Sales vs. Advertising

• Suppose you are a data scientist on the marketing team and the company wants to improve the sales of their premiere product

• You want to understand the relationship between advertising budget and total sales

• The goal is to advise the marketing team about how to set the advertising budget based on their target sales goals

Advertising vs. Sales

glimpse(advertising)

## Rows: 200
## Columns: 4
## $ tv        <dbl> 230.1, 44.5, 17.2, 151.5, 180.8, 8.7, 57.5, 120.2, 8.6, 199…
## $ radio     <dbl> 37.8, 39.3, 45.9, 41.3, 10.8, 48.9, 32.8, 19.6, 2.1, 2.6, 5…
## $ newspaper <dbl> 69.2, 45.1, 69.3, 58.5, 58.4, 75.0, 23.5, 11.6, 1.0, 21.2, …
## $ sales     <dbl> 22.1, 10.4, 9.3, 18.5, 12.9, 7.2, 11.8, 13.2, 4.8, 10.6, 8.…

• Observations: 200 markets

• Variables:

  • tv: Spending on TV ads (in $thousands)
  • radio: Spending on radio ads (in $thousands)
  • newspaper: Spending on newspaper ads (in $thousands)
  • sales: total sales (in $millions)

Terminology

• sales is the response variable
  • variable whose variation we want to understand / variable we wish to predict
  • also known as outcome or dependent variable

• tv, radio, newspaper are the predictor variables
  • variables used to account for variation in the outcome
  • also known as explanatory, independent, or input variables

Let's look at the data

Each line represents model we could use to predict sales using tv, radio, or newspaper

Let's look at the data

Model

• Goal: Define f

• How do we define f?

  • Make an assumption about the functional form f
  • Use the data to fit a model based on that form

How to define f

In general,

1. Choose the functional form of f, i.e. choose the appropriate model given the data
   • Ex: f is a linear model f(X)=β0+β1X1+⋯+βpXp

1. Use the data to fit (or train) the model, i.e. estimate the model parameters
   • Ex: Find estimates of β0,β1,…,βp

Why?

Prediction:

What do we expect sales to be in a market where there is $100,000 spent on TV ads, $30,000 spent on radio ads, and $10,000 spent on newspaper ads?

Inference:

What is the relationship between spending on TV ads and sales after accounting for spending on radio and newspaper ads?

Course Outline