Predicting Sales Using Advertising Spending

• One of the most common statistical methods
• Used in business, finance, healthcare, and science
• Helps predict outcomes using historical data

The simple linear regression model is:

\[ Y = \beta_0 + \beta_1X + \epsilon \]

Where:

• \(Y\) = response variable
• \(X\) = predictor variable
• \(\beta_0\) = intercept
• \(\beta_1\) = slope
• \(\epsilon\) = error term

The prediction equation is:

\[ \hat{Y} = \beta_0 + \beta_1X \]

Example:

\[ Sales = 40 + 2(Advertising) \]

If advertising increases by $1, sales increase by approximately $2.

sales <- data.frame(
  advertising = c(5,10,15,20,25,30,35,40),
  sales = c(50,60,75,80,90,100,110,120)
)

sales

##   advertising sales
## 1           5    50
## 2          10    60
## 3          15    75
## 4          20    80
## 5          25    90
## 6          30   100
## 7          35   110
## 8          40   120

model <- lm(sales ~ advertising,
            data = sales)

coef(model)

## (Intercept) advertising 
##   41.428571    1.964286

• Advertising and sales move together.
• Regression can predict future sales.
• Regression is useful in business analytics.