Example of Linear Regression in Real Life

You might have read lot of tutorials on Linear Regression and already have the assumption - Linear Regression is not easy to Understand. We will make Linear Regression very easy for you. Let's boil down each concept and learn with help of Examples. If you have no idea what Linear regression is, this tutorial will be help you understand the basics.

Linear regression might sound like a complex term, but it’s actually a very simple concept. Linear Regression is all about finding patterns in data. When two things are connected, (like - hours of study and test scores, OR temperature and ice cream sales) linear regression helps us understand and predict how one affects the other.

Basically, Linear Regression is asking if Thing-1 will change, how Thing-2 will respond? Answer of this question is often found by drawing a straight line through data points on a graph.

How Does Linear Regression Work?

Linear regression helps us answer questions about relationships in data. For example:

• Is there a consistent connection between the amount of time you spend studying and your test scores?
• Can we predict future trends based on past data?

This is done by identifying two types of variables:

• Independent Variable: The thing we control or know (e.g., hours studied).
• Dependent Variable: The thing we want to predict (e.g., test scores).

Linear regression tries to find the best-fit line through the data. This line is like a rule or formula that tells us:

When the independent variable (e.g., hours studied) increases, how much does the dependent variable (e.g., test scores) increase or decrease?
If we know the independent variable’s value, what’s the most likely value for the dependent variable?

What is Best Fit Line?

Among all possible lines you could draw through the data, linear regression finds the one that minimizes the errors (the gaps between the line and the points). This is called the line of best fit.

Understand Linear Regression with Help of Example

The more time you spend in studying, the better your test scores. Linear regression helps us find the relationship between these two things and use that relationship to make predictions.

Think of it like this:

• You collect some data: how many hours you studied and the scores you got on tests.
• You plot this data on a graph.
• Then, you draw a straight line through the points in such a way that it’s as close as possible to all the points. This line shows the trend.

Once you have this line, you can use it to make predictions. For example, if you studied 5 hours for a test, the line can help you estimate what score you’re likely to get.

Intuition Behind Linear Regression

Let’s say you’re tracking how much time you spend studying and the test scores you get. You gather the following data:

Hours of Study Test Score

2 50

4 70

6 90

If you plot this data on a graph:

• The x-axis represents the hours of study.
• The y-axis represents the test score.

You will see the points roughly form a straight-line pattern. Linear regression helps us draw the best possible straight line through these points. Once we have the line, we can use it to predict scores for other study hours, like 3, 5, or even 8 hours.

Math Behind Linear Regression

The equation of a straight line is:

y = mx + c

where,

y: The value we want to predict (your test score).
x: The value we know (hours of study).
m: The slope of the line (how much yy changes when xx changes by 1 unit).
c: The y-intercept (the value of yy when x=0x=0).

Step 1: Find the Slope (m)

The slope shows how much y (test score) changes for every 1 unit increase in x (study hours). From the data:

Change in x Change in y
From 2 to 4 From 50 to 70
From 4 to 6 From 70 to 90

The slope is:

m = Change in y / Change in x
= 20 / 2 =10

So, for every extra hour of studying, your test score increases by 10 points.

Step 2: Find the Y-Intercept (c)

The y-intercept is the value of y when x=0 (what your score would be if you didn’t study at all).

Let’s use one of the data points, say (2, 50) to find c :

y = mx + c

50 = 10(2) + c
50 = 20+ c
c = 30

So, the equation of the line is y = 10x + 30

Step 3: Using the Equation to Make Predictions

Now that we have the equation y=10x+30, we can use it to predict test scores for any amount of study time.

If you study for 3 hours: y = 10(3) + 30 = 60
If you study for 5 hours: y = 10(5) + 30 = 80

So, you can expect a score of 80, if you study for 5 Hours.

If you want to score at least 90, how much should you study?

90 = 10x + 30
90 - 30 = 10x
x = 60/10 = 6 hours.

In above example:

• The slope (m=10) tells us how much the score improves for each extra hour of study.
• The y-intercept (c=30) tells us the starting score when no studying is done.

Goal of Linear Regression

The main goal of linear regression is to find the values of m (slope) and c (y-intercept) that define the best-fit line. Once we have these values, we can:

Understand the relationship between x and y.
Make predictions about y for any given value of x.

