Contents

###### Daily Dose 030 | Probability and Statistics

#### How can you solve Linear Regression problems faster?

Why is it important to know how to solve Linear Regression problems faster?

Welp, every system we deal with as engineers gets *implemented into a complex web of elements* having variable inputs and outputs –

All of which, have a **direct 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 video, we dive into a FE Exam Practice Problem in the subject of ENGINEERING PROBABILITY & STATISTICS, specifically learning how to hack a LEAST SQUARES LINEAR REGRESSION LINE.

Specifically, we will be showing you how you can solve LINEAR REGRESSION problems faster using your NCEES Approved Calculator.

In previous videos, we showed you how to solve this type of FE Exam practice problem both manually as well as using your TI-36x PRO.

Now we show you how to speed things up using your Casio FX115es Plus.

###### Key Definition

## What is LEAST SQUARES LINEAR REGRESSION?

In Engineering Probability and Statistics, we can deploy the method of LEAST SQUARES as a standard approach in our REGRESSION ANALYSIS, or LINEAR REGRESSION ANALYSIS.

REGRESSION ANALYSIS results in a single regression equation where the coefficients represent the relationship between each independent variable and the dependent variable.

With a REGRESSION EQUATION defined, we are able to approximate and make predictions of how our dependent variable will be affected by the independent variables.

###### The Process

## How can you solve Linear Regression problems faster?

Without a doubt, we engineers need to learn how to solve Linear Regression problems faster, especially on the FE Exam.

This problem type will be encountered, that’s a given, but how will you proceed with solving it.

There are two ways, fast or slow.

Either way, you are going to at least need to know the steps, here’s the general process for solving a Linear Regression problem on your FE Exam:

**Step 1: Collect the Data**Begin by gathering the data points (x, y) that you will use to perform the linear regression analysis. Ensure you have two sets of related data: independent variable (x) and dependent variable (y).

**Step 2: Plot the Data**Plot the data points on a graph to visually inspect the relationship between the variables. This can help determine if a linear model is appropriate for your data. HINT: You won’t be doing this if you choose to go the faster route.

**Step 3: Calculate the Mean of X and Y**Find the mean (average) values of your x data points and y data points separately. The mean values are used in further calculations to find the slope and y-intercept of the regression line.

**Step 4: Calculate the Slope (m)**Use the formula m = Σ((x – mean(x)) * (y – mean(y))) / Σ((x – mean(x))^2) to calculate the slope of the line. This formula quantifies the relationship between x and y.

**Step 5: Calculate the Y-intercept (b)**With the slope found, calculate the y-intercept of the line using b = mean(y) – m * mean(x). The y-intercept is where the line crosses the y-axis.

**Step 6: Formulate the Regression Equation**Construct the equation of the line, which is y = mx + b. Now, you have the linear regression equation based on your data.

**Step 7: Make Predictions**Use the regression equation to make predictions. By substituting x values into your equation, you can predict corresponding y values.

**Step 8: Assess the Model Fit**Finally, evaluate how well your linear model fits the data. You can do this by calculating the coefficient of determination (R²), which gives the proportion of the variance in the dependent variable that is predictable from the independent variable.

Following these steps will help you solve Linear Regression problems manually, but there is a faster way.

Check out the video and see how to solve Linear Regression problems faster on the FE Exam.

As always, we are here to help, Prepineer