Linear Regression

We compute linear relationships to predict the future! Well…​sort of. Given a dataset, like ages of animals v. how long before they’re adopted, we try to compute the relationship between age and weeks so that we can predict how long a new animal might stay, based on their age.

When we compute linear relationships, we’re talking about straight-line patterns that appear on a scatter plot.

A scatter plot has an x- and y-axis, which get special names when looking for relationships. The y-axis is called the response variable, and the x-axis is called the explanatory variable. In our example, we are trying to figure out how much of the weeks variable is explained by the age variable.

Linear Regression* is a way of computing the line of best fit, which tries to draw a line as close as possible to all the points. (Want details? It minimizes the sum of the squares of the vertical distances from the points to the line. There’s a reason we use computers to do this!)

Slope is how much we predict the response variable will increase or decrease for each unit that the explanatory variable increases. In our example, a slope of 0.5 would mean "we predict that each additional year of age means an extra half-week in the shelter". (What would a slope of 3 mean?)

Sample size matters! The number of data values is also relevant. We’d be more convinced of a positive relationship in general between cat age and time to adoption if a correlation of +0.57 were based on 50 cats instead of 5.