The Slope of a Fitted Line
Student Summary
Here is a scatter plot that we have seen before. As noted earlier, we can see from the scatter plot that taller dogs tend to weigh more than shorter dogs.
Another way to say it is that weight tends to increase as height increases.
When we have a positive association between two variables, an increase in one means there tends to be an increase in the other.
We can quantify this tendency by fitting a line to the data and finding its slope.
For example, the equation of the fitted line is w=4.27h−37, where h is the height of the dog and w is the predicted weight of the dog.
The slope is 4.27, which tells us that for every 1-inch increase in dog height, the weight is predicted to increase by 4.27 pounds.
In our example of the fuel efficiency and weight of a car, the slope of the fitted line shown is -0.01.
This tells us that for every 1-kilogram increase in the weight of the car, the fuel efficiency is predicted to decrease by 0.01 mile per gallon (or, after multiplying both values by 100, every 100-kilogram increase corresponds to a predicted decrease of 1 mpg).
When we have a negative association between two variables, an increase in one means there tends to be a decrease in the other.
Visual / Anchor Chart
