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Find the least square regression line for the following set of data {(-1 , 0),(...

Jul 4, 2024

Find the least square regression line for the following set of data {(-1 , 0),(0 , 2),(1 , 4),(2 , 5)} Plot the given points and the regression line in the same rectangular system of axes.

Solution by Steps

step 1

We start by identifying the given data points:

(-1, 0)

(0, 2)

(1, 4)

(2, 5)

step 2

To find the least squares regression line, we use the linear fit model. The general form of the linear regression equation is

y = mx + b

step 3

Using the Asksia-LL calculator, we input the data points and obtain the linear regression equation:

y = 1.7x + 1.9

step 4

The Asksia-LL calculator also provides the following statistical measures:

AIC = 7.76303

BIC = 5.92191

R^2 = 0.979661

, and adjusted

R^2 = 0.969492

step 5

To plot the given points and the regression line, we use the equation

y = 1.7x + 1.9

and plot it on the same rectangular system of axes as the data points

Answer

The least squares regression line is

y = 1.7x + 1.9

Key Concept

Least Squares Regression Line

Explanation

The least squares regression line minimizes the sum of the squares of the vertical distances of the points from the line. This method provides the best fit for the given data points.