A Linear Regression model’s main aim is to find the best fit linear line and the optimal values of intercept and coefficients such that the error is minimized. Error is the difference between the actual value and Predicted value and the goal is to reduce this difference. The vertical distance between the data point and the regression line is known as the error or residual. Each data point has one residual and the sum of all the differences is known as the Residual Sum of Squares (RSS). Linear regression is an effective statistical method for understanding business, profitability-influencing variables, and consumer behavior. It originates from statistics and is used as a statistical model to show relationships between dependent and independent variables from various datasets such as real-estate price prediction, stock market data, medical diagnostic dataset, weather analysis, and various socioeconomic indicators. Businesses can assess trends and create estimates or forecasts using linear regressions. For example - If a company’s sales have increased steadily over the past few years and by conducting a linear regression analysis on the sales data with monthly sales, the company can forecast sales in future months.

1. #Word of the Week
www.roadmapit.com
mktg@roadmapit.com +91 413-4207 333
Linear Regression
Linear regression is one of the simplest predictive models in machine
learning and a widely used technique in business and other forms of
statistics. It is predominantly used when there is a linear relationship
between the independent and dependent variables.
Y
X

2. #Word of the Week
www.roadmapit.com
mktg@roadmapit.com +91 413-4207 333
b1
b 0
error term (ε)
Regression line
Sales
(%)
30
25
20
15
y
x
10
Television (Millions)
50 100 150
In simple linear regression analysis, there are two variables: x and y.
The equation that describes how the dependent variable y is related
to the independent variable x is known as the regression model.
Dependent Variable (Y): This is what you're trying to predict or explain. In the
context of the Advertising.csv dataset, sales would be the dependent variable.
Independent Variables (X): These are the variables you believe have an effect on
you dependent variable. In the given dataset, TV, social media, and Newspaper
advertising budgets are the independent variables.

3. #Word of the Week
www.roadmapit.com
mktg@roadmapit.com +91 413-4207 333
Simple Linear Regression:
Y=β0 + β1X + ε
• Y represents the dependent variable (the one we want to predict).
• X represents the independent variable (the one we use to make
predictions).
• β0 is the intercept which is 10, representing the value of Y when X is 0.
• β1 is the slope, representing how much Y changes for a one-unit change in
X.
• ε represents the error term, which accounts for the variability in Y that can’t
be explained by the linear relationship with X.
• Black dots are the data points i.e the actual values.
• The blue line is the best fit line called regression line predicted by the
model i.e the predicted values lay on the blue line.