the given points, input the points into a spreadsheet and use the built-in linear regression function. The result is the equation for the line of best fit, which has minimal total squared error for the given data points.

Step-by-step solution

Input Data in Spreadsheet

Start by entering the given points into two columns of a spreadsheet. One column should contain the x-values (-4,-2,2,4), while the second column should contain the corresponding y-values (-1,0,4,5).

Use Regression Function

Most spreadsheet software has built-in functions for linear regression. Use the regression functionality to find the slope (m) and y-intercept (b) values for the list of points. The software should provide a form of the equation \(y = mx + b\), with specific numerical values for m and b.

Interpret the Result

The obtained equation represents the line of best fit, or the regression line, for the given points. It offers the least squares fit to the data, meaning it minimizes the total squared distance between the predicted y-values (computed from the equation) and the actual y-values (from the data).