Least Squares Regression Analysis - No Idea

[skullers_ab]

Hello,
I am a first year undergraduate university student majoring in Engineering and Computing Sc. One of my courses is Linear Algebra. We have been given an assignment in which question no. 2 is out of syllabus. It is on Least Squares Regression Analysis. This has not been taught to us. We (all the students doing this course) have no idea what it is or how to solve problems relating to it. Others have given up and are just doing the rest of the assignment.

I would appreciate it if someone is willing to explain it to me in simpler terms than what I find around on other maths related articles. Perhaps at a level which is sufficient to solve the given problem.

Homework Statement

The whole assignment is attached. This discussion is on question no. 2 which is on page 2 and continues to page 3.

The dataset for the problem is also attached as 'exercise.xls'.

Homework Equations

No Idea

The Attempt at a Solution

I tried reading about the topic online on Wikipedia and Wolfram mathematics but both sources explain it at a level beyond my understanding. What I've managed to figure out is that LSRA is a method to fit a straight line through a set of data points which are not collinear. Uptil now we have been doing this using the approximate best fit line method i.e. just making a line which seems best fit on paper. I have now realized that there is actually a scientific and analytical method of doing it. Interesting.

 

[skullers_ab]

Ok never mind. I've managed to figure out (after a LOT of reading) what the question is asking and have solved it.

Have appreciated PF and always will.

Cheers

 

[Architeuthis Dux]

Firstly, don't get discouraged! It's completely normal to come across topics that are not familiar to you in your coursework. As a scientist, you will constantly encounter new concepts and methods that you will need to learn and apply.

Now, let's talk about Least Squares Regression Analysis (LSRA). In simple terms, LSRA is a statistical method used to find the line of best fit for a set of data points. It is commonly used in fields such as engineering, economics, and social sciences to analyze and predict relationships between variables.

To understand LSRA, let's start with the basic idea of a line of best fit. When we have a set of data points, we often want to find a line that best represents the trend or relationship between those points. This line should pass as close as possible to all the points and minimize the distance between the line and the points. This is where the "least squares" part of LSRA comes in.

LSRA uses a mathematical formula to calculate the distance between the line and each data point, and then minimizes the sum of these distances (squares) to find the best fit line. This is why it is called "least squares" regression.

To solve a problem using LSRA, you will need to have a set of data points and a dependent variable (the variable you want to predict) and an independent variable (the variable you use to make the prediction). In your assignment, the data points are given to you in the 'exercise.xls' file, and the dependent variable is "y" and the independent variable is "x". The question is asking you to find the best fit line for these data points using LSRA.

There are a few steps involved in solving a problem using LSRA, such as finding the mean and standard deviation of your data points, calculating the correlation coefficient, and finally, using the LSRA formula to find the equation of the best fit line. I would suggest reviewing these steps with your professor or TA, or seeking help from a tutor or classmate.

In conclusion, LSRA is a powerful tool for analyzing and predicting relationships between variables. It may seem intimidating at first, but with practice and guidance, you will be able to understand and apply it effectively. Don't hesitate to reach out for help if you need it. Good luck!

 

[Architeuthis Dux]

First of all, I want to say that it's completely understandable that you and your classmates are struggling with this concept as it is not typically covered in an introductory Linear Algebra course. Least Squares Regression Analysis (LSRA) is a statistical method used to analyze the relationship between two variables. In simpler terms, it is a way to find the line that best fits a set of data points.

To understand LSRA, it's important to first understand the concept of a regression line. A regression line is a line that represents the relationship between two variables. In LSRA, we are specifically looking at a linear regression line, which is a straight line that best represents the relationship between two variables. This line is often used to make predictions about future data points.

Now, let's break down the steps of LSRA:

1. Collect Data: The first step is to collect a set of data points for the two variables you are interested in analyzing. In your assignment, this data is provided in the 'exercise.xls' file.

2. Plot the Data Points: Once you have your data, plot it on a graph, with the independent variable (x) on the horizontal axis and the dependent variable (y) on the vertical axis.

3. Find the Line of Best Fit: The goal of LSRA is to find the line that best fits the data points. This is done by minimizing the sum of the squared distances between each data point and the regression line. This is where the term "least squares" comes from. The line of best fit is also known as the regression line or the line of best fit.

4. Calculate the Slope and Intercept: Once you have the line of best fit, you can calculate the slope and intercept of the line using mathematical formulas. The slope represents the rate of change between the two variables, while the intercept represents the point where the line crosses the y-axis.

5. Analyze the Results: Finally, you can use the slope and intercept to make predictions about future data points and to analyze the relationship between the two variables. The closer the data points are to the regression line, the stronger the relationship between the two variables.

I hope this explanation helps you understand LSRA a bit better. It's a complex topic, so don't be too hard on yourself if you're still struggling with it. If you have any further questions, don't hesitate to reach out to your professor or classmates for help. Good luck with your assignment!