Ice cream shop sales prediction

Say our favorite ice cream shop has asked us to help predict how many ice creams they can expect to sell on a given day. They are convinced that the temperature outside has a strong influence on their sales, so they have collected data on the number of ice creams sold at a given temperature. We agree to help them, and the first thing we do is make a scatter plot of the data they collected:

We can observe an upward trend in the scatter plot: more ice creams are sold at higher temperatures. In order to help out the ice cream shop, though, we need to find a way to make predictions from this data. We can use a technique called regression to model the relationship between temperature and ice cream sales with an equation. Using this equation, we will be able to predict ice cream sales at a given temperature.

There are many types of regression that will yield a different type of equation, such as linear (which we will use for this example) and logistic. Our first step will be to identify the dependent variable, which is the quantity we want to predict (ice cream sales), and the variables we will use to predict it, which are called independent variables. While we can have many independent variables, our ice cream sales example only has one: temperature. Therefore, we will use simple linear regression to model the relationship as a line:

The regression line in the previous scatter plot yields the following equation for the relationship:

Suppose that today the temperature is 35°C—we would plug that in for temperature in the equation. The result predicts that the ice cream shop will sell 24.54 ice creams. This prediction is along the red line in the previous plot. Note that the ice cream shop can't actually sell fractions of ice cream.

Before leaving the model in the hands of the ice cream shop, it's important to discuss the difference between the dotted and solid portions of the regression line that we obtained. This we will do in the next post.