Question

Use the regression capabilities of a graphing utility or a spreadsheet to find the least squares regression line for the given points. $$ (0,6),(4,3),(5,0),(8,-4),(10,-5) $$

Short answer

The regression line will be in the form of \(y = mx + c\), where m and c are calculated with your regression tool. The result will vary depending on the method and tool used for regression.

Step-by-step solution

Input Data Points

Firstly, list the given data points in two columns in your chosen tool (graphing utility or spreadsheet), with the first column for x-coordinates and the second for y-coordinates. Here are your points: (0,6), (4,3), (5,0), (8,-4), (10,-5).

Perform Regression Analysis

Next, use the regression feature of your tool to perform a linear regression for the data points. In general, this will use a least squares model to find the line of best fit.

Retrieve Regression Line

Once the regression analysis is done, your tool will provide an equation of the form \(y = mx + c\), which is the equation of the regression line. In this case, m represents the slope and c represents the y-intercept.