Problem 13 - 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. $$ (-3,4),(-1,2),(1,1),(3,0) $$

Step-by-Step Solution

Answer

The equation of the least squares regression line can be found using a graphing utility or a spreadsheet by first inputting the given points, then executing the regression function within the software, and finally interpreting the output which will give the equation in the form \(y = ax + b\), where 'a' is the slope and 'b' is the y-intercept.

Step 1: Input the coordinates

First, the points (-3,4),(-1,2),(1,1),(3,0) need to be inputted into a graphing utility or a spreadsheet. Each 'x' value will be accompanied by the corresponding 'y' value in the coordinate point.

Step 2: Calculate Regression Line

Next, use the regression function (usually labeled as 'regression' or 'linreg' in the calculator or spreadsheet) to generate the least squares regression line. This regression tool uses the method of least squares to minimize the total squared vertical distance between the points and the line.

Step 3: Interpret the output

The output of the regression function will typically be in the form \(y = ax + b\), where 'a' is the slope of the line and 'b' is the y-intercept. The slope 'a' represents the change in 'y' for each one-unit increase in 'x', while the y-intercept 'b' represents the value of 'y' when 'x' is zero.