Linear Regression Explained

Understanding Linear Regression

Linear regression is used when the goal is to predict a numeric outcome—like price, score, or quantity—based on a set of input features.

It assumes that there’s a straight-line relationship between the inputs and the output.

Each input feature is assigned a weight that reflects its influence on the outcome. Features with a stronger relationship to the target variable will be assigned larger weights, while less relevant features will have smaller or near-zero weights.

Demonstrating Linear Regression

Let's say, you want to use linear regression to predict the final grade a student will receive in a course based on features like attendance rate, homework scores, and midterm exam performance.

• Attendance rate (e.g., 0.95 means 95% attendance)

• Homework average (e.g., out of 100)

• Midterm exam score (e.g., out of 100)

• Age (e.g., in years)

Linear regression builds a model like this:

Let’s say the regression model finds these coefficients:

Final Grade = 5 + .1(Attendance) + 0.4(Homework) + 0.5(Midterm) + .002 (Age)

And you plug in a student:

• Attendance = 90

• Homework = 85

• Midterm = 88

• Age = 21

Predicted Grade = 5 + .1(90) + 0.4(85) + 0.5(88) + 0.02(21) = 92.42

What This Tells Us:

• Midterm scores and homework have a strong positive influence — higher scores → higher predicted grades

• Age has almost no effect — its weight is very small (0.02)

So, the model learns which features matter most. For example, age has little impact, while midterm scores and attendance have a stronger influence on the predicted final grade.