Question

Use the regression capabilities of a graphing utility or a spreadsheet to find the least squares regression line for the given points. $$ (6,4),(1,2),(3,3),(8,6),(11,8),(13,8) $$

Short answer

The regression line will be given in the form \(y=a+bx\). The exact values for a and b will depend on the specific calculation made by your chosen graphing utility or spreadsheet software.

Step-by-step solution

Understand the concept

A regression line is a straight line that best fits the data points on a scatter plot. This can be found using the least squares method, which minimizes the sum of the square of the residuals.

Input the data

Input the points into your designated technology, usually in two lists: one for x-coordinates and one for y-coordinates. The given points are $(6,4), (1,2), (3,3), (8,6), (11,8),$ and $(13,8)$.

Perform the regression

Navigate to the statistics function or designated function for regressions and select 'Linear Regression’ or 'Least Squares Regression Line'. Apply this function to your inputted data.

Extract the equation

The regression function will output an equation in the form \(y=a+bx\), where \(a\) is the y-intercept and \(b\) is the slope of the line. This is your least squares regression line.