Problem 18 - 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 line for the given points. $$ (6,4),(1,2),(3,3),(8,6),(11,8),(13,8) $$

Step-by-Step Solution

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 1: 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.

Step 2: 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 $(13,8)$.

Step 3: 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.

Step 4: 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.