Contents

###### Daily Dose 021 | Probability and Statistics

#### How can you hack Linear Regression problems?

When it comes to taking the FE Exam, you need to know how to solve Linear Regression problems fast.

Every system we as engineers design will get *implemented into a complex web of elements* having variable inputs and outputs –

All of which, **impact** how our designs operate holistically in a real life context.

At Prepineer, we believe it’s important *for all engineers* to be well versed in using predictable analysis as a tool for designing *reliably safe* and *optimized* systems that better the communities around us.

In this lesson, we dive into a FE Exam Practice Problem in the subject of ENGINEERING PROBABILITY & STATISTICS, specifically learning how to develop a LEAST SQUARES LINEAR REGRESSION LINE.

In a past FE Exam lesson, we carried this process out manually. In this lesson, we will show you how to solve Linear Regression problems fast using your NCEES approved calculator.

###### Key Definition

## What is LEAST SQUARES LINEAR REGRESSION?

The method of LEAST SQUARES is a standard approach in REGRESSION ANALYSIS, or LINEAR REGRESSION ANALYSIS, used to approximate the solution of sets of equations in which there are more equations than unknowns.

LEAST SQUARES means that the overall solution minimizes the sum of the squares of the residuals made in the results of every single equation.

At the end of the day, LEAST SQUARES LINEAR REGRESSION is a way of making sense of scattered data by drawing a straight line that passes as closely as possible to all the data points. It’s a powerful tool for predictions, understanding trends, and making decisions based on data.

###### The Process

## What is the process to solve least squares linear regression problems?

Let’s talk linear regressions, but more importantly how to solve linear regression problems fast on your upcoming FE Exam.

Imagine you have a bunch of points scattered on a graph, and you are asked to find a single line that best represents all those points – this is exactly what least squares linear regression allows you to do.

It’s like trying to find the best path through a busy street – you want a route that’s closest to all the important stops.

In data terms, this ‘best fit’ line helps us understand the relationship between two things, like how the hours spent studying might relate to the scores on your FE Exam.

There are a few ways to pull this off, one is to do it manually, which we do here.

The other, is to hack it using your NCEES approved calculator either your TI-36x PRO or Casio FX115es Plus – here is the process:

## Linear Regression on the TI-36X Pro:

**Enter Data:**Press`2nd`

+`DATA`

(above the`7`

key) to enter the Data editor. Enter your x-values and y-values, pressing`ENTER`

after each entry.**Switch to STAT Mode:**Press`MODE`

, select`STAT`

, and press`ENTER`

.**Choose Linear Regression:**Press`2nd`

+`STAT VAR`

(above the`8`

key), select`LinReg(ax+b)`

, and press`ENTER`

.**View Regression Coefficients:**The calculator displays the slope (`a`

) and y-intercept (`b`

).**Construct the Equation:**Use the values of`a`

and`b`

to write the equation`y = ax + b`

.

## Linear Regression on the Casio FX-115ES Plus:

**Enter Data:**Press`MODE`

three times for`STAT`

mode, select`2: A+BX`

, and enter your data points, pressing`=`

or`M+`

after each entry.**Calculate Regression Coefficients:**After all data points are entered, press`AC`

, then`SHIFT`

>`1`

(STAT) >`5`

(REG), and press`2`

for slope (`A`

),`3`

for y-intercept (`B`

).**Construct the Equation:**Use the values of`A`

and`B`

to write the equation`y = Ax + B`

.

These problems can certainly present themselves more difficult than they are because of all the data that you will be presented. However, following the step by step process for whichever calculator you will be using will ensure that you are able to solve linear regressions problems fast, no matter how hard they initially appaer.

And with all of that being stated, check out the video and see how we can go about solving this type of problem in the most efficient manner.

As always, we are here to help, Prepineer