For example:

If m>0, it means there’s a positive relationship (as x increases, y also increases).
If m<0, it means there’s a negative relationship (as x increases, y decreases).

Linear regression assumes that the relationship between x and y is linear. It means the trend can be represented by a straight line.

Real Life Example of Linear Regression

From the above explanation, we have the complete intuition of Linear Regression. We have also seen one mathematical examples. Now, let's see some more real life examples of Linear Regression.

Example #1 - Predicting the Popularity of Social Media Posts

We often see some random Instagram reel go viral, while many others don't, WHY?

The engagement on a post (likes, shares, comments, or views) often depends on a variety of factors.

• Topics people like to See or with Surprise/Wow factor.
• Time of posting (morning, afternoon, or evening).
• Type of content (photo, video, or text).
• Use of hashtags or trending topics.
• Length of the post (short and snappy vs. detailed).

But how do you determine which factors truly matter and how they impact engagement? This is where linear regression comes in. By analyzing past post data, linear regression helps uncover patterns and predict how successful a post will be.

Imagine you are a content creator who is trying to optimize engagement on social media. You have observed these factors -

• Posts made in the evening get more likes.
• Posts with fewer than 10 hashtags tend to perform better.
• Videos consistently get more views than images or text posts.
  

You might already sense a pattern, but linear regression helps you quantify these relationships. Linear regression analyzes the historical performance of your posts and identifies which factors matter the most and by how much.

For example, it can help you figure out:

How much engagement increases if you post in the evening instead of the morning.
How the number of hashtags affects the number of likes.
Whether content type has a stronger effect than posting time.

Using linear regression, you can build a model that predicts engagement for each combination of posting time, content type, and hashtag count.

Example #2 - Predicting House Prices

The price of a house depends on factors like its size, location, number of rooms, and age. Linear regression helps us analyze how one of these factors, such as the size of the house, influences the price.

If you look at data from houses sold in your neighborhood, you might notice a trend: bigger houses generally cost more. Linear regression draws a straight line through this data to represent the relationship. This line helps predict the price of a house based on its size, even if you don’t have all the details. By analyzing past sales data, linear regression can draw a line that shows how house size influences its price. If a house is 1,000 square feet larger than another, how much more expensive is it likely to be?

Why It’s Useful: Buyers can use this to estimate how much they should budget for a house, and sellers can price their homes competitively.

Example: If houses in a specific area cost $100 per square foot on average, you can predict that a 1,500-square-foot house might cost around $150,000.

Example #3 - Predicting Exam Scores Based on Study Time

We have already seen this above, with mathematical explanation.

Students often notice that the more time they dedicate to studying, the better they perform on tests. Linear regression helps us find that connection. By looking at your past exams, you might see a pattern: more study hours generally lead to higher scores. Linear regression identifies this pattern and helps predict your score for a given number of study hours. It also shows how effective your studying is (e.g., how much your score improves for every extra hour you study).

Example #4 - Forecasting Sales for a Business

Sales are often influenced by factors like time of year, advertising, or customer trends. Linear regression helps businesses predict future sales by analyzing these patterns. For example, a toy store might notice that sales increase every December because of the holidays. By looking at past sales data, linear regression can identify the trend and forecast how much the store is likely to sell this year, helping them plan their inventory and marketing.

Example: If data shows that sales increase by 10% every December compared to November, the store can predict how much to order and prepare accordingly.

Example #5 - Predicting Sports Performance

Sports coaches and teams often analyze player performance to improve strategies. For instance, how does practice time influence a player’s performance during a game? Linear regression can help.

Suppose a basketball coach tracks how many practice shots each player takes and their accuracy during games. Over time, they might see that players who take more practice shots tend to perform better. Linear regression helps identify this trend, showing the impact of practice on performance and predicting how well a player might perform if they practice more.

Why It’s Useful: Teams and coaches can use this to create better training schedules and optimize player performance.

Example: If data shows that for every 100 extra practice shots, a player's shooting percentage increases by 2%, a player practicing 500 additional shots might improve their shooting accuracy by 10%.

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Article Tags :

• Machine Learning
• AI-ML-DS

Practice Tags :

• Machine Learning