## Linear Regression

When performing linear regression, we are trying to find linear relationships between variables. Suppose we have a cat shelter and want to know how many extra cans of cat food we need to buy after receiving new cats. A simple approach would be to find the average number of cans a cat eats per day (**z**) and multiply it by the number of new cats (**x**). This is a linear relationship: if the number of cats increases by **x**, make sure to buy **x** times **z** cans of cat food. Of course, other variables might affect how much a new cat eats, such as age, breed, and weight at birth. We could possibly make a better linear model by adding these as predictors.

Imagine we had measured the amount of food eaten by **85** cats, along with their weight at birth (in grams). For budgeting reasons, we wish to predict the amount of food (number of cans) a newborn cat will eat per day when it grows up. We can plot these variables against each other, as shown in *Figure 5.2*: