Linear regression is a fundamental predictive model in machine learning, commonly used in business when there's a linear relationship between independent and dependent variables. The model includes a dependent variable (y) which is predicted based on independent variables (x), with the equation representing this relationship being y=β0 + β1x + ε. Key components of the model include the intercept (β0), slope (β1), and an error term (ε) that accounts for variability not explained by the model.

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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

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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.

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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